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Add coding exercises for Facebook interviews

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Add attempts at solving coding problems to Briefcase.
This commit is contained in:
William Carroll 2020-11-12 14:37:29 +00:00
parent d2d772e43e
commit aa66d9b83d
66 changed files with 2994 additions and 0 deletions
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71
scratch/facebook/anglocize-int.py Normal file
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THOUSAND = int(1e3)
MILLION = int(1e6)
BILLION = int(1e9)
TRILLION = int(1e12)
facts = {
1: "One",
2: "Two",
3: "Three",
4: "Four",
5: "Five",
6: "Six",
7: "Seven",
8: "Eight",
9: "Nine",
10: "Ten",
11: "Eleven",
12: "Twelve",
13: "Thirteen",
14: "Fourteen",
15: "Fifteen",
16: "Sixteen",
17: "Seventeen",
18: "Eighteen",
19: "Nineteen",
20: "Twenty",
30: "Thirty",
40: "Forty",
50: "Fifty",
60: "Sixty",
70: "Seventy",
80: "Eighty",
90: "Ninety",
100: "Hundred",
THOUSAND: "Thousand",
MILLION: "Million",
BILLION: "Billion",
TRILLION: "Trillion",
}
def anglocize(x):
# ones
if x >= 0 and x < 10:
pass
# tens
elif x < 100:
pass
# hundreds
elif x < THOUSAND:
pass
# thousands
elif x < MILLION:
pass
# millions
elif x < BILLION:
pass
# billion
elif x < TRILLION:
pass
# trillion
else:
pass
x = 1234
assert anglocize(x) == "One Thousand, Two Hundred Thirty Four"

70
scratch/facebook/balanced-binary-tree.py Normal file
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from collections import deque
class Node(object):
# __init__ :: T(A)
def __init__(self, value=None, left=None, right=None):
self.value = value
self.left = left
self.right = right
# insert_left :: T(A) -> A -> T(A)
def insert_left(self, value):
self.left = Node(value)
return self.left
# insert_right :: T(A) -> A -> T(A)
def insert_right(self, value):
self.right = Node(value)
return self.right
# is_superbalanced :: T(A) -> Bool
def is_superbalanced(self):
xs = deque()
min_depth, max_depth = float('inf'), float('-inf')
xs.append((self, 0))
while xs:
x, d = xs.popleft()
# Only redefine the depths at leaf nodes
if not x.left and not x.right:
min_depth, max_depth = min(min_depth, d), max(max_depth, d)
if x.left:
xs.append((x.left, d + 1))
if x.right:
xs.append((x.right, d + 1))
return max_depth - min_depth <= 1
# __repr__ :: T(A) -> String
def __repr__(self):
result = ''
xs = deque()
xs.append((self, 0))
while xs:
node, indent = xs.popleft()
result += '{i}{x}\n'.format(i=' ' * indent, x=node.value)
if node.left:
xs.append((node.left, indent + 2))
if node.right:
xs.append((node.right, indent + 2))
return result
# from_array :: List(A) -> T(A)
def from_array(values):
xs = deque()
root = Node()
xs.append(root)
for value in values:
node = xs.popleft()
node.value = value
node.left = Node()
xs.append(node.left)
node.right = Node()
xs.append(node.right)
return root
x = from_array([1, 1, 1, 1, 1, 1, 1])
print(x)
print(x.is_superbalanced())
x = Node(1, Node(2), Node(3))
print(x)
print(x.is_superbalanced())

112
scratch/facebook/breakfast-generator.py Normal file
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# After being inspired by...
# craftinginterpreters.com/representing-code.html
# ...I'm implementing the breakfast generator that the author describes
# therein.
import random
import string
# Breakfast
def breakfast():
fn = random.choice([
lambda: " ".join([protein(), "with", breakfast(), "on the side"]),
lambda: protein(),
lambda: bread(),
])
return fn()
def protein():
fn = random.choice([
lambda: " ".join([qualifier(), "crispy", "bacon"]),
lambda: "sausage",
lambda: " ".join([cooking_method(), "sausage"]),
])
return fn()
def qualifier():
fn = random.choice([
lambda: "really",
lambda: "super",
lambda: " ".join(["really", qualifier()]),
])
return fn()
def cooking_method():
return random.choice([
"scrambled",
"poached",
"fried",
])
def bread():
return random.choice([
"toast",
"biscuits",
"English muffin",
])
print(breakfast())
# Expression Language
# Because Python is a strictly evaluated language any functions that are
# mutually recursive won't terminate and will overflow our stack. Therefore, any
# non-terminals expressed in an alternative are wrapped in lambdas as thunks.
def expression():
fn = random.choice([
lambda: literal(),
lambda: binary(),
])
return fn()
def literal():
return str(random.randint(0, 100))
def binary():
return " ".join([expression(), operator(), expression()])
def operator():
return random.choice(["+", "*"])
print(expression())
# Lox
def lox_expression():
fn = random.choice([
lambda: lox_literal(),
lambda: lox_unary(),
lambda: lox_binary(),
lambda: lox_grouping(),
])
return fn()
def lox_literal():
fn = random.choice([
lambda: str(random.randint(0, 100)),
lambda: lox_string(),
lambda: random.choice(["true", "false"]),
lambda: "nil",
])
return fn()
def lox_string():
return "\"{}\"".format(
"".join(random.choice(string.ascii_lowercase)
for _ in range(random.randint(0, 25))))
def lox_grouping():
return "(" + lox_expression() + ")"
def lox_unary():
return random.choice(["-", "!"]) + lox_expression()
def lox_binary():
return lox_expression() + lox_operator() + lox_expression()
def lox_operator():
return random.choice(["==", "!=", "<", "<=", ">", ">=", "+", "-", "*", "/"])
print(lox_expression())

