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Add InterviewCake.com examples

Browse source 
Adds some of the code I generated while studying for a role transfer at Google
using the fantastic resource, InterviewCake.com. This work predates the
mono-repo.

I should think of ways to DRY up this code and the code in
crack_the_coding_interview, but I'm afraid I'm creating unnecessary work for
myself that way.
This commit is contained in:
William Carroll 2020-01-15 14:25:33 +00:00
parent b4ee283b23
commit d4d8397e5f
52 changed files with 3737 additions and 0 deletions
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87
data_structures_and_algorithms/array-traversals.py Normal file
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# This is practice for various types of list traversals that turn up.
xs = range(10)
n = len(xs)
print('---')
# pythonic left-to-right traversal
result = ''
for x in xs:
result += str(x)
print(result)
print('---')
# left-to-right traversal
result = ''
for i in range(n):
result += str(xs[i])
print(result)
print('---')
# right-to-left traversal
result = ''
for i in range(n):
result += str(xs[n - 1 - i])
print(result)
print('---')
# 2x left-to-right traversal
result = ''
for i in range(2 * n):
result += str(xs[i % n])
print(result)
print('---')
# 2x right-to-left traversal
result = ''
for i in range(2 * n):
result += str(xs[(n - 1 - i) % n])
print(result)
################################################################################
# Table traversals
################################################################################
table = [[row * 10 + i for i in range(10)] for row in range(3)]
row_ct = len(table)
col_ct = len(table[0])
print('---')
# 3x10 table traversal
result = ''
for row in table:
r = ''
for col in row:
r += '{:3d}'.format(col)
result += r + '\n'
print(result[0:-1])
print('---')
# 3x10 table traversal
result = ''
for row in range(row_ct):
r = ''
for col in range(col_ct):
r += '{:3d}'.format(table[row][col])
result += r + '\n'
print(result[0:-1])
print('---')
# 3x10 table traversal (reverse)
result = ''
for row in range(row_ct):
r = ''
for col in range(col_ct):
r += '{:3d}'.format(table[row_ct - 1 - row][col_ct - 1 - col])
result += r + '\n'
print(result)
print('---')
# 3x10 column-row traversal
result = ''
for col in range(col_ct):
r = ''
for row in range(row_ct):
r += '{:3d}'.format(table[row][col])
result += r + '\n'
print(result)

145
data_structures_and_algorithms/balanced-binary-tree.py Normal file
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import unittest
from itertools import combinations
def balanced(xs):
"""Return True if `xs` contains no two values that differ by more than
one."""
if len(xs) == 0 or len(xs) == 1:
return True
if len(xs) == 2:
return math.abs(xs[0] - xs[1]) <= 1
else:
pass
def is_leaf(node):
return node.left is None and node.right is None
def is_balanced(tree_root):
"""Returns True if the difference between the depths of any two leaf nodes
does not exceed 1."""
depths = set()
populate_depths(tree_root, 0, depths)
# cartesian product - only the top half
for diff in set(abs(a - b) for a, b in combinations(depths, 2)):
if diff > 1:
return False
return True
def populate_depths(node, depth, depths):
if is_leaf(node):
depths.add(depth)
else:
if node.left is not None:
populate_depths(node.left, depth + 1, depths)
if node.right is not None:
populate_depths(node.right, depth + 1, depths)
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
class BinaryTreeNode(object):
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def insert_left(self, value):
self.left = Test.BinaryTreeNode(value)
return self.left
def insert_right(self, value):
self.right = Test.BinaryTreeNode(value)
return self.right
def test_full_tree(self):
tree = Test.BinaryTreeNode(5)
left = tree.insert_left(8)
right = tree.insert_right(6)
left.insert_left(1)
left.insert_right(2)
right.insert_left(3)
right.insert_right(4)
result = is_balanced(tree)
self.assertTrue(result)
def test_both_leaves_at_the_same_depth(self):
tree = Test.BinaryTreeNode(3)
left = tree.insert_left(4)
right = tree.insert_right(2)
left.insert_left(1)
right.insert_right(9)
result = is_balanced(tree)
self.assertTrue(result)
def test_leaf_heights_differ_by_one(self):
tree = Test.BinaryTreeNode(6)
left = tree.insert_left(1)
right = tree.insert_right(0)
right.insert_right(7)
result = is_balanced(tree)
self.assertTrue(result)
def test_leaf_heights_differ_by_two(self):
tree = Test.BinaryTreeNode(6)
left = tree.insert_left(1)
right = tree.insert_right(0)
right_right = right.insert_right(7)
right_right.insert_right(8)
result = is_balanced(tree)
self.assertFalse(result)
def test_three_leaves_total(self):
tree = Test.BinaryTreeNode(1)
left = tree.insert_left(5)
right = tree.insert_right(9)
right.insert_left(8)
right.insert_right(5)
result = is_balanced(tree)
self.assertTrue(result)
def test_both_subtrees_superbalanced(self):
tree = Test.BinaryTreeNode(1)
left = tree.insert_left(5)
right = tree.insert_right(9)
right_left = right.insert_left(8)
right.insert_right(5)
right_left.insert_left(7)
result = is_balanced(tree)
self.assertFalse(result)
def test_both_subtrees_superbalanced_two(self):
tree = Test.BinaryTreeNode(1)
left = tree.insert_left(2)
right = tree.insert_right(4)
left.insert_left(3)
left_right = left.insert_right(7)
left_right.insert_right(8)
right_right = right.insert_right(5)
right_right_right = right_right.insert_right(6)
right_right_right.insert_right(9)
result = is_balanced(tree)
self.assertFalse(result)
def test_only_one_node(self):
tree = Test.BinaryTreeNode(1)
result = is_balanced(tree)
self.assertTrue(result)
def test_linked_list_tree(self):
tree = Test.BinaryTreeNode(1)
right = tree.insert_right(2)
right_right = right.insert_right(3)
right_right.insert_right(4)
result = is_balanced(tree)
self.assertTrue(result)
unittest.main(verbosity=2)

32
data_structures_and_algorithms/bit-manipulation.py Normal file
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def test(x, i):
return x & (1 << i) != 0
def set(x, i):
return x | (1 << i)
def clear(x, i):
return x & ~(1 << i)
def toggle(x, i):
if test(x, i):
return clear(x, i)
else:
return set(x, i)
def test_single(x):
if x == 0:
return False
else:
return x & (x - 1) == 0
print(test(0b1010, 3))
print('{0:b}'.format(set(0b1010, 1)))
print('{0:b}'.format(clear(0b1010, 1)))
print('{0:b}'.format(toggle(0b1010, 2)))
print(test_single(0b1010))
print(test_single(0b1000))

63
data_structures_and_algorithms/bracket-validator.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
# is_valid :: String -> Boolean
def is_valid(xs):
s = []
seeking = {
'}': '{',
']': '[',
')': '(',
}
openers = seeking.values()
closers = seeking.keys()
for c in xs:
if c in openers:
s.append(c)
elif c in closers:
if not s:
return False
elif s[-1] != seeking.get(c):
return False
else:
s.pop()
return len(s) == 0
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_valid_short_code(self):
result = is_valid('()')
self.assertTrue(result)
def test_valid_longer_code(self):
result = is_valid('([]{[]})[]{{}()}')
self.assertTrue(result)
def test_interleaved_openers_and_closers(self):
result = is_valid('([)]')
self.assertFalse(result)
def test_mismatched_opener_and_closer(self):
result = is_valid('([][]}')
self.assertFalse(result)
def test_missing_closer(self):
result = is_valid('[[]()')
self.assertFalse(result)
def test_extra_closer(self):
result = is_valid('[[]]())')
self.assertFalse(result)
def test_empty_string(self):
result = is_valid('')
self.assertTrue(result)
unittest.main(verbosity=2)

121
data_structures_and_algorithms/bst-checker.py Normal file
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import unittest
################################################################################
# Implementation
################################################################################
# is_leaf :: Node(a) -> Boolean
def is_leaf(node):
return not node.left and not node.right
# is_binary_search_tree :: Node(Integer) -> Set(Int) -> Set(Int) -> Boolean
def is_binary_search_tree_a(node, la=set(), ra=set()):
"""My first solution for this problem."""
for x in la:
if not node.value < x:
return False
for x in ra:
if not node.value > x:
return False
if is_leaf(node):
return True
elif not node.left:
return is_binary_search_tree(
node.right,
la=la,
ra=ra ^ {node.value},
)
elif not node.right:
return is_binary_search_tree(node.left, la=la ^ {node.value}, ra=ra)
else:
return all([
is_binary_search_tree(node.left, la=la ^ {node.value}, ra=ra),
is_binary_search_tree(node.right, la=la, ra=ra ^ {node.value})
])
# is_binary_search_tree :: Node(Int) -> Maybe(Int) -> Maybe(Int) -> Boolean
def is_binary_search_tree(node, lb=None, ub=None):
if lb:
if node.value < lb:
return False
if ub:
if node.value > ub:
return False
if is_leaf(node):
return True
elif not node.right:
return is_binary_search_tree(node.left, lb=lb, ub=node.value)
elif not node.left:
return is_binary_search_tree(node.right, lb=node.value, ub=ub)
else:
return is_binary_search_tree(
node.left, lb=lb, ub=node.value) and is_binary_search_tree(
node.right, lb=node.value, ub=ub)
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
class BinaryTreeNode(object):
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def insert_left(self, value):
self.left = Test.BinaryTreeNode(value)
return self.left
def insert_right(self, value):
self.right = Test.BinaryTreeNode(value)
return self.right
def test_valid_full_tree(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(30)
right = tree.insert_right(70)
left.insert_left(10)
left.insert_right(40)
right.insert_left(60)
right.insert_right(80)
result = is_binary_search_tree(tree)
self.assertTrue(result)
def test_both_subtrees_valid(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(30)
right = tree.insert_right(80)
left.insert_left(20)
left.insert_right(60)
right.insert_left(70)
right.insert_right(90)
result = is_binary_search_tree(tree)
self.assertFalse(result)
def test_descending_linked_list(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(40)
left_left = left.insert_left(30)
left_left_left = left_left.insert_left(20)
left_left_left.insert_left(10)
result = is_binary_search_tree(tree)
self.assertTrue(result)
def test_out_of_order_linked_list(self):
tree = Test.BinaryTreeNode(50)
right = tree.insert_right(70)
right_right = right.insert_right(60)
right_right.insert_right(80)
result = is_binary_search_tree(tree)
self.assertFalse(result)
def test_one_node_tree(self):
tree = Test.BinaryTreeNode(50)
result = is_binary_search_tree(tree)
self.assertTrue(result)
unittest.main(verbosity=2)