79
scratch/facebook/bst-checker.py Normal file
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from collections import deque
class Node(object):
def __init__(self, value, left=None, right=None):
self.value = value
self.left = left
self.right = right
def insert_left(self, value):
self.left = Node(value)
return self.left
def insert_right(self, value):
self.right = Node(value)
return self.right
def min(self):
xs = deque()
result = float('inf')
xs.append(self)
while xs:
node = xs.popleft()
result = min(result, node.value)
if node.left:
xs.append(node.left)
if node.right:
xs.append(node.right)
return result
def max(self):
xs = deque()
result = float('-inf')
xs.append(self)
while xs:
node = xs.popleft()
result = max(result, node.value)
if node.left:
xs.append(node.left)
if node.right:
xs.append(node.right)
return result
def is_bst(self):
result = True
if self.left:
result = result and self.left.max() < self.value
if self.right:
result = result and self.right.min() > self.value
return result
x = Node(
50,
Node(
17,
Node(
12,
Node(9),
Node(14),
),
Node(
23,
Node(19),
),
),
Node(
72,
Node(
54,
None,
Node(67)
),
Node(76),
),
)
assert x.is_bst()
print("Success!")

19
scratch/facebook/cafe-order-checker.py Normal file
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def orders_are_sorted(take_out, dine_in, audit):
if len(take_out) + len(dine_in) != len(audit):
return False
i, j = 0, 0
for x in audit:
if i < len(take_out) and take_out[i] == x:
i += 1
elif j < len(dine_in) and dine_in[j] == x:
j += 1
else:
return False
return True
assert orders_are_sorted([1,3,5], [2,4,6], [1,2,4,3,6,5])
assert not orders_are_sorted([1,3,5], [2,4,6], [1,2,4,5,6,3])
assert orders_are_sorted([], [2,4,6], [2,4,6])
print("Success!")

61
scratch/facebook/cake_thief.py Normal file
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from math import floor
def print_table(table):
print('\n-- TABLE --')
for row in range(len(table)):
x = ''
for col in range(len(table[row])):
x += ' ' + str(table[row][col])
print(x)
def leftover(capacity, kg):
n = floor(capacity / kg)
return n, capacity - (n * kg)
def init_table(num_rows, num_cols):
table = []
for _ in range(num_rows):
row = []
for _ in range(num_cols):
row.append(0)
table.append(row)
return table
def get(table, row, col):
if row < 0 or col < 0:
return 0
return table[row][col]
def max_haul(items, capacity):
table = init_table(len(items), capacity)
for row in range(len(table)):
for col in range(len(table[row])):
curr_capacity = col + 1
kg, val = items[row]
# A
a = get(table, row - 1, col)
# B
n, lo = leftover(curr_capacity, kg)
b = (val * n) + get(table, row - 1, lo - 1)
# commit
if kg > curr_capacity:
table[row][col] = a
else:
print(n, lo)
table[row][col] = max([a, b])
print_table(table)
return table[-1][-1]
# There are multiple variants of this problem:
# 1. We're allowed to take multiple of each item.
# 2. We can only take one of each item.
# 3. We can only take a fixed amount of each item.
items = [(7,160), (3,90), (2,15)]
capacity = 20
result = max_haul(items, capacity)
expected = None
print("Result: {} == Expected: {}".format(result, expected))
assert result == expected
print("Success!")

46
scratch/facebook/camping-knapsack.py Normal file
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from utils import get, init_table, print_table
def max_haul(capacity, items, names):
table = init_table(rows=len(items), cols=capacity, default=0)
items_table = init_table(rows=len(items), cols=capacity, default=[])
for row in range(len(table)):
for col in range(len(table[row])):
kg, value = items[row]
curr_capacity = col + 1
if kg > curr_capacity:
a = 0
else:
a = value + get(table, row - 1, curr_capacity - kg - 1)
b = get(table, row - 1, col)
if a > b:
rest = get(items_table, row - 1, curr_capacity - kg - 1)
knapsack = [names.get(items[row])]
if rest:
knapsack += rest
else:
knapsack = get(items_table, row - 1, col)
table[row][col] = max([a, b])
items_table[row][col] = knapsack
print_table(table)
return items_table[-1][-1]
water = (3, 10)
book = (1, 3)
food = (2, 9)
jacket = (2, 5)
camera = (1, 6)
items = [water, book, food, jacket, camera]
result = max_haul(6, items, {
water: 'water',
book: 'book',
food: 'food',
jacket: 'jacket',
camera: 'camera',
})
expected = ['camera', 'food', 'water']
print(result, expected)
assert result == expected
print("Success!")

50
scratch/facebook/coin.py Normal file
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def init_table(rows=0, cols=0, default=None):
table = []
for _ in range(rows):
row = []
for _ in range(cols):
row.append(default)
table.append(row)
return table
def print_table(table):
result = ''
for row in range(len(table)):
x = ''
for col in range(len(table[row])):
x += str(table[row][col]) + ' '
result += x + '\n'
print(result)
def get(table, row, col):
if row < 0 or col < 0:
return 0
else:
return table[row][col]
def make_change(coins, amt):
table = init_table(rows=len(coins), cols=amt, default=0)
for row in range(len(table)):
for col in range(len(table[row])):
coin = coins[row]
curr_amt = col + 1
pull_down = get(table, row - 1, col)
if curr_amt < coin:
table[row][col] = pull_down
elif curr_amt == coin:
table[row][col] = pull_down + 1
else:
leftover = get(table, row, curr_amt - coin - 1)
table[row][col] = pull_down + leftover
print_table(table)
return table[-1][-1]
# 1 2 3 4
# 1 1 1 1 1
# 2 1 1 2 2
# 3 1 1 3 4
result = make_change([3,2,1], 4)
print(result)

19
scratch/facebook/delete-node.py Normal file
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from linked_list import Node, from_list
def delete(node):
if not node.next:
node.value = None
else:
node.value = node.next.value
node.next = node.next.next
one = Node(1)
two = Node(2)
three = Node(3)
one.next = two
two.next = three
print(one)
delete(two)
print(one)

38
scratch/facebook/dijkstras.py Normal file
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from heapq import heappush, heappop
import random
# Dijkstra's algorithm will traverse a directed graph with weighted edges. If
# the edges aren't weighted, we can pretend that each edges weighs 1. The
# algorithm will find the shortest path between points A and B.
def dijkstra(a, b, graph):
h = []
seen = set()
heappush(h, (0, a, [a], []))
while h:
km, x, path, steps = heappop(h)
if x == b:
for a, b, d in steps:
print("{} -> {} => {}".format(a, b, d))
return path, km
seen.add(x)
for c, dist in graph[x]:
if c not in seen:
heappush(h, (km + dist, c, path + [c], steps + [(x, c, dist)]))
return [], float('inf')
graph = {
1: [(3, 9), (2, 7), (6, 14)],
2: [(1, 7), (3, 10), (4, 15)],
3: [(1, 9), (6, 2), (4, 11), (2, 10)],
4: [(5, 6), (2, 15), (3, 11)],
5: [(4, 6), (6, 9)],
6: [(5, 9), (3, 2), (1, 14)],
}
beg = random.choice(list(graph.keys()))
end = random.choice(list(graph.keys()))
print("Searching for the shortest path from {} -> {}".format(beg, end))
print(dijkstra(beg, end, graph))

39
scratch/facebook/evaluator.hs Normal file
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module Evaluator where
data Token
= TokenInt Integer
| TokenAdd
| TokenMultiply
deriving (Eq, Show)
newtype AST = AST [Token]
deriving (Eq, Show)
tokens :: [Token]
tokens =
[ TokenInt 13
, TokenAdd
, TokenInt 2
, TokenMultiply
, TokenInt 4
, TokenAdd
, TokenInt 7
, TokenAdd
, TokenInt 3
, TokenMultiply
, TokenInt 8
]
-- expression -> addition ;
-- addition -> multiplication ( "+" multiplication )* ;
-- multiplication -> terminal ( "*" terminal )* ;
-- terminal -> NUMBER ;
parseExpression :: [Token] -> ([Token], AST)
parseExpression tokens = do
lhs, rest = parseMultiplication tokens
parseMulitplication :: [Token] -> ([Token], AST)
main :: IO ()
main = print $ parse tokens