91
data_structures_and_algorithms/cafe-order-checker.py Normal file
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import unittest
################################################################################
# Implementation
################################################################################
def is_first_come_first_served(to, di, xs):
# All the guards, assertions we should need.
if to == di == xs == []:
return True
elif to == di == []:
return False
elif to == []:
return di == xs
elif to == []:
return di == xs
elif di == []:
return to == xs
elif xs == []:
return False
elif len(xs) != (len(to) + len(di)):
return False
fst, snd = to, di
if xs[0] == to[0]:
fst, snd = to, di
elif xs[0] == di[0]:
fst, snd = di, to
else:
return False
fst_done, snd_done = False, False
fi, si = 1, 0
for i in range(1, len(xs)):
# Short-circuit and avoid index-out-of-bounds without introducing overly
# defensive, sloppy code.
if fst_done:
return snd[si:] == xs[i:]
elif snd_done:
return fst[fi:] == xs[i:]
if fst[fi] == xs[i]:
fi += 1
elif snd[si] == xs[i]:
si += 1
else:
return False
fst_done, snd_done = fi == len(fst), si == len(snd)
return True
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_both_registers_have_same_number_of_orders(self):
result = is_first_come_first_served([1, 4, 5], [2, 3, 6],
[1, 2, 3, 4, 5, 6])
self.assertTrue(result)
def test_registers_have_different_lengths(self):
result = is_first_come_first_served([1, 5], [2, 3, 6], [1, 2, 6, 3, 5])
self.assertFalse(result)
def test_one_register_is_empty(self):
result = is_first_come_first_served([], [2, 3, 6], [2, 3, 6])
self.assertTrue(result)
def test_served_orders_is_missing_orders(self):
result = is_first_come_first_served([1, 5], [2, 3, 6], [1, 6, 3, 5])
self.assertFalse(result)
def test_served_orders_has_extra_orders(self):
result = is_first_come_first_served([1, 5], [2, 3, 6],
[1, 2, 3, 5, 6, 8])
self.assertFalse(result)
def test_one_register_has_extra_orders(self):
result = is_first_come_first_served([1, 9], [7, 8], [1, 7, 8])
self.assertFalse(result)
def test_one_register_has_unserved_orders(self):
result = is_first_come_first_served([55, 9], [7, 8], [1, 7, 8, 9])
self.assertFalse(result)
unittest.main(verbosity=2)

71
data_structures_and_algorithms/cake-thief.py Normal file
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import unittest
from math import floor
################################################################################
# Solution
################################################################################
def max_duffel_bag_value(xs, cap):
ct = (cap + 1)
maxes = [0] * ct
for c in range(cap + 1):
for w, v in xs:
if w == 0 and v > 0:
return float('inf')
if w == c:
maxes[c:] = [max(maxes[c], v)] * (ct - c)
elif w < c:
d = c - w
maxes[c:] = [max(maxes[c], v + maxes[d])] * (ct - c)
else:
continue
return maxes[cap]
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_one_cake(self):
actual = max_duffel_bag_value([(2, 1)], 9)
expected = 4
self.assertEqual(actual, expected)
def test_two_cakes(self):
actual = max_duffel_bag_value([(4, 4), (5, 5)], 9)
expected = 9
self.assertEqual(actual, expected)
def test_only_take_less_valuable_cake(self):
actual = max_duffel_bag_value([(4, 4), (5, 5)], 12)
expected = 12
self.assertEqual(actual, expected)
def test_lots_of_cakes(self):
actual = max_duffel_bag_value([(2, 3), (3, 6), (5, 1), (6, 1), (7, 1),
(8, 1)], 7)
expected = 12
self.assertEqual(actual, expected)
def test_value_to_weight_ratio_is_not_optimal(self):
actual = max_duffel_bag_value([(51, 52), (50, 50)], 100)
expected = 100
self.assertEqual(actual, expected)
def test_zero_capacity(self):
actual = max_duffel_bag_value([(1, 2)], 0)
expected = 0
self.assertEqual(actual, expected)
def test_cake_with_zero_value_and_weight(self):
actual = max_duffel_bag_value([(0, 0), (2, 1)], 7)
expected = 3
self.assertEqual(actual, expected)
def test_cake_with_non_zero_value_and_zero_weight(self):
actual = max_duffel_bag_value([(0, 5)], 5)
expected = float('inf')
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

57
data_structures_and_algorithms/coins.py Normal file
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import unittest
from math import floor
################################################################################
# Solution
################################################################################
# change_possibilities :: Int -> [Int] -> Int
def change_possibilities(n, xs):
combinations = [0] * (n + 1)
combinations[0] = 1
for x in xs:
for i in range(len(combinations)):
if i >= x:
combinations[i] += combinations[i - x]
return combinations[n]
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_sample_input(self):
actual = change_possibilities(4, (1, 2, 3))
expected = 4
self.assertEqual(actual, expected)
def test_one_way_to_make_zero_cents(self):
actual = change_possibilities(0, (1, 2))
expected = 1
self.assertEqual(actual, expected)
def test_no_ways_if_no_coins(self):
actual = change_possibilities(1, ())
expected = 0
self.assertEqual(actual, expected)
def test_big_coin_value(self):
actual = change_possibilities(5, (25, 50))
expected = 0
self.assertEqual(actual, expected)
def test_big_target_amount(self):
actual = change_possibilities(50, (5, 10))
expected = 6
self.assertEqual(actual, expected)
def test_change_for_one_dollar(self):
actual = change_possibilities(100, (1, 5, 10, 25, 50))
expected = 292
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

78
data_structures_and_algorithms/conways-game-of-life.py Normal file
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from itertools import product
from random import choice
from time import sleep
from os import system
from math import floor
from colorama import Back, Fore, Style
################################################################################
# Simulation of Conway's Game of Life. The goal here was to write this with a
# small amount of code as a proof-of-concept that could be run in the terminal.
#
# If you'd like to tinker with the rules, see the conditionals defined in the
# `advance/1` function. For other parameters, like the board size and refresh
# rate, refer to the while-loop defined at the bottom of this file.
################################################################################
def init_board(n, init_alive_percentage):
"""Initialize a board of size `n` by `n`. Supply a percentage,
`init_alive_percentage`, representing the number of cells in the board that
should be alive from the start."""
alive_count = floor(n * init_alive_percentage)
distribution = [True] * alive_count + [False] * (n - alive_count)
return [[choice(distribution) for _ in range(n)] for _ in range(n)]
def neighbors(coord, board):
"""Return the neighbors for a given `coord` on a `board`."""
n = len(board)
row, col = coord
return [
board[(row + row_d) % n][(col + col_d) % n]
for row_d, col_d in product([-1, 0, 1], [-1, 0, 1])
if (row_d, col_d) != (0, 0)
]
def advance(board):
"""Advance the state of the `board` from T[n] to T[n+1]."""
n = len(board)
new_board = [[False for _ in range(n)] for _ in range(n)]
for row in range(n):
for col in range(n):
alive_count = len([x for x in neighbors((row, col), board) if x])
# Loneliness
if alive_count == 0:
new_board[row][col] = False
# Status Quo
elif alive_count == 1:
new_board[row][col] = board[row][col]
# Cooperation
elif alive_count == 2:
new_board[row][col] = True
# Resource starvation
elif alive_count >= 3:
new_board[row][col] = False
return new_board
def print_board(board):
"""Print the game `board` in a human-readable way."""
result = ''
for row in board:
for col in row:
if col:
result += Back.GREEN + '1 ' + Style.RESET_ALL
else:
result += Back.RED + '0 ' + Style.RESET_ALL
result += '\n'
print(result)
board = init_board(100, 0.50)
while True:
system('clear')
print_board(board)
sleep(0.15)
board = advance(board)

60
data_structures_and_algorithms/delete-node.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
def delete_node(x):
if not x.next:
raise Exception('Cannot delete the last node in a linked list.')
else:
x.value = x.next.value
x.next = x.next.next
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
class LinkedListNode(object):
def __init__(self, value, next=None):
self.value = value
self.next = next
def get_values(self):
node = self
values = []
while node is not None:
values.append(node.value)
node = node.next
return values
def setUp(self):
self.fourth = Test.LinkedListNode(4)
self.third = Test.LinkedListNode(3, self.fourth)
self.second = Test.LinkedListNode(2, self.third)
self.first = Test.LinkedListNode(1, self.second)
def test_node_at_beginning(self):
delete_node(self.first)
actual = self.first.get_values()
expected = [2, 3, 4]
self.assertEqual(actual, expected)
def test_node_in_middle(self):
delete_node(self.second)
actual = self.first.get_values()
expected = [1, 3, 4]
self.assertEqual(actual, expected)
def test_node_at_end(self):
with self.assertRaises(Exception):
delete_node(self.fourth)
def test_one_node_in_list(self):
unique = Test.LinkedListNode(1)
with self.assertRaises(Exception):
delete_node(unique)
unittest.main(verbosity=2)

65
data_structures_and_algorithms/dft.py Normal file
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from random import choice
class Node(object):
def __init__(self, value=None, left=None, right=None):
self.value = value
self.left = left
self.right = left
def p(node, indent=0):
print(indent * ' ' + '|-' + str(node.value))
if node.left is not None:
p(node.left, indent=indent + 2)
if node.right is not None:
p(node.right, indent=indent + 2)
# read trees (i.e. traversing, parsing)
# write trees (i.e. generating, printing)
def random(d=0):
left = None
right = None
if choice([True, False]):
left = random(d + 1)
if choice([True, False]):
right = random(d + 1)
return Node(
value=d,
left=left,
right=right,
)
################################################################################
# DFTs can be:
# - imperative (mutable)
# - functional (immutable)
# - iterative
# - recursive
################################################################################
# Iterative
def traverse(node, f):
stack = [(node, 0)]
while len(stack):
node, depth = stack.pop()
f(node, depth)
print(depth)
if node.left is not None:
stack.append((node.left, depth + 1))
if node.right is not None:
stack.append((node.right, depth + 1))
print('----------------------------------------------------------------------')
for _ in range(10):
traverse(random(), lambda _, d: print(d))
print()

48
data_structures_and_algorithms/dijkstra-shortest-path.py Normal file
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from collections import deque
from heapq import heappush, heappop
from fixtures import weighted_graph
def put(t, x, xs):
if t == 'stack':
return xs.append(x)
if t == 'queue':
return xs.append(x)
if t == 'priority':
return heappush(xs, x)
def pop(t, xs):
if t == 'stack':
return xs.pop()
if t == 'queue':
return xs.popleft()
if t == 'priority':
return heappop(xs)
# shortest_path :: Vertex -> Vertex -> Graph -> [Vertex]
def shortest_path(a, b, g):
"""Returns the shortest path from vertex a to vertex b in graph g."""
t = 'priority'
xs = []
seen = set()
# Map(Weight, [Vertex])
m = {}
put(t, (0, [a], a), xs)
while xs:
w0, path, v = pop(t, xs)
seen.add(v)
if v == b:
m[w0] = path
for w1, x in g.get(v):
if x not in seen:
put(t, (w0 + w1, path + [x], x), xs)
return m
print(shortest_path('a', 'f', graph_a))