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# After stumbling through my first technical screen, I'm going to drill
# algorithms for implementing evaluators for a toy expression language:
# e.g. 2 + 13 * 3 + 5 * 2
#
# As of now, I'm aware of a few algorithms for solving this:
# - DONE: Convert infix expression to Polish notation and evaluate the Polish
# notation.
# - DONE: Evaluate the tokens using two stacks and avoid converting it.
# - DONE: Create a tree of depth two to encode the operator precedence and
# evaluate that AST.
# - TODO: Convert the infix expression to a prefix expression
# - TODO: Write a recursive descent parser and evaluate the AST.
operators = {
'*': 1,
'+': 0,
}
def tokenize(xs):
result = []
i = 0
while i < len(xs):
current = xs[i]
if current == ' ':
i += 1
continue
elif current in operators.keys():
result.append(current)
i += 1
else:
i += 1
while i < len(xs) and xs[i] in {str(n) for n in range(10)}:
current += xs[i]
i += 1
result.append(int(current))
return result
# Convert infix to postfix; evaluate postfix
# I believe this is known as the Shunting-Yards algorithm
def postfix(tokens):
result = []
s = []
for token in tokens:
if type(token) == int:
result.append(token)
else:
while s and operators[token] < operators[s[-1]]:
result.append(s.pop())
s.append(token)
while s:
result.append(s.pop())
return result
def do_evaluate_with_polish_notation(tokens):
s = []
for token in tokens:
if token == '*':
s.append(s.pop() * s.pop())
elif token == '+':
s.append(s.pop() + s.pop())
else:
s.append(token)
return s[-1]
def evaluate_with_polish_notation(expr):
tokens = tokenize(expr)
print("Tokens: {}".format(tokens))
pn = postfix(tokens)
print("Postfix: {}".format(pn))
result = do_evaluate_with_polish_notation(pn)
print("Result: {}".format(result))
return result
# Evaluate Tokens
def apply_operator(op, a, b):
if op == '*':
return a * b
elif op == '+':
return a + b
def do_evaluate_tokens(tokens):
vals = []
ops = []
for token in tokens:
if type(token) == int:
vals.append(token)
elif token == '*':
ops.append(token)
elif token == '+':
while ops and operators[token] < operators[ops[-1]]:
vals.append(apply_operator(ops.pop(), vals.pop(), vals.pop()))
ops.append(token)
else:
raise Exception("Unexpected token: {}".format(token))
while ops:
vals.append(apply_operator(ops.pop(), vals.pop(), vals.pop()))
return vals[-1]
def evaluate_tokens(expr):
tokens = tokenize(expr)
print("Tokens: {}".format(tokens))
result = do_evaluate_tokens(tokens)
print("Result: {}".format(result))
return result
# Ad Hoc Tree
def parse(tokens):
result = []
series = []
for token in tokens:
if type(token) == int:
series.append(token)
elif token == '*':
continue
elif token == '+':
result.append(series)
series = []
else:
raise Exception("Unexpected token: {}".format(token))
result.append(series)
return result
def product(xs):
result = 1
for x in xs:
result *= x
return result
def do_evaluate_ad_hoc_tree(ast):
return sum([product(xs) for xs in ast])
def evaluate_ad_hoc_tree(expr):
tokens = tokenize(expr)
print("Tokens: {}".format(tokens))
ast = parse(tokens)
print("AST: {}".format(ast))
result = do_evaluate_ad_hoc_tree(ast)
print("Result: {}".format(result))
return result
# Recursive Descent Parser
# expression -> addition ;
# addition -> multiplication ( "+" multiplication )* ;
# multiplication -> terminal ( "*" terminal )* ;
# terminal -> NUMBER ;
class Parser(object):
def __init__(self, tokens):
self.tokens = tokens
self.i = 0
# mutations
def advance(self):
self.i += 1
def consume(self):
result = self.curr()
self.advance()
return result
# predicates
def match(self, x):
if self.curr() == x:
self.advance()
return True
return False
def tokens_available(self):
return self.i < len(self.tokens)
# getters
def prev(self):
return self.tokens[self.i - 1]
def curr(self):
return self.tokens[self.i] if self.tokens_available() else None
def next(self):
return self.tokens[self.i + 1]
def parse_expression(tokens):
parser = Parser(tokens)
return parse_addition(parser)
def parse_addition(parser):
result = parse_multiplication(parser)
while parser.match("+"):
op = parser.prev()
rhs = parse_multiplication(parser)
result = ["+", result, rhs]
return result
def parse_multiplication(parser):
result = parse_terminal(parser)
while parser.match("*"):
op = parser.prev()
rhs = parse_terminal(parser)
result = ["*", result, rhs]
return result
def parse_terminal(parser):
# If we reach here, the current token *must* be a number.
return parser.consume()
def evaluate_ast(ast):
if type(ast) == int:
return ast
else:
op, lhs, rhs = ast[0], ast[1], ast[2]
return apply_operator(op, evaluate_ast(lhs), evaluate_ast(rhs))
def evaluate_recursive_descent(expr):
tokens = tokenize(expr)
print("Tokens: {}".format(tokens))
ast = parse_expression(tokens)
print("AST: {}".format(ast))
result = evaluate_ast(ast)
return result
methods = {
'Polish Notation': evaluate_with_polish_notation,
'Evaluate Tokens': evaluate_tokens,
'Ad Hoc Tree': evaluate_ad_hoc_tree,
'Recursive Descent': evaluate_recursive_descent,
}
for name, fn in methods.items():
expr = "13 + 2 * 4 + 7 + 3 * 8"
print("Evaluating \"{}\" using the \"{}\" method...".format(expr, name))
assert fn(expr) == eval(expr)
print("Success!")

22
scratch/facebook/find-duplicate-optimize-for-space.py Normal file
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import random
def find_duplicate(xs):
print(xs)
# entry point in our cycle is the duplicate
i = xs[0]
j = xs[xs[0]]
while i != j:
print(i, xs[i], j, xs[j])
i = xs[i]
j = xs[xs[j]]
# detect cycle
j = 0
while i != j:
i = xs[i]
j = xs[j]
return xs[i]
n = random.randint(5, 10)
xs = [random.randint(0, n - 1) for _ in range(n)]
result = find_duplicate(xs)
print(xs, result)

47
scratch/facebook/find-rotation-point.py Normal file
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from math import floor
def find_rotation(xs):
if xs[0] < xs[-1]:
return xs[0]
beg, end = 0, len(xs) - 1
found = False
count = 10
while not found and count >= 0:
i = beg + floor((end - beg) / 2)
if xs[beg] < xs[i]:
beg = i
i = beg + floor((end - beg) / 2)
elif xs[beg] > xs[i]:
end = i
found = xs[i - 1] > xs[i]
count -= 1
return xs[i]
xs = [(['ptolemaic',
'retrograde',
'supplant',
'undulate',
'xenoepist',
'zebra',
'asymptote',
'babka',
'banoffee',
'engender',
'karpatka',
'othellolagkage',
], "asymptote"),
(['asymptote',
'babka',
'banoffee',
'engender',
'karpatka',
'othellolagkage',
], "asymptote"),
]
for x, expected in xs:
result = find_rotation(x)
print(x, result)
assert result == expected
print("Success!")

17
scratch/facebook/find-unique-int-among-duplicates.py Normal file
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import random
def find_duplicate(xs):
mini, maxi, acc = xs[0], xs[0], xs[0]
for i in range(1, len(xs)):
mini = min(mini, xs[i])
maxi = max(maxi, xs[i])
acc = acc ^ xs[i]
mask = mini
for i in range(mini + 1, maxi + 1):
mask = mask ^ i
return mask ^ acc
xs = [5, 3, 4, 1, 5, 2]
print(xs)
result = find_duplicate(xs)
print(result)

60
scratch/facebook/graph-coloring.py Normal file
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from collections import deque
class Palette(object):
def __init__(self, n):
self.i = 0
self.colors = list(range(n))
def get(self):
return self.colors[self.i]
def advance(self):
self.i += 1 % len(self.colors)
class GraphNode(object):
def __init__(self, label):
self.label = label
self.neighbors = set()
self.color = None
def __repr__(self):
result = []
xs = deque()
xs.append(self)
seen = set()
while xs:
node = xs.popleft()
result.append('{} ({})'.format(node.label, str(node.color)))
seen.add(node.label)
for c in node.neighbors:
if c.label not in seen:
xs.append(c)
return ', '.join(result)
def color_graph(graph, d):
seen = set()
start = graph
xs = deque()
palette = Palette(d + 1)
xs.append((start, palette.get()))
while xs:
x, color = xs.popleft()
x.color = color
seen.add(x.label)
for c in x.neighbors:
if c.label not in seen:
palette.advance()
xs.append((c, palette.get()))
a = GraphNode('a')
b = GraphNode('b')
c = GraphNode('c')
a.neighbors.add(b)
b.neighbors.add(a)
b.neighbors.add(c)
c.neighbors.add(b)
print(a)
color_graph(a, 3)
print(a)

20
scratch/facebook/highest-product-of-3.py Normal file
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def hi_product(xs):
lowest_one, highest_one = min(xs[0], xs[1]), max(xs[0], xs[1])
lowest_two, highest_two = xs[0] * xs[1], xs[0] * xs[1]
highest = float('-inf')
for x in xs[2:]:
highest = max(highest, highest_two * x, lowest_two * x)
lowest_one = min(lowest_one, x)
highest_one = max(highest_one, x)
lowest_two = min(lowest_two, highest_one * x, lowest_one * x)
highest_two = max(highest_two, highest_one * x, lowest_one * x)
return highest
xs = [([-10,-10,1,3,2], 300),
([1,10,-5,1,-100], 5000)]
for x, expected in xs:
result = hi_product(x)
print(x, result)
assert result == expected
print("Success!")