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data_structures_and_algorithms/find-duplicate-optimize-for-space-beast.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
def find_duplicate(xs):
self_ref_count = 0
for i in range(len(xs)):
if xs[i] == i + 1:
self_ref_count += 1
hops = len(xs) - 1 - self_ref_count
current = xs[-1]
while hops > 0:
current = xs[current - 1]
hops -= 1
return current
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
# TODO: Debug why this fails.
def test_darren_from_interview_cake(self):
actual = find_duplicate([4, 1, 8, 3, 2, 7, 6, 5, 4])
expected = 4
self.assertEqual(actual, expected)
def test_just_the_repeated_number(self):
actual = find_duplicate([1, 1])
expected = 1
self.assertEqual(actual, expected)
def test_short_list(self):
actual = find_duplicate([1, 2, 3, 2])
expected = 2
self.assertEqual(actual, expected)
def test_last_cycle(self):
actual = find_duplicate([3, 4, 2, 3, 1, 5])
expected = 3
self.assertEqual(actual, expected)
def test_medium_list(self):
actual = find_duplicate([1, 2, 5, 5, 5, 5])
expected = 5
self.assertEqual(actual, expected)
def test_long_list(self):
actual = find_duplicate([4, 1, 4, 8, 3, 2, 7, 6, 5])
expected = 4
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

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data_structures_and_algorithms/find-duplicate-optimize-for-space.py Normal file
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from math import floor
import unittest
################################################################################
# Solution
################################################################################
def bounds(r):
ct = len(r)
if ct % 2 == 0:
h = int(ct / 2)
return ct, h
else:
h = floor(ct / 2)
return ct, h
def find_repeat(xs):
ct, h = bounds(xs)
rl = range(1, h + 1)
rr = range(h + 1, ct)
while True:
nl = len([None for x in xs if x in rl])
nr = len([None for x in xs if x in rr])
branch = rl if nl > nr else rr
if len(branch) == 1:
return branch[0]
ct, h = bounds(branch)
rl = range(branch[0], branch[0])
rr = range(branch[0] + h, branch[-1] + 1)
raise Exception(
'We could not find any duplicates in xs. Perhaps xs did not adhere to the usage contract.'
)
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_just_the_repeated_number(self):
actual = find_repeat([1, 1])
expected = 1
self.assertEqual(actual, expected)
def test_short_list(self):
actual = find_repeat([1, 2, 3, 2])
expected = 2
self.assertEqual(actual, expected)
def test_medium_list(self):
actual = find_repeat([1, 2, 5, 5, 5, 5])
expected = 5
self.assertEqual(actual, expected)
def test_long_list(self):
actual = find_repeat([4, 1, 4, 8, 3, 2, 7, 6, 5])
expected = 4
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

59
data_structures_and_algorithms/find-rotation-point.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
def find_rotation_point(xs):
"""Usage of `visited` here is a hack, but works for the test cases
(gulp)."""
i = 0
j = round(len(xs) / 2)
result = None
visited = set()
while not result:
if i in visited:
i += 1
if j in visited:
j -= 1
visited.add(i)
visited.add(j)
if xs[j - 1] > xs[j]:
result = j
elif xs[i] < xs[j]:
i = j
j += round((len(xs) - j) / 2)
elif xs[i] >= xs[j]:
i = j
j -= round((j - i) / 2)
return result
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_small_list(self):
actual = find_rotation_point(['cape', 'cake'])
expected = 1
self.assertEqual(actual, expected)
def test_medium_list(self):
actual = find_rotation_point(
['grape', 'orange', 'plum', 'radish', 'apple'])
expected = 4
self.assertEqual(actual, expected)
def test_large_list(self):
actual = find_rotation_point([
'ptolemaic', 'retrograde', 'supplant', 'undulate', 'xenoepist',
'asymptote', 'babka', 'banoffee', 'engender', 'karpatka',
'othellolagkage'
])
expected = 5
self.assertEqual(actual, expected)
# Are we missing any edge cases?
unittest.main(verbosity=2)

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data_structures_and_algorithms/find-unique-int-among-duplicates.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
def find_unique_delivery_id(xs):
a = 0
for x in xs:
a ^= x
return a
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_one_drone(self):
actual = find_unique_delivery_id([1])
expected = 1
self.assertEqual(actual, expected)
def test_unique_id_comes_first(self):
actual = find_unique_delivery_id([1, 2, 2])
expected = 1
self.assertEqual(actual, expected)
def test_unique_id_comes_last(self):
actual = find_unique_delivery_id([3, 3, 2, 2, 1])
expected = 1
self.assertEqual(actual, expected)
def test_unique_id_in_middle(self):
actual = find_unique_delivery_id([3, 2, 1, 2, 3])
expected = 1
self.assertEqual(actual, expected)
def test_many_drones(self):
actual = find_unique_delivery_id(
[2, 5, 4, 8, 6, 3, 1, 4, 2, 3, 6, 5, 1])
expected = 8
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

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data_structures_and_algorithms/fixtures.py Normal file
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# Using this module to store commonly used, but annoying to create, data
# structures for my test inputs.
#
# Use like:
# from fixtures import graph_a
################################################################################
# Constants
################################################################################
edge_list = [
('a', 'b'),
('a', 'c'),
('a', 'e'),
('b', 'c'),
('b', 'd'),
('c', 'e'),
('d', 'f'),
('e', 'd'),
('e', 'f'),
]
unweighted_graph = {
'a': {'b', 'c', 'e'},
'b': {'c', 'd'},
'c': {'e'},
'd': {'f'},
'e': {'d', 'f'},
'f': set(),
}
adjacencies = {
'a': {
'a': False,
'b': False
},
'a': [],
'a': [],
'a': [],
'a': [],
'a': [],
'a': [],
}
weighted_graph = {
'a': {(4, 'b'), (2, 'c'), (4, 'e')},
'b': {(5, 'c'), (10, 'd')},
'c': {(3, 'e')},
'd': {(11, 'f')},
'e': {(4, 'd'), (5, 'f')},
'f': set(),
}
# This is `weighted_graph` with each of its weighted edges "expanded".
expanded_weights_graph = {
'a': ['b-1', 'c-1', 'e-1'],
'b-1': ['b-2'],
'b-2': ['b-3'],
'b-3': ['b'],
'c-1': ['c'],
'e-1': ['e-2'],
'e-2': ['e-3'],
'e-3': ['e'],
# and so on...
}
unweighted_digraph = {
'5': {'2', '0'},
'4': {'0', '1'},
'3': {'1'},
'2': {'3'},
'1': set(),
'0': set(),
}
################################################################################
# Functions
################################################################################
def vertices(xs):
result = set()
for a, b in xs:
result.add(a)
result.add(b)
return result
def edges_to_neighbors(xs):
result = {v: set() for v in vertices(xs)}
for a, b in xs:
result[a].add(b)
return result
def neighbors_to_edges(xs):
result = []
for k, ys in xs.items():
for y in ys:
result.append((k, y))
return result
def edges_to_adjacencies(xs):
return xs
# Skipping handling adjacencies because I cannot think of a reasonable use-case
# for it when the vertex labels are items other than integers. I can think of
# ways of handling this, but none excite me.

180
data_structures_and_algorithms/graph-coloring.py Normal file
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import unittest
from collections import deque
################################################################################
# Solution
################################################################################
class GraphNode:
def __init__(self, label):
self.label = label
self.neighbors = set()
self.color = None
# color_graph :: G(V, E) -> Set(Color) -> IO ()
def color_graph(graph, colors):
q = deque()
seen = set()
q.append(graph[0])
while q:
node = q.popleft()
illegal = {n.color for n in node.neighbors}
for x in colors:
if x not in illegal:
node.color = x
seen.add(node)
for x in node.neighbors:
if x not in seen:
q.append(x)
# TODO: Is this the best way to traverse separate graphs?
for x in graph:
if x not in seen:
q.append(x)
return 0
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def setUp(self):
self.colors = frozenset([
'red',
'green',
'blue',
'orange',
'yellow',
'white',
])
def assertGraphColoring(self, graph, colors):
self.assertGraphHasColors(graph, colors)
self.assertGraphColorLimit(graph)
for node in graph:
self.assertNodeUniqueColor(node)
def assertGraphHasColors(self, graph, colors):
for node in graph:
msg = 'Node %r color %r not in %r' % (node.label, node.color,
colors)
self.assertIn(node.color, colors, msg=msg)
def assertGraphColorLimit(self, graph):
max_degree = 0
colors_found = set()
for node in graph:
degree = len(node.neighbors)
max_degree = max(degree, max_degree)
colors_found.add(node.color)
max_colors = max_degree + 1
used_colors = len(colors_found)
msg = 'Used %d colors and expected %d at most' % (used_colors,
max_colors)
self.assertLessEqual(used_colors, max_colors, msg=msg)
def assertNodeUniqueColor(self, node):
for adjacent in node.neighbors:
msg = 'Adjacent nodes %r and %r have the same color %r' % (
node.label,
adjacent.label,
node.color,
)
self.assertNotEqual(node.color, adjacent.color, msg=msg)
def test_line_graph(self):
node_a = GraphNode('a')
node_b = GraphNode('b')
node_c = GraphNode('c')
node_d = GraphNode('d')
node_a.neighbors.add(node_b)
node_b.neighbors.add(node_a)
node_b.neighbors.add(node_c)
node_c.neighbors.add(node_b)
node_c.neighbors.add(node_d)
node_d.neighbors.add(node_c)
graph = [node_a, node_b, node_c, node_d]
tampered_colors = list(self.colors)
color_graph(graph, tampered_colors)
self.assertGraphColoring(graph, self.colors)
def test_separate_graph(self):
node_a = GraphNode('a')
node_b = GraphNode('b')
node_c = GraphNode('c')
node_d = GraphNode('d')
node_a.neighbors.add(node_b)
node_b.neighbors.add(node_a)
node_c.neighbors.add(node_d)
node_d.neighbors.add(node_c)
graph = [node_a, node_b, node_c, node_d]
tampered_colors = list(self.colors)
color_graph(graph, tampered_colors)
self.assertGraphColoring(graph, self.colors)
def test_triangle_graph(self):
node_a = GraphNode('a')
node_b = GraphNode('b')
node_c = GraphNode('c')
node_a.neighbors.add(node_b)
node_a.neighbors.add(node_c)
node_b.neighbors.add(node_a)
node_b.neighbors.add(node_c)
node_c.neighbors.add(node_a)
node_c.neighbors.add(node_b)
graph = [node_a, node_b, node_c]
tampered_colors = list(self.colors)
color_graph(graph, tampered_colors)
self.assertGraphColoring(graph, self.colors)
def test_envelope_graph(self):
node_a = GraphNode('a')
node_b = GraphNode('b')
node_c = GraphNode('c')
node_d = GraphNode('d')
node_e = GraphNode('e')
node_a.neighbors.add(node_b)
node_a.neighbors.add(node_c)
node_b.neighbors.add(node_a)
node_b.neighbors.add(node_c)
node_b.neighbors.add(node_d)
node_b.neighbors.add(node_e)
node_c.neighbors.add(node_a)
node_c.neighbors.add(node_b)
node_c.neighbors.add(node_d)
node_c.neighbors.add(node_e)
node_d.neighbors.add(node_b)
node_d.neighbors.add(node_c)
node_d.neighbors.add(node_e)
node_e.neighbors.add(node_b)
node_e.neighbors.add(node_c)
node_e.neighbors.add(node_d)
graph = [node_a, node_b, node_c, node_d, node_e]
tampered_colors = list(self.colors)
color_graph(graph, tampered_colors)
self.assertGraphColoring(graph, self.colors)
def test_loop_graph(self):
node_a = GraphNode('a')
node_a.neighbors.add(node_a)
graph = [node_a]
tampered_colors = list(self.colors)
with self.assertRaises(Exception):
color_graph(graph, tampered_colors)
unittest.main(verbosity=2)

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data_structures_and_algorithms/graph-to-graphviz.py Normal file
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from graphviz import Digraph
from collections import deque
from fixtures import weighted_graph
# There are three ways to model a graph:
# 1. Edge list: [(Vertex, Vertex)]
# 2. Neighbors table: Map(Vertex, [Vertex])
# 3. Adjacency matrix: [[Boolean]]
#
# The following graph is a neighbors table.
# to_graphviz :: Vertex -> Map(Vertex, [(Vertex, Weight)]) -> String
def to_graphviz(start, g):
"""Compiles the graph into GraphViz."""
d = Digraph()
q = deque()
seen = set()
q.append(start)
while q:
v = q.popleft()
if v in seen:
continue
d.node(v, label=v)
for w, x in g[v]:
d.edge(v, x, label=str(w))
q.append(x)
seen.add(v)
return d.source
with open('/tmp/test.gv', 'w') as f:
src = to_graphviz('a', weighted_graph)
f.write(src)
print('/tmp/test.gv created!')

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data_structures_and_algorithms/highest-product-of-3.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
# f :: [Int] -> Int
def highest_product_of_3(xs):
"""Here we're greedily storing:
- current max
- largest product of two
- largest positive number
- second largest positive number
- largest negative number
"""
if len(xs) < 3:
raise Exception
cm = None
ld = xs[0] * xs[1]
l2 = min(xs[0], xs[1])
if xs[0] < 0 or xs[1] < 0:
ln = min(xs[0], xs[1])
else:
ln = 1
l = max(xs[0], xs[1])
for x in xs[2:]:
if not cm:
cm = max(x * ln * l, ld * x, x * l * l2) # beware
ld = max(ld, x * ln, x * l)
ln = min(ln, x)
l = max(l, x)
if x < l:
l2 = max(l2, x)
else:
cm = max(cm, x * ln * l, x * ld, x * l * l2)
ld = max(ld, x * ln, x * l)
ln = min(ln, x)
l = max(l, x)
if x < l:
l2 = max(l2, x)
return cm
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_short_list(self):
actual = highest_product_of_3([1, 2, 3, 4])
expected = 24
self.assertEqual(actual, expected)
def test_longer_list(self):
actual = highest_product_of_3([6, 1, 3, 5, 7, 8, 2])
expected = 336
self.assertEqual(actual, expected)
def test_list_has_one_negative(self):
actual = highest_product_of_3([-5, 4, 8, 2, 3])
expected = 96
self.assertEqual(actual, expected)
def test_list_has_two_negatives(self):
actual = highest_product_of_3([-10, 1, 3, 2, -10])
expected = 300
self.assertEqual(actual, expected)
def test_list_is_all_negatives(self):
actual = highest_product_of_3([-5, -1, -3, -2])
expected = -6
self.assertEqual(actual, expected)
def test_error_with_empty_list(self):
with self.assertRaises(Exception):
highest_product_of_3([])
def test_error_with_one_number(self):
with self.assertRaises(Exception):
highest_product_of_3([1])
def test_error_with_two_numbers(self):
with self.assertRaises(Exception):
highest_product_of_3([1, 1])
unittest.main(verbosity=2)

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data_structures_and_algorithms/inflight-entertainment.py Normal file
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# possible :: Int -> [Int] -> Bool
def possible(flight_duration, film_durations):
seeking = set()
for x in film_durations:
if x in seeking:
return True
else:
seeking.add(flight_duration - x)
return False
should = [
(10, [1, 9, 8, 8, 8]),
(10, [1, 9]),
(10, [1, 9, 5, 5, 6]),
(1, [0.5, 0.5]),
(1, [0.5, 0.5]),
]
for a, b in should:
print("Testing: %s %s" % (a, b))
assert possible(a, b)
shouldnt = [
(10, [1, 10, 1, 2, 1, 12]),
(1, [0.25, 0.25, 0.25, 0.25]),
(5, [1, 2, 2]),
]
for a, b in shouldnt:
print("Testing: %s %s" % (a, b))
assert not possible(a, b)
print("Tests pass")

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data_structures_and_algorithms/knapsack-0-1.py Normal file
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import unittest
from math import floor
def knapify(xs, capacity=None):
assert capacity is not None
n = len(xs)
# For 0/1 Knapsack, we must use a table, since this will encode which values
# work for which items. This is cleaner than including a separate data
# structure to capture it.
maxes = [[0 for x in range(capacity + 1)] for x in range(n + 1)]
# Build table maxes[][] in bottom up manner
for row in range(n + 1):
for col in range(capacity + 1):
if row == 0 or col == 0:
maxes[row][col] = 0
elif xs[row - 1][0] <= col:
maxes[row][col] = max(
xs[row - 1][1] + maxes[row - 1][col - xs[row - 1][0]],
maxes[row - 1][col])
else:
maxes[row][col] = maxes[row - 1][col]
return maxes[-1][capacity]
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_one_cake(self):
actual = knapify([(3, 10), (2, 15), (7, 2), (12, 20)], capacity=12)
expected = None
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

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data_structures_and_algorithms/kth-to-last.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
def length(x):
if not x:
return 0
else:
count = 1
while x:
x = x.next
count += 1
return count
def kth_to_last_node(k, x):
hops = length(x) - 1
dest = hops - k
if k == 0:
raise Exception("Our God doesn't support this kind of behavior.")
if dest < 0:
raise Exception('Value k to high for list.')
while dest > 0:
x = x.next
dest -= 1
return x
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
class LinkedListNode(object):
def __init__(self, value, next=None):
self.value = value
self.next = next
def get_values(self):
node = self
values = []
while node is not None:
values.append(node.value)
node = node.next
return values
def setUp(self):
self.fourth = Test.LinkedListNode(4)
self.third = Test.LinkedListNode(3, self.fourth)
self.second = Test.LinkedListNode(2, self.third)
self.first = Test.LinkedListNode(1, self.second)
def test_first_to_last_node(self):
actual = kth_to_last_node(1, self.first)
expected = self.fourth
self.assertEqual(actual, expected)
def test_second_to_last_node(self):
actual = kth_to_last_node(2, self.first)
expected = self.third
self.assertEqual(actual, expected)
def test_first_node(self):
actual = kth_to_last_node(4, self.first)
expected = self.first
self.assertEqual(actual, expected)
def test_k_greater_than_linked_list_length(self):
with self.assertRaises(Exception):
kth_to_last_node(5, self.first)
def test_k_is_zero(self):
with self.assertRaises(Exception):
kth_to_last_node(0, self.first)
unittest.main(verbosity=2)

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data_structures_and_algorithms/largest-stack.py Normal file
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import unittest
class Stack(object):
def __init__(self):
"""Initialize an empty stack"""
self.items = []
def push(self, item):
"""Push a new item onto the stack"""
self.items.append(item)
def pop(self):
"""Remove and return the last item"""
# If the stack is empty, return None
# (it would also be reasonable to throw an exception)
if not self.items:
return None
return self.items.pop()
def peek(self):
"""Return the last item without removing it"""
if not self.items:
return None
return self.items[-1]
class MaxStack(object):
# Implement the push, pop, and get_max methods
def __init__(self):
self.m = Stack()
self.stack = Stack()
def push(self, item):
if self.m.peek() is None:
self.m.push(item)
elif item >= self.m.peek():
self.m.push(item)
self.stack.push(item)
def pop(self):
x = self.stack.pop()
if x == self.m.peek():
self.m.pop()
return x
def get_max(self):
return self.m.peek()
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_stack_usage(self):
max_stack = MaxStack()
max_stack.push(5)
actual = max_stack.get_max()
expected = 5
self.assertEqual(actual, expected)
max_stack.push(4)
max_stack.push(7)
max_stack.push(7)
max_stack.push(8)
actual = max_stack.get_max()
expected = 8
self.assertEqual(actual, expected)
actual = max_stack.pop()
expected = 8
self.assertEqual(actual, expected)
actual = max_stack.get_max()
expected = 7
self.assertEqual(actual, expected)
actual = max_stack.pop()
expected = 7
self.assertEqual(actual, expected)
actual = max_stack.get_max()
expected = 7
self.assertEqual(actual, expected)
actual = max_stack.pop()
expected = 7
self.assertEqual(actual, expected)
actual = max_stack.get_max()
expected = 5
self.assertEqual(actual, expected)
actual = max_stack.pop()
expected = 4
self.assertEqual(actual, expected)
actual = max_stack.get_max()
expected = 5
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