51
scratch/facebook/infix-to-postfix.py Normal file
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operators = {
'*': 1,
'+': 0,
}
def tokenize(xs):
result = []
i = 0
while i < len(xs):
current = xs[i]
if current in operators.keys():
result.append(current)
i += 1
continue
else:
i += 1
while i < len(xs) and xs[i] in {str(n) for n in range(10)}:
current += xs[i]
i += 1
result.append(int(current))
return result
def postfix(xs):
result = []
s = []
for x in xs:
if x in operators.keys():
while s and operators[s[-1]] >= operators[x]:
result.append(s.pop())
s.append(x)
else:
result.append(x)
while s:
result.append(s.pop())
return result
def evaluate(xs):
s = []
for x in xs:
print(s, x)
if x == '*':
s.append(s.pop() * s.pop())
elif x == '+':
s.append(s.pop() + s.pop())
else:
s.append(x)
print(s)
return s[-1]
print(evaluate(postfix(tokenize("12+3*10"))))

29
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from random import choice
from utils import init_table
def get(movie, seeking):
return any([movie in xs for xs in seeking.values()])
def set_complement(movie, seeking):
for duration, xs in seeking.items():
seeking[duration].add(duration - movie)
def choose_movies(tolerance, duration, movies):
seeking = {duration + i: set() for i in range(-1 * tolerance, tolerance + 1)}
for movie in movies:
if get(movie, seeking):
return movie, duration - movie
else:
set_complement(movie, seeking)
return None
tolerance = 20
duration = choice([1, 2, 3]) * choice([1, 2]) * choice([15, 30, 45])
movies = [choice([1, 2, 3]) * choice([15, 30, 45]) for _ in range(10)]
print("Seeking two movies for a duration of [{}, {}] minutes".format(duration - tolerance, duration + tolerance))
print(movies)
result = choose_movies(tolerance, duration, movies)
if result:
print("{} + {} = {}".format(result[0], result[1], duration))
else:
print(":( We're sad because we couldn't find two movies for a {} minute flight".format(duration))

42
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from utils import get, init_table, print_table
# This problem has a few variants:
# - limited supply of each item
# - unlimited supply of each item
# - fractional amounts of each item (e.g. rice)
def max_haul(capacity, items):
min_kg = min([kg for _, kg in items])
max_kg = max([kg for _, kg in items])
cols = int(max_kg / min_kg)
fr_col_index = lambda index: min_kg * index + min_kg
to_col_index = lambda capacity: int((capacity - min_kg) * cols / max_kg)
table = init_table(rows=len(items), cols=cols, default=0)
for row in range(len(table)):
for col in range(len(table[row])):
curr_capacity = fr_col_index(col)
value, kg = items[row]
if kg > curr_capacity:
a = 0
else:
a = value + get(table, row - 1, to_col_index(curr_capacity - kg))
b = get(table, row - 1, col)
table[row][col] = max([a, b])
print_table(table)
return table[-1][-1]
guitar = (1500, 1)
stereo = (3000, 4)
laptop = (2000, 3)
necklace = (2000, 0.5)
items = [necklace, guitar, stereo, laptop]
capacity = 4
result = max_haul(capacity, items)
expected = 4000
print(result, expected)
assert result == expected
print("Success!")

26
scratch/facebook/kth-to-last-node-in-singly-linked-list.py Normal file
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from linked_list import Node, from_list
def kth_to_last_node(k, node):
one = node
two = node
for _ in range(k - 1):
if not one:
return None
one = one.next
while one.next:
one = one.next
two = two.next
return two.value
xs = from_list(["Angel Food", "Bundt", "Cheese", "Devil's Food", "Eccles"])
result = kth_to_last_node(2, xs)
print(result)
assert result == "Devil's Food"
print("Success!")
xs = from_list(["Angel Food", "Bundt"])
result = kth_to_last_node(30, xs)
print(result)
assert result is None
print("Success!")

70
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import random
# Write an evaluator for a small language:
# - operators: '+', '*'
# - operands: Integers
#
# E.g. evaluate("2+14*90+5*16")
def tokenize(xs):
result = []
i = 0
while i < len(xs):
current = xs[i]
if current in {'*', '+'}:
result.append(current)
i += 1
continue
elif current == ' ':
i += 1
continue
else:
i += 1
while i < len(xs) and xs[i] in {str(x) for x in range(10)}:
current += xs[i]
i += 1
result.append(int(current))
return result
def ast(tokens):
result = []
series = []
for token in tokens:
if token == '+':
result.append(series)
series = []
elif token == '*':
continue
else:
series.append(token)
if series:
result.append(series)
return result
def product(xs):
result = 1
for x in xs:
result *= x
return result
def evaluate(x):
tokens = tokenize(x)
tree = ast(tokens)
return sum([product(xs) for xs in tree])
n = 7
operands = [random.randint(0, 100) for _ in range(n)]
operators = [random.choice(['+','*']) for _ in range(n - 1)]
expr = []
for i in range(n - 1):
expr.append(operands[i])
expr.append(operators[i])
expr.append(operands[-1])
expr = ' '.join([str(x) for x in expr])
print("Expression: {}".format(expr))
print("Tokens: {}".format(tokenize(expr)))
print("AST: {}".format(ast(tokenize(expr))))
print("Answer: {}".format(evaluate(expr)))
assert evaluate(expr) == eval(expr)
print("Success!")