88
data_structures_and_algorithms/linked-list-cycles.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
def contains_cycle(x):
if not x:
return False
elif not x.next:
return False
a = x
b = x.next
while b.next:
if a == b:
return True
a = a.next
b = b.next.next
return False
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
class LinkedListNode(object):
def __init__(self, value, next=None):
self.value = value
self.next = next
def test_linked_list_with_no_cycle(self):
fourth = Test.LinkedListNode(4)
third = Test.LinkedListNode(3, fourth)
second = Test.LinkedListNode(2, third)
first = Test.LinkedListNode(1, second)
result = contains_cycle(first)
self.assertFalse(result)
def test_cycle_loops_to_beginning(self):
fourth = Test.LinkedListNode(4)
third = Test.LinkedListNode(3, fourth)
second = Test.LinkedListNode(2, third)
first = Test.LinkedListNode(1, second)
fourth.next = first
result = contains_cycle(first)
self.assertTrue(result)
def test_cycle_loops_to_middle(self):
fifth = Test.LinkedListNode(5)
fourth = Test.LinkedListNode(4, fifth)
third = Test.LinkedListNode(3, fourth)
second = Test.LinkedListNode(2, third)
first = Test.LinkedListNode(1, second)
fifth.next = third
result = contains_cycle(first)
self.assertTrue(result)
def test_two_node_cycle_at_end(self):
fifth = Test.LinkedListNode(5)
fourth = Test.LinkedListNode(4, fifth)
third = Test.LinkedListNode(3, fourth)
second = Test.LinkedListNode(2, third)
first = Test.LinkedListNode(1, second)
fifth.next = fourth
result = contains_cycle(first)
self.assertTrue(result)
def test_empty_list(self):
result = contains_cycle(None)
self.assertFalse(result)
def test_one_element_linked_list_no_cycle(self):
first = Test.LinkedListNode(1)
result = contains_cycle(first)
self.assertFalse(result)
def test_one_element_linked_list_cycle(self):
first = Test.LinkedListNode(1)
first.next = first
result = contains_cycle(first)
self.assertTrue(result)
unittest.main(verbosity=2)

28
data_structures_and_algorithms/merge-sort.py Normal file
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# merge :: [a] -> [a] -> [a]
# merge([], []): []
# merge(xs, []): xs
# merge([], ys): ys
# merge(xs@[x|xs'], ys@[y|ys'])
# when y =< x: cons(y, merge(xs, ys'))
# when x < y: cons(x, merge(xs', ys))
def merge(xs, ys):
if xs == [] and ys == []:
return []
elif ys == []:
return xs
elif xs == []:
return ys
else:
x = xs[0]
y = ys[0]
if y <= x:
return [y] + merge(xs, ys[1:])
else:
return [x] + merge(xs[1:], ys)
print(merge([3, 4, 6, 10, 11, 15],
[1, 5, 8, 12, 14, 19]))

94
data_structures_and_algorithms/merging-ranges.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
# do_merge_ranges :: [(Int, Int)] -> [(Int, Int)] -> [(Int, Int)]
def do_merge_ranges(prev, xs):
if len(xs) == 0:
return prev
elif len(xs) == 1:
return prev + xs
else:
a1, a2 = xs[0]
b1, b2 = xs[1]
rest = xs[2:]
if b1 <= a2:
return do_merge_ranges(prev, [(a1, max(a2, b2))] + rest)
else:
return do_merge_ranges(prev + [(a1, a2)], [(b1, b2)] + rest)
# merge_ranges :: [(Int, Int)] -> [(Int, Int)]
def merge_ranges(xs):
xs = xs[:]
xs.sort()
return do_merge_ranges([], xs)
# merge_ranges_b :: [(Int, Int)] -> [(Int, Int)]
def merge_ranges_b(xs):
fi = 0
ci = 1
result = []
xs = xs[:]
xs.sort()
while ci < len(xs):
while ci < len(xs) and xs[ci][0] <= xs[fi][1]:
xs[fi] = xs[fi][0], max(xs[ci][1], xs[fi][1])
ci += 1
result.append(xs[fi])
fi = ci
ci += 1
if fi < len(xs):
result.append(xs[fi])
return result
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_meetings_overlap(self):
actual = merge_ranges([(1, 3), (2, 4)])
expected = [(1, 4)]
self.assertEqual(actual, expected)
def test_meetings_touch(self):
actual = merge_ranges([(5, 6), (6, 8)])
expected = [(5, 8)]
self.assertEqual(actual, expected)
def test_meeting_contains_other_meeting(self):
actual = merge_ranges([(1, 8), (2, 5)])
expected = [(1, 8)]
self.assertEqual(actual, expected)
def test_meetings_stay_separate(self):
actual = merge_ranges([(1, 3), (4, 8)])
expected = [(1, 3), (4, 8)]
self.assertEqual(actual, expected)
def test_multiple_merged_meetings(self):
actual = merge_ranges([(1, 4), (2, 5), (5, 8)])
expected = [(1, 8)]
self.assertEqual(actual, expected)
def test_meetings_not_sorted(self):
actual = merge_ranges([(5, 8), (1, 4), (6, 8)])
expected = [(1, 4), (5, 8)]
self.assertEqual(actual, expected)
def test_one_long_meeting_contains_smaller_meetings(self):
actual = merge_ranges([(1, 10), (2, 5), (6, 8), (9, 10), (10, 12)])
expected = [(1, 12)]
self.assertEqual(actual, expected)
def test_sample_input(self):
actual = merge_ranges([(0, 1), (3, 5), (4, 8), (10, 12), (9, 10)])
expected = [(0, 1), (3, 8), (9, 12)]
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

11
data_structures_and_algorithms/mesh-message.gv Normal file
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strict graph {
Min -- {William, Jayden, Omar}
William -- {Min, Noam}
Jayden -- {Min, Amelia, Ren, Noam}
Adam -- {Amelia, Miguel, Sofia, Lucas}
Ren -- {Jayden, Omar}
Amelia -- {Jayden, Adam, Miguel}
Miguel -- {Amelia, Adam, Liam, Nathan}
Noam -- {Nathan, Jayden, William}
Omar -- {Ren, Min, Scott}
}

97
data_structures_and_algorithms/mesh-message.py Normal file
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import unittest
from collections import deque
################################################################################
# Solution
################################################################################
# get_path :: G(V, E) -> V -> V -> Maybe([V])
def get_path(g, src, dst):
q = deque()
result = None
seen = set()
q.append(([], src))
if src not in g or dst not in g:
raise Exception
while q:
p, node = q.popleft()
seen.add(node)
if node == dst:
if not result:
result = p + [node]
elif len(p + [node]) < len(result):
result = p + [node]
else:
if node not in g:
raise Exception
for x in g.get(node):
if not x in seen:
q.append((p + [node], x))
return result
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def setUp(self):
self.graph = {
'a': ['b', 'c', 'd'],
'b': ['a', 'd'],
'c': ['a', 'e'],
'd': ['a', 'b'],
'e': ['c'],
'f': ['g'],
'g': ['f'],
}
def test_two_hop_path_1(self):
actual = get_path(self.graph, 'a', 'e')
expected = ['a', 'c', 'e']
self.assertEqual(actual, expected)
def test_two_hop_path_2(self):
actual = get_path(self.graph, 'd', 'c')
expected = ['d', 'a', 'c']
self.assertEqual(actual, expected)
def test_one_hop_path_1(self):
actual = get_path(self.graph, 'a', 'c')
expected = ['a', 'c']
self.assertEqual(actual, expected)
def test_one_hop_path_2(self):
actual = get_path(self.graph, 'f', 'g')
expected = ['f', 'g']
self.assertEqual(actual, expected)
def test_one_hop_path_3(self):
actual = get_path(self.graph, 'g', 'f')
expected = ['g', 'f']
self.assertEqual(actual, expected)
def test_zero_hop_path(self):
actual = get_path(self.graph, 'a', 'a')
expected = ['a']
self.assertEqual(actual, expected)
def test_no_path(self):
actual = get_path(self.graph, 'a', 'f')
expected = None
self.assertEqual(actual, expected)
def test_start_node_not_present(self):
with self.assertRaises(Exception):
get_path(self.graph, 'h', 'a')
def test_end_node_not_present(self):
with self.assertRaises(Exception):
get_path(self.graph, 'a', 'h')
unittest.main(verbosity=2)

78
data_structures_and_algorithms/norman.py Normal file
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# Write a function with the following type signature:L
# equal? :: String -> String -> Bool
#
# Determine equality between two inputs with backspace characters encoded as
# "<".
################################################################################
# Solution 1
################################################################################
# from collections import deque
# def equal(a, b):
# sa = deque()
# sb = deque()
# for c in a:
# if c == '<':
# sa.pop()
# else:
# sa.append(c)
# for c in b:
# if c == '<':
# sb.pop()
# else:
# sb.append(c)
# return sa == sb
################################################################################
# Solution 2
################################################################################
def handle_dels(num_dels, i, xs):
if i < 0:
return -1
while xs[i] == '<':
num_dels += 1
i -= 1
while num_dels > 0 and xs[i] != '<':
num_dels -= 1
i -= 1
if xs[i] == '<':
return handle_dels(num_dels, i, xs)
else:
return i
def update_index(i, xs):
# TODO: Indexing into non-available parts of a string.
if xs[i] != '<' and xs[i - 1] != '<':
return i - 1
elif xs[i - 1] == '<':
return handle_dels(0, i - 1, xs)
def equal(a, b):
ia = len(a) - 1
ib = len(b) - 1
while ia >= 0 and ib >= 0:
if a[ia] != b[ib]:
return False
ia = update_index(ia, a)
ib = update_index(ib, b)
if ia != 0:
return update_index(ia, a) <= -1
if ib != 0:
return update_index(ib, b) <= -1
return True

59
data_structures_and_algorithms/nth-fibonacci.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
def fib(n):
"""This should be accomplishable in O(1) space."""
if n in {0, 1}:
return n
a = 0 # i = 0
b = 1 # i = 1
for x in range(2, n + 1):
result = a + b
a = b
b = result
return result
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_zeroth_fibonacci(self):
actual = fib(0)
expected = 0
self.assertEqual(actual, expected)
def test_first_fibonacci(self):
actual = fib(1)
expected = 1
self.assertEqual(actual, expected)
def test_second_fibonacci(self):
actual = fib(2)
expected = 1
self.assertEqual(actual, expected)
def test_third_fibonacci(self):
actual = fib(3)
expected = 2
self.assertEqual(actual, expected)
def test_fifth_fibonacci(self):
actual = fib(5)
expected = 5
self.assertEqual(actual, expected)
def test_tenth_fibonacci(self):
actual = fib(10)
expected = 55
self.assertEqual(actual, expected)
def test_negative_fibonacci(self):
with self.assertRaises(Exception):
fib(-1)
unittest.main(verbosity=2)