50
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def tokenize(xs):
result = []
i = 0
while i < len(xs):
curr = xs[i]
if curr in {'*','+'}:
result.append(curr)
i += 1
continue
i += 1
while i < len(xs) and xs[i] in {str(x) for x in range(10)}:
curr += xs[i]
i += 1
result.append(int(curr))
return result
def parse(tokens):
result = []
series = []
for token in tokens:
if token == '*':
continue
elif token == '+':
result.append(series)
series = []
else:
series.append(token)
if series:
result.append(series)
return result
def product(xs):
result = 1
for x in xs:
result *= x
return result
def evaluate(tree):
return sum([product(xs) for xs in tree])
print(evaluate(parse(tokenize("2+30*8*9+10"))))

15
scratch/facebook/largest-contiguous-sum.py Normal file
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def find_sum(xs):
result = float('-inf')
streak = 0
for x in xs:
result = max(result, streak, x)
if streak + x <= 0:
streak = x
else:
streak += x
return result
x = [2,-8,3,-2,4,-10]
assert find_sum(x) == 5
print("Success!")

49
scratch/facebook/largest-stack.py Normal file
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from stack import Stack, from_list
from heapq import heapify, heappush, heappop
from random import shuffle
class MaxStack(Stack):
def __init__(self):
self.max = Stack()
super().__init__()
def __repr__(self):
return super().__repr__()
def push(self, x):
super().push(x)
max = self.get_max()
if not max:
self.max.push(x)
else:
self.max.push(max if x < max else x)
def pop(self):
self.max.pop()
return super().pop()
def get_max(self):
return self.max.peek()
xs = list(range(1, 11))
shuffle(xs)
stack = MaxStack()
for x in xs:
stack.push(x)
print(stack)
result = stack.get_max()
print(result)
assert result == 10
popped = stack.pop()
print("Popped: {}".format(popped))
print(stack)
while popped != 10:
assert stack.get_max() == 10
popped = stack.pop()
print("Popped: {}".format(popped))
print(stack)
assert stack.get_max() != 10
print("Success!")

26
scratch/facebook/linked-list-cycles.py Normal file
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import random
from linked_list import Node
def contains_cycle(node):
one = node
two = node
while two.next and two.next.next:
one = one.next
two = two.next.next
if one == two:
return True
return False
xs = Node(1, Node(2, Node(3)))
assert not contains_cycle(xs)
print("Success!")
a = Node(1)
b = Node(2)
c = Node(3)
a.next = b
b.next = c
c.next = random.choice([a, b, c])
assert contains_cycle(a)
print("Success!")

22
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class Node(object):
def __init__(self, value=None, next=None):
self.value = value
self.next = next
def __repr__(self):
result = []
node = self
while node:
result.append(str(node.value))
node = node.next
return 'LinkedList({xs})'.format(xs=', '.join(result))
def from_list(xs):
head = Node(xs[0])
node = head
for x in xs[1:]:
node.next = Node(x)
node = node.next
return head
list = from_list(['A', 'B', 'C'])

42
scratch/facebook/london-knapsack.py Normal file
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from utils import get, init_table, print_table
def optimal_itinerary(duration, items):
min_duration = min([duration for duration, _ in items])
max_duration = max([duration for duration, _ in items])
table = init_table(rows=len(items), cols=int(max_duration / min_duration), default=0)
to_index = lambda duration: int(duration / min_duration) - 1
to_duration = lambda i: i * min_duration + min_duration
for row in range(len(table)):
for col in range(len(table[row])):
curr_duration = to_duration(col)
duration, value = items[row]
if duration > curr_duration:
a = 0
else:
a = value + get(table, row - 1, to_index(curr_duration - duration))
b = get(table, row - 1, col)
table[row][col] = max([a, b])
print_table(table)
return table[-1][-1]
# You're in London for two days, and you'd like to see the following
# attractions. How can you maximize your time spent in London?
westminster = (0.5, 7)
globe_theater = (0.5, 6)
national_gallery = (1, 9)
british_museum = (2, 9)
st_pauls_cathedral = (0.5, 8)
items = [
westminster,
globe_theater,
national_gallery,
british_museum,
st_pauls_cathedral,
]
result = optimal_itinerary(2, items)
expected = 24
print(result, expected)
assert result == expected
print("Success!")

20
scratch/facebook/longest-common-substring.py Normal file
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from utils import get, init_table, print_table
def longest_common_substring(a, b):
"""
Computes the length of the longest string that's present in both `a` and
`b`.
"""
table = init_table(rows=len(b), cols=len(a), default=0)
for row in range(len(table)):
for col in range(len(table[row])):
if b[row] == a[col]:
table[row][col] = 1 + get(table, row - 1, col - 1)
return max([max(row) for row in table])
dictionary = ["fish", "vista"]
result = [longest_common_substring("hish", x) for x in dictionary]
expected = [3, 2]
print(result, expected)
assert result == expected
print("Success!")