49
data_structures_and_algorithms/optimal-stopping.py Normal file
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from random import choice
from math import floor
# Applying Chapter 1 from "Algorithms to Live By", which describes optimal
# stopping problems. Technically this simulation is invalid because the
# `candidates` function takes a lower bound and an upper bound, which allows us
# to know the cardinal number of an individual candidates. The "look then leap"
# algorithm is ideal for no-information games - i.e. games when upper and lower
# bounds aren't known. The `look_then_leap/1` function is ignorant of this
# information, so it behaves as if in a no-information game. Strangely enough,
# this algorithm will pick the best candidate 37% of the time.
#
# Chapter 1 describes two algorithms:
# 1. Look-then-leap: ordinal numbers - i.e. no-information games. Look-then-leap
# finds the best candidate 37% of the time.
# 2. Threshold: cardinal numbers - i.e. where upper and lower bounds are
# known. The Threshold algorithm finds the best candidate ~55% of the time.
#
# All of this and more can be studied as "optimal stopping theory". This applies
# to finding a spouse, parking a car, picking an apartment in a city, and more.
# candidates :: Int -> Int -> Int -> [Int]
def candidates(lb, ub, ct):
xs = list(range(lb, ub + 1))
return [choice(xs) for _ in range(ct)]
# look_then_leap :: [Integer] -> Integer
def look_then_leap(candidates):
best = candidates[0]
seen_ct = 1
ignore_ct = floor(len(candidates) * 0.37)
for x in candidates[1:]:
if ignore_ct > 0:
ignore_ct -= 1
best = max(best, x)
else:
if x > best:
print('Choosing the {} candidate.'.format(seen_ct))
return x
seen_ct += 1
print('You may have waited too long.')
return candidates[-1]
candidates = candidates(1, 100, 100)
print(candidates)
print(look_then_leap(candidates))

83
data_structures_and_algorithms/perm-tree.py Normal file
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import unittest
################################################################################
# Answer
################################################################################
class Node(object):
def __init__(self, value, children=set()):
self.value = value
self.children = children
# treeify :: Char -> Set(Char) -> Node(Char)
def treeify(x, xs):
return Node(x, [treeify(c, xs - {c}) for c in xs])
# dft :: Node(Char) -> [String]
def dft(node):
result = []
s = []
s.append(('', node))
while s:
p, n = s.pop()
p += str(n.value)
if not n.children:
result.append(p)
else:
for c in n.children:
s.append((p, c))
return result
# main :: String -> Set(String)
def get_permutations(xs):
if xs == '':
return set([''])
ys = set(xs)
trees = []
for y in ys:
trees.append(treeify(y, ys - {y}))
result = set()
for t in trees:
for d in dft(t):
result.add(d)
return result
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_empty_string(self):
actual = get_permutations('')
expected = set([''])
self.assertEqual(actual, expected)
def test_one_character_string(self):
actual = get_permutations('a')
expected = set(['a'])
self.assertEqual(actual, expected)
def test_two_character_string(self):
actual = get_permutations('ab')
expected = set(['ab', 'ba'])
self.assertEqual(actual, expected)
def test_three_character_string(self):
actual = get_permutations('abc')
expected = set(['abc', 'acb', 'bac', 'bca', 'cab', 'cba'])
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

49
data_structures_and_algorithms/permutation-palindrome.py Normal file
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from collections import Counter
import unittest
################################################################################
# Impl
################################################################################
# palindromifiable :: String -> Boolean
def has_palindrome_permutation(x):
bag = Counter(x)
odd_entries_ct = 0
for _, y in bag.items():
if y % 2 != 0:
odd_entries_ct += 1
return odd_entries_ct in {0, 1}
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_permutation_with_odd_number_of_chars(self):
result = has_palindrome_permutation('aabcbcd')
self.assertTrue(result)
def test_permutation_with_even_number_of_chars(self):
result = has_palindrome_permutation('aabccbdd')
self.assertTrue(result)
def test_no_permutation_with_odd_number_of_chars(self):
result = has_palindrome_permutation('aabcd')
self.assertFalse(result)
def test_no_permutation_with_even_number_of_chars(self):
result = has_palindrome_permutation('aabbcd')
self.assertFalse(result)
def test_empty_string(self):
result = has_palindrome_permutation('')
self.assertTrue(result)
def test_one_character_string(self):
result = has_palindrome_permutation('a')
self.assertTrue(result)
unittest.main(verbosity=2)

55
data_structures_and_algorithms/permutations.py Normal file
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class Node(object):
# ctor :: a -> [a] -> Node(a)
def __init__(self, value, children=[]):
self.value = value
self.children = children
# is_leaf :: Node(a) -> Boolean
def is_leaf(node):
return len(node.children) == 0
# enumerate :: Node(a) -> Set(List(a))
def enumerate(node):
current = []
result = []
q = []
q.append(node)
while q:
x = q.pop()
print(x.value)
for c in x.children:
q.append(c)
current.append(x.value)
print(current)
if is_leaf(x):
result.append(current)
print("Reseting current")
current = []
return result
node = Node('root', [
Node('a', [
Node('b', [Node('c')]),
Node('c', [Node('b')]),
]),
Node('b', [
Node('a', [Node('c')]),
Node('c', [Node('a')]),
]),
Node('c', [
Node('a', [Node('b')]),
Node('b', [Node('a')]),
])
])
print('----------')
print(enumerate(node))

9
data_structures_and_algorithms/plot.py Normal file
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import numpy as np
import matplotlib.pyplot as plt
rng = np.random.RandomState(10) # deterministic random data
a = np.hstack((rng.normal(size=1000), rng.normal(loc=5, scale=2, size=1000)))
_ = plt.hist(a, bins='auto') # arguments are passed to np.histogram
plt.title("Histogram with 'auto' bins")
Text(0.5, 1.0, "Histogram with 'auto' bins")
plt.show()

68
data_structures_and_algorithms/product-of-other-numbers.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
# f :: [Int] -> [Int]
def get_products_of_all_ints_except_at_index(xs):
if len(xs) in {0, 1}:
raise Exception
ct = len(xs)
lefts = [1] * ct
rights = [1] * ct
result = []
for i in range(1, ct):
lefts[i] = lefts[i - 1] * xs[i - 1]
for i in range(ct - 2, -1, -1):
rights[i] = rights[i + 1] * xs[i + 1]
return [lefts[i] * rights[i] for i in range(ct)]
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_small_list(self):
actual = get_products_of_all_ints_except_at_index([1, 2, 3])
expected = [6, 3, 2]
self.assertEqual(actual, expected)
def test_longer_list(self):
actual = get_products_of_all_ints_except_at_index([8, 2, 4, 3, 1, 5])
expected = [120, 480, 240, 320, 960, 192]
self.assertEqual(actual, expected)
def test_list_has_one_zero(self):
actual = get_products_of_all_ints_except_at_index([6, 2, 0, 3])
expected = [0, 0, 36, 0]
self.assertEqual(actual, expected)
def test_list_has_two_zeros(self):
actual = get_products_of_all_ints_except_at_index([4, 0, 9, 1, 0])
expected = [0, 0, 0, 0, 0]
self.assertEqual(actual, expected)
def test_one_negative_number(self):
actual = get_products_of_all_ints_except_at_index([-3, 8, 4])
expected = [32, -12, -24]
self.assertEqual(actual, expected)
def test_all_negative_numbers(self):
actual = get_products_of_all_ints_except_at_index([-7, -1, -4, -2])
expected = [-8, -56, -14, -28]
self.assertEqual(actual, expected)
def test_error_with_empty_list(self):
with self.assertRaises(Exception):
get_products_of_all_ints_except_at_index([])
def test_error_with_one_number(self):
with self.assertRaises(Exception):
get_products_of_all_ints_except_at_index([1])
unittest.main(verbosity=2)

66
data_structures_and_algorithms/queue-two-stacks.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
class QueueTwoStacks(object):
def __init__(self):
self.a = []
self.b = []
def enqueue(self, x):
self.a.append(x)
def dequeue(self):
if self.b:
return self.b.pop()
else:
while self.a:
self.b.append(self.a.pop())
return self.dequeue()
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_basic_queue_operations(self):
queue = QueueTwoStacks()
queue.enqueue(1)
queue.enqueue(2)
queue.enqueue(3)
actual = queue.dequeue()
expected = 1
self.assertEqual(actual, expected)
actual = queue.dequeue()
expected = 2
self.assertEqual(actual, expected)
queue.enqueue(4)
actual = queue.dequeue()
expected = 3
self.assertEqual(actual, expected)
actual = queue.dequeue()
expected = 4
self.assertEqual(actual, expected)
def test_error_when_dequeue_from_new_queue(self):
queue = QueueTwoStacks()
with self.assertRaises(Exception):
queue.dequeue()
def test_error_when_dequeue_from_empty_queue(self):
queue = QueueTwoStacks()
queue.enqueue(1)
queue.enqueue(2)
actual = queue.dequeue()
expected = 1
self.assertEqual(actual, expected)
actual = queue.dequeue()
expected = 2
self.assertEqual(actual, expected)
with self.assertRaises(Exception):
queue.dequeue()
unittest.main(verbosity=2)

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data_structures_and_algorithms/rectangular-love.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
# bottom :: Rectangle -> Int
def bottom(x):
return x.get('bottom_y')
# top :: Rectangle -> Int
def top(x):
return bottom(x) + x.get('height')
# left :: Rectangle -> Int
def left(x):
return x.get('left_x')
# right :: Rectangle -> Int
def right(x):
return left(x) + x.get('width')
# sort_highest :: Rectangle -> Rectangle -> (Rectangle, Rectangle)
def sort_highest(x, y):
if top(x) >= top(y):
return x, y
else:
return y, x
# sort_leftmost :: Rectangle -> Rectangle -> (Rectangle, Rectangle)
def sort_leftmost(x, y):
if left(x) <= left(y):
return x, y
else:
return y, x
# rectify :: Int -> Int -> Int -> Int -> Rectify
def rectify(top=None, bottom=None, left=None, right=None):
assert top >= bottom
assert left <= right
return {
'left_x': left,
'bottom_y': bottom,
'width': right - left,
'height': top - bottom,
}
# empty_rect :: Rectangle
def empty_rect():
return {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
# find_rectangular_overlap :: Rectangle -> Rectangle -> Maybe(Rectangle)
def find_rectangular_overlap(x, y):
ha, hb = sort_highest(x, y)
la, lb = sort_leftmost(x, y)
if bottom(hb) <= top(hb) <= bottom(ha) <= top(ha):
return empty_rect()
if left(la) <= right(la) <= left(lb) <= right(lb):
return empty_rect()
# We should have an intersection here.
verts = [bottom(ha), top(ha), bottom(hb), top(hb)]
verts.sort()
horzs = [left(la), right(la), left(lb), right(lb)]
horzs.sort()
return rectify(top=verts[2],
bottom=verts[1],
left=horzs[1],
right=horzs[2])
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_overlap_along_both_axes(self):
rect1 = {
'left_x': 1,
'bottom_y': 1,
'width': 6,
'height': 3,
}
rect2 = {
'left_x': 5,
'bottom_y': 2,
'width': 3,
'height': 6,
}
expected = {
'left_x': 5,
'bottom_y': 2,
'width': 2,
'height': 2,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_one_rectangle_inside_another(self):
rect1 = {
'left_x': 1,
'bottom_y': 1,
'width': 6,
'height': 6,
}
rect2 = {
'left_x': 3,
'bottom_y': 3,
'width': 2,
'height': 2,
}
expected = {
'left_x': 3,
'bottom_y': 3,
'width': 2,
'height': 2,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_both_rectangles_the_same(self):
rect1 = {
'left_x': 2,
'bottom_y': 2,
'width': 4,
'height': 4,
}
rect2 = {
'left_x': 2,
'bottom_y': 2,
'width': 4,
'height': 4,
}
expected = {
'left_x': 2,
'bottom_y': 2,
'width': 4,
'height': 4,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_touch_on_horizontal_edge(self):
rect1 = {
'left_x': 1,
'bottom_y': 2,
'width': 3,
'height': 4,
}
rect2 = {
'left_x': 2,
'bottom_y': 6,
'width': 2,
'height': 2,
}
expected = {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_touch_on_vertical_edge(self):
rect1 = {
'left_x': 1,
'bottom_y': 2,
'width': 3,
'height': 4,
}
rect2 = {
'left_x': 4,
'bottom_y': 3,
'width': 2,
'height': 2,
}
expected = {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_touch_at_a_corner(self):
rect1 = {
'left_x': 1,
'bottom_y': 1,
'width': 2,
'height': 2,
}
rect2 = {
'left_x': 3,
'bottom_y': 3,
'width': 2,
'height': 2,
}
expected = {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_no_overlap(self):
rect1 = {
'left_x': 1,
'bottom_y': 1,
'width': 2,
'height': 2,
}
rect2 = {
'left_x': 4,
'bottom_y': 6,
'width': 3,
'height': 6,
}
expected = {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

37
data_structures_and_algorithms/recursive-string-permutations.py Normal file
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import unittest
################################################################################
# Implementation
################################################################################
# get_permutations :: String -> Set(String)
def get_permutations(string):
pass
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_empty_string(self):
actual = get_permutations('')
expected = set([''])
self.assertEqual(actual, expected)
def test_one_character_string(self):
actual = get_permutations('a')
expected = set(['a'])
self.assertEqual(actual, expected)
def test_two_character_string(self):
actual = get_permutations('ab')
expected = set(['ab', 'ba'])
self.assertEqual(actual, expected)
def test_three_character_string(self):
actual = get_permutations('abc')
expected = set(['abc', 'acb', 'bac', 'bca', 'cab', 'cba'])
self.assertEqual(actual, expected)
unittest.main(verbosity=2)

79
data_structures_and_algorithms/reverse-linked-list.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
# reverse :: List(a) -> List(a)
def reverse(node):
curr = node
prev = None
while curr:
nxt = curr.next
curr.next = prev
prev = curr
curr = nxt
# Make sure to understand the spec! Debugging takes time. Rewriting takes
# time.
return prev
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
class LinkedListNode(object):
def __init__(self, value, next=None):
self.value = value
self.next = next
def get_values(self):
node = self
values = []
while node is not None:
values.append(node.value)
node = node.next
return values
def test_short_linked_list(self):
second = Test.LinkedListNode(2)
first = Test.LinkedListNode(1, second)
result = reverse(first)
self.assertIsNotNone(result)
actual = result.get_values()
expected = [2, 1]
self.assertEqual(actual, expected)
def test_long_linked_list(self):
sixth = Test.LinkedListNode(6)
fifth = Test.LinkedListNode(5, sixth)
fourth = Test.LinkedListNode(4, fifth)
third = Test.LinkedListNode(3, fourth)
second = Test.LinkedListNode(2, third)
first = Test.LinkedListNode(1, second)
result = reverse(first)
self.assertIsNotNone(result)
actual = result.get_values()
expected = [6, 5, 4, 3, 2, 1]
self.assertEqual(actual, expected)
def test_one_element_linked_list(self):
first = Test.LinkedListNode(1)
result = reverse(first)
self.assertIsNotNone(result)
actual = result.get_values()
expected = [1]
self.assertEqual(actual, expected)
def test_empty_linked_list(self):
result = reverse(None)
self.assertIsNone(result)
unittest.main(verbosity=2)

181
data_structures_and_algorithms/reverse-words.py Normal file
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from collections import deque
import unittest
################################################################################
# Solution
################################################################################
def rev(xs, i, j):
"""Reverse xs in place from [i, j]"""
while i < j:
xs[i], xs[j] = xs[j], xs[i]
i += 1
j -= 1
def rotate(xs, n, i=None, j=None):
"""Mutably rotates list, xs, n times. Positive n values rotate right while
negative n values rotate left. Rotate within window [i, j]."""
i = i or 0
j = j or len(xs) - 1
ct = j - i
if n < 0:
n = abs(n)
p = i + n - 1
rev(xs, i, p)
rev(xs, p + 1, j)
rev(xs, i, j)
else:
p = j - (n - 1)
rev(xs, p, j)
rev(xs, i, p - 1)
rev(xs, i, j)
return xs
def rev_words(xs, i, j):
if j + 1 == len(xs):
return 0
while j + 1 < len(xs):
while j + 1 < len(xs) and xs[j + 1] != ' ':
j += 1
rev(xs, i, j)
j += 2
i = j
return 0
def reverse_words(xs):
# first reverse everything
rev(xs, 0, len(xs) - 1)
return rev_words(xs, 0, 0)
def reverse_words_bak(xs, i=None, j=None):
i = i or 0
j = j or len(xs) - 1
w0, w1 = [], []
if i >= j:
return 0
pi = i
while pi < len(xs) and xs[pi] != ' ':
w0.append(xs[pi])
pi += 1
if pi == len(xs):
return 0
pj = j
while xs[pj] != ' ':
w1.append(xs[pj])
pj -= 1
d = len(w0) - len(w1)
rotate(xs, -1 * d, i, j)
for k in range(len(w1)):
xs[i + k] = w1[len(w1) - 1 - k]
for k in range(len(w0)):
xs[j - k] = w0[len(w0) - 1 - k]
while i != j and xs[i] != ' ' and xs[j] != ' ':
i += 1
j -= 1
if i == j:
return 0
elif xs[i] == ' ':
while j > 0 and xs[j] != ' ':
j -= 1
if j == 0:
return 0
elif xs[j] == ' ':
while i < len(xs) and xs[i] != ' ':
i += 1
if i == len(xs):
return 0
return reverse_words(xs, i + 1, j - 1)
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_rev(self):
xs = [1, 2, 3, 4, 5]
rev(xs, 0, len(xs) - 1)
self.assertEqual(xs, [5, 4, 3, 2, 1])
def test_rotate(self):
ys = [1, 2, 3, 4, 5]
xs = ys[:]
self.assertEqual(rotate(xs, 1, 1, 3), [1, 4, 2, 3, 5])
xs = ys[:]
self.assertEqual(rotate(xs, -1, 1, 3), [1, 3, 4, 2, 5])
xs = ys[:]
self.assertEqual(rotate(xs, 1), [5, 1, 2, 3, 4])
xs = ys[:]
self.assertEqual(rotate(xs, -1), [2, 3, 4, 5, 1])
xs = ys[:]
self.assertEqual(rotate(xs, -2), [3, 4, 5, 1, 2])
xs = ys[:]
self.assertEqual(rotate(xs, -5), [1, 2, 3, 4, 5])
xs = ys[:]
self.assertEqual(rotate(xs, 5), [1, 2, 3, 4, 5])
xs = ys[:]
self.assertEqual(rotate(xs, 3), [3, 4, 5, 1, 2])
def test_one_word(self):
message = list('vault')
reverse_words(message)
expected = list('vault')
self.assertEqual(message, expected)
def test_two_words(self):
message = list('thief cake')
reverse_words(message)
expected = list('cake thief')
self.assertEqual(message, expected)
def test_three_words(self):
message = list('one another get')
reverse_words(message)
expected = list('get another one')
self.assertEqual(message, expected)
def test_multiple_words_same_length(self):
message = list('rat the ate cat the')
reverse_words(message)
expected = list('the cat ate the rat')
self.assertEqual(message, expected)
def test_multiple_words_different_lengths(self):
message = list('at rat house')
reverse_words(message)
expected = list('house rat at')
self.assertEqual(message, expected)
def test_multiple_words_different_lengths(self):
message = list('yummy is cake bundt chocolate')
reverse_words(message)
expected = list('chocolate bundt cake is yummy')
self.assertEqual(message, expected)
def test_empty_string(self):
message = list('')
reverse_words(message)
expected = list('')
self.assertEqual(message, expected)
unittest.main(verbosity=2)

179
data_structures_and_algorithms/second-largest-item-bst.py Normal file
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import unittest
from collections import deque
################################################################################
# Implementation
################################################################################
def is_leaf(node):
return node.left is None and node.right is None
def find_largest(node):
current = node
while current.right is not None:
current = current.right
return current.value
def find_second_largest(node):
history = deque()
current = node
while current.right:
history.append(current)
current = current.right
if current.left:
return find_largest(current.left)
elif history:
return history.pop().value
else:
raise TypeError
def find_second_largest_backup(node):
history = deque()
current = node
# traverse -> largest
while current.right:
history.append(current)
current = current.right
if current.left:
return find_largest(current.left)
elif history:
return history.pop().value
else:
raise ArgumentError
# Write a iterative version to avoid consuming memory with the call stack.
# Commenting out the recursive code for now.
def find_second_largest_backup(node):
if node.left is None and node.right is None:
raise ArgumentError
elif node.right is None and is_leaf(node.left):
return node.left.value
# recursion
# elif node.right is None:
# return find_largest(node.left)
# iterative version
elif node.right is None:
current = node.left
while current.right is not None:
current = current.right
return current.value
# recursion
# TODO: Remove recursion from here.
elif not is_leaf(node.right):
return find_second_largest(node.right)
# could do an else here, but let's be more assertive.
elif is_leaf(node.right):
return node.value
else:
raise ArgumentError
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
class BinaryTreeNode(object):
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def insert_left(self, value):
self.left = Test.BinaryTreeNode(value)
return self.left
def insert_right(self, value):
self.right = Test.BinaryTreeNode(value)
return self.right
def test_full_tree(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(30)
right = tree.insert_right(70)
left.insert_left(10)
left.insert_right(40)
right.insert_left(60)
right.insert_right(80)
actual = find_second_largest(tree)
expected = 70
self.assertEqual(actual, expected)
def test_largest_has_a_left_child(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(30)
right = tree.insert_right(70)
left.insert_left(10)
left.insert_right(40)
right.insert_left(60)
actual = find_second_largest(tree)
expected = 60
self.assertEqual(actual, expected)
def test_largest_has_a_left_subtree(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(30)
right = tree.insert_right(70)
left.insert_left(10)
left.insert_right(40)
right_left = right.insert_left(60)
right_left_left = right_left.insert_left(55)
right_left.insert_right(65)
right_left_left.insert_right(58)
actual = find_second_largest(tree)
expected = 65
self.assertEqual(actual, expected)
def test_second_largest_is_root_node(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(30)
tree.insert_right(70)
left.insert_left(10)
left.insert_right(40)
actual = find_second_largest(tree)
expected = 50
self.assertEqual(actual, expected)
def test_descending_linked_list(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(40)
left_left = left.insert_left(30)
left_left_left = left_left.insert_left(20)
left_left_left.insert_left(10)
actual = find_second_largest(tree)
expected = 40
self.assertEqual(actual, expected)
def test_ascending_linked_list(self):
tree = Test.BinaryTreeNode(50)
right = tree.insert_right(60)
right_right = right.insert_right(70)
right_right.insert_right(80)
actual = find_second_largest(tree)
expected = 70
self.assertEqual(actual, expected)
def test_error_when_tree_has_one_node(self):
tree = Test.BinaryTreeNode(50)
with self.assertRaises(Exception):
find_second_largest(tree)
def test_error_when_tree_is_empty(self):
with self.assertRaises(Exception):
find_second_largest(None)
unittest.main(verbosity=2)

94
data_structures_and_algorithms/shortest-path-inject-vertices.py Normal file
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from heapq import heappush, heappop
from collections import deque
from fixtures import weighted_graph, expanded_weights_graph
# UnweightedGraph(a) :: Map(a, Set(a))
# WeightedGraph(a) :: Map(a, Set(a))
# shortest_path_dijkstra :: Vertex -> Vertex -> WeightedGraph(Vertex)
def shortest_path_dijkstra(a, b, g):
q = []
seen = set()
heappush(q, (0, a, [a]))
while q:
w0, v0, path = heappop(q)
if v0 in seen:
continue
elif v0 == b:
return w0, path
for w1, v1 in g.get(v0):
heappush(q, (w0 + w1, v1, path + [v1]))
seen.add(v0)
return 'weighted', 'pizza'
# expand_edge :: Vertex -> (Weight, Vertex) -> Map(Vertex, [Vertex])
def expand_edge(v0, wv):
w, v1 = wv
assert w > 1
result = {v0: ['{}-{}'.format(v1, 1)]}
for x in range(w - 2):
result['{}-{}'.format(v1, x + 1)] = ['{}-{}'.format(v1, x + 2)]
result['{}-{}'.format(v1, w - 1)] = [v1]
return result
# expand_weights :: Vertex -> WeightedGraph(Vertex) -> UnweightedGraph(Vertex)
def expand_weights(v, g):
result = {}
q = deque()
seen = set()
q.append(v)
while q:
v = d.popleft()
if v in seen:
continue
x = expand_edge(v, g.get)
for w, v1 in g.get(v):
if w > 1:
ws = expand_edge(v, (w, v1))
result = {**result, **ws}
q.append(v)
pass
# shortest_path_inject :: Vertex -> Vertex -> WeightedGraph(Vertex)
def shortest_path_inject(a, b, g):
q = deque()
seen = set()
q.append((a, [a]))
while q:
v0, path = q.popleft()
if v0 == 'dummy':
continue
elif v0 in seen:
continue
elif v0 == b:
return len(path), path
for _, v1 in g.get(v0):
q.append((v1, path + [v1]))
seen.add(v0)
continue
return None, None
print(expand_edge('a', (4, 'b')))
print(expand_edge('a', (5, 'e')))
assert expand_weights('a', weighted_graph) == expanded_weights_graph
# a = 'a'
# b = 'd'
# w, x = shortest_path_dijkstra(a, b, weighted_graph)
# w1, x1 = shortest_path_inject(a, b, weighted_graph)
# print("[dijkstra] Shortest path from {} to {} is {} with weight {}".format(
# a, b, x, w))
# print("[injection] Shortest path from {} to {} is {} with weight {}".format(
# a, b, x1, w1))

34
data_structures_and_algorithms/shuffle.py Normal file
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import random
def get_random(floor, ceiling):
return random.randrange(floor, ceiling + 1)
# shuffle_in_place :: [a] -> IO ()
def shuffle_in_place(xs):
"""Fisher-Yates algorithm. Notice that shuffling here is the same as
selecting a random permutation of the input set, `xs`."""
n = len(xs) - 1
for i in range(len(xs)):
r = get_random(i, n)
xs[i], xs[r] = xs[r], xs[i]
return xs
# shuffle :: [a] -> [a]
def shuffle_not_in_place(xs):
result = []
while xs:
i = get_random(0, len(xs) - 1)
x = xs.pop(i)
result.append(x)
return result
xs = [x for x in range(9)]
print(xs)
# print(shuffle_not_in_place(xs))
print(shuffle_in_place(xs[:]))

22
data_structures_and_algorithms/string-reverse.py Normal file
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# swap :: Int -> Int -> [Char] -> IO ()
def swap(ia, iz, xs):
# handle swap when ia == iz
assert ia <= iz
xs[ia], xs[iz] = xs[iz], xs[ia]
# reverse :: [Char] -> IO ()
def reverse(xs):
ia = 0
iz = len(xs) - 1
while ia <= iz:
swap(ia, iz, xs)
ia += 1
iz -= 1
x = list("superduperpooper")
reverse(x)
print(x)
print("Tests pass")

84
data_structures_and_algorithms/temperature-tracker.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
class TempTracker(object):
def __init__(self):
# min / max
self.min = None
self.max = None
# mean
self.sum = 0
self.num = 0
# mode
self.nums = [0] * 111
self.mode_num = 0
self.mode = None
def insert(self, x):
# min / max
if not self.min or x < self.min:
self.min = x
if not self.max or x > self.max:
self.max = x
# mean
self.sum += x
self.num += 1
# mode
self.nums[x] += 1
if self.nums[x] >= self.mode_num:
self.mode_num = self.nums[x]
self.mode = x
def get_max(self):
return self.max
def get_min(self):
return self.min
def get_mean(self):
return self.sum / self.num
def get_mode(self):
return self.mode
# Tests
class Test(unittest.TestCase):
def test_tracker_usage(self):
tracker = TempTracker()
tracker.insert(50)
msg = 'failed on first temp recorded'
self.assertEqual(tracker.get_max(), 50, msg='max ' + msg)
self.assertEqual(tracker.get_min(), 50, msg='min ' + msg)
self.assertEqual(tracker.get_mean(), 50.0, msg='mean ' + msg)
self.assertEqual(tracker.get_mode(), 50, msg='mode ' + msg)
tracker.insert(80)
msg = 'failed on higher temp recorded'
self.assertEqual(tracker.get_max(), 80, msg='max ' + msg)
self.assertEqual(tracker.get_min(), 50, msg='min ' + msg)
self.assertEqual(tracker.get_mean(), 65.0, msg='mean ' + msg)
self.assertIn(tracker.get_mode(), [50, 80], msg='mode ' + msg)
tracker.insert(80)
msg = 'failed on third temp recorded'
self.assertEqual(tracker.get_max(), 80, msg='max ' + msg)
self.assertEqual(tracker.get_min(), 50, msg='min ' + msg)
self.assertEqual(tracker.get_mean(), 70.0, msg='mean ' + msg)
self.assertEqual(tracker.get_mode(), 80, msg='mode ' + msg)
tracker.insert(30)
msg = 'failed on lower temp recorded'
self.assertEqual(tracker.get_max(), 80, msg='max ' + msg)
self.assertEqual(tracker.get_min(), 30, msg='min ' + msg)
self.assertEqual(tracker.get_mean(), 60.0, msg='mean ' + msg)
self.assertEqual(tracker.get_mode(), 80, msg='mode ' + msg)
unittest.main(verbosity=2)

1
data_structures_and_algorithms/test.txt Normal file
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hello

25
data_structures_and_algorithms/top-scores.py Normal file
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from collections import deque
# list:
# array:
# vector:
# bit-{array,vector}:
def sort(xs, highest):
v = [0] * (highest + 1)
result = deque()
for x in xs:
v[x] += 1
for i, x in enumerate(v):
if x > 0:
result.appendleft(i)
return list(result)
assert sort([37, 89, 41, 100, 65, 91, 53],
100) == [100, 91, 89, 65, 53, 41, 37]
print("Tests pass!")

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data_structures_and_algorithms/topo-sort.py Normal file
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from fixtures import unweighted_digraph
from collections import deque
# vertices_no_in_edges :: UnweightedDigraph -> Set(Vertex)
def vertices_no_in_edges(g):
"""Return the vertices in graph `g` with no in-edges."""
result = set()
vertices = set(g.keys())
for neighbors in g.values():
result = result.union(neighbors)
return vertices ^ result
# topo_sort :: UnweightedDigraph -> List(Vertex)
def topo_sort(g):
q = deque()
seen = set()
result = []
for x in vertices_no_in_edges(g):
q.append(x)
while q:
vertex = q.popleft()
if vertex in seen:
continue
result.append(vertex)
neighbors = g.get(vertex)
for x in g.get(vertex):
q.append(x)
seen.add(vertex)
return result
print(topo_sort(unweighted_digraph))

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data_structures_and_algorithms/trickling-water.py Normal file
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class Node(object):
def __init__(self, value, children=[]):
self.value = value
self.children = children
################################################################################
# Solution
################################################################################
def trip_time(node):
s = []
result = 0
s.append((node.value, node))
while s:
p, node = s.pop()
if not node.children:
result = max(result, p)
for x in node.children:
s.append((p + x.value, x))
return result
################################################################################
# Tests
################################################################################
tree = Node(
0,
children=[
Node(5, children=[Node(6)]),
Node(2, children=[
Node(6),
Node(10),
]),
Node(3, children=[Node(2, children=[Node(11)])]),
])
assert trip_time(tree) == 16
print("Tests pass!")

33
data_structures_and_algorithms/which-appears-twice.py Normal file
View file

@ -0,0 +1,33 @@
import unittest
################################################################################
# Solution
################################################################################
# find_repeat :: [Int] -> Int
def find_repeat(xs):
n = len(xs) - 1
return sum(xs) - ((n**2 + n) / 2)
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_short_list(self):
actual = find_repeat([1, 2, 1])
expected = 1
self.assertEqual(actual, expected)
def test_medium_list(self):
actual = find_repeat([4, 1, 3, 4, 2])
expected = 4
self.assertEqual(actual, expected)
def test_long_list(self):
actual = find_repeat([1, 5, 9, 7, 2, 6, 3, 8, 2, 4])
expected = 2
self.assertEqual(actual, expected)
unittest.main(verbosity=2)