44
scratch/facebook/merge-sorted-arrays.py Normal file
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def merge_sorted(xs, ys):
result = []
i, j = 0, 0
while i < len(xs) and j < len(ys):
if xs[i] <= ys[j]:
result.append(xs[i])
i += 1
else:
result.append(ys[j])
j += 1
while i < len(xs):
result.append(xs[i])
i += 1
while j < len(ys):
result.append(ys[j])
j += 1
return result
# A
result = merge_sorted([3, 4, 6, 10, 11, 15], [1, 5, 8, 12, 14, 19])
print(result)
assert result == [1, 3, 4, 5, 6, 8, 10, 11, 12, 14, 15, 19]
# B
result = merge_sorted([], [1,2,3])
print(result)
assert result == [1,2,3]
# C
result = merge_sorted([1,2,3], [])
print(result)
assert result == [1,2,3]
# D
result = merge_sorted([], [])
print(result)
assert result == []
# Wahoo!
print("Success!")

23
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def merge(xs):
xs.sort()
result = xs[0:1]
for a, b in xs[1:]:
y, z = result[-1]
if a <= z:
result[-1] = (y, max(b, z))
else:
result.append((a, b))
return result
inputs = [([(0,1),(3,5),(4,8),(10,12),(9,10)], [(0,1),(3,8),(9,12)]),
([(1,2),(2,3)], [(1,3)]),
([(1,5),(2,3)], [(1,5)]),
([(1,10),(2,6),(3,5),(7,9)], [(1,10)]),
]
for x, expected in inputs:
result = merge(x)
print(x)
print(result)
assert result == expected
print("Success!")

40
scratch/facebook/mesh-message.py Normal file
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from heapq import heappush, heappop
import random
def shortest_path(a, b, graph):
seen = set()
h = []
heappush(h, (0, a, [a]))
while h:
km, x, path = heappop(h)
if x == b:
return path
for c in graph[x]:
if c not in seen:
heappush(h, (km + 1, c, path + [c]))
raise Exception("We were unable to find a path from {} to {}".format(a, b))
graph = {
'Min' : ['William', 'Jayden', 'Omar'],
'William' : ['Min', 'Noam'],
'Jayden' : ['Min', 'Amelia', 'Ren', 'Noam'],
'Ren' : ['Jayden', 'Omar'],
'Amelia' : ['Jayden', 'Adam', 'Miguel'],
'Adam' : ['Amelia', 'Miguel', 'Sofia', 'Lucas'],
'Miguel' : ['Amelia', 'Adam', 'Liam', 'Nathan'],
'Noam' : ['Nathan', 'Jayden', 'William'],
'Omar' : ['Ren', 'Min', 'Scott'],
'Liam' : ['Ren'],
'Nathan' : ['Noam'],
'Scott' : [],
}
result = shortest_path('Jayden', 'Adam', graph)
print(result)
assert result == ['Jayden', 'Amelia', 'Adam']
print('Success!')
beg = random.choice(list(graph.keys()))
end = random.choice(list(graph.keys()))
print("Attempting to find the shortest path between {} and {}".format(beg, end))
print(shortest_path(beg, end, graph))

71
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from heapq import heappush, heappop
import random
def to_vertex_list(graph):
result = {}
for a, b, kg in graph:
if a in result:
result[a].append((b, kg))
else:
result[a] = [(b, kg)]
if b in result:
result[b].append((a, kg))
else:
result[b] = [(a, kg)]
return result
def mst(graph):
graph = to_vertex_list(graph)
beg = random.choice(list(graph.keys()))
h = []
result = []
seen = set()
for c, kg in graph[beg]:
heappush(h, (kg, beg, c))
while h:
kg, beg, end = heappop(h)
# detect cycles
if end in seen:
continue
# use the edge
seen.add(beg)
seen.add(end)
result.append((beg, end))
for c, kg in graph[end]:
heappush(h, (kg, end, c))
return result
graphs = [
[
('A', 'B', 7),
('A', 'D', 5),
('B', 'D', 9),
('E', 'D', 15),
('F', 'D', 6),
('F', 'G', 11),
('F', 'E', 8),
('G', 'E', 9),
('C', 'E', 5),
('B', 'E', 7),
('B', 'C', 8),
],
[
('A', 'B', 4),
('A', 'C', 8),
('B', 'C', 11),
('B', 'E', 8),
('C', 'D', 7),
('C', 'F', 1),
('D', 'E', 2),
('D', 'F', 6),
('E', 'G', 7),
('E', 'H', 4),
('F', 'H', 2),
('G', 'H', 14),
('G', 'I', 9),
('H', 'I', 10),
],
]
for graph in graphs:
print(mst(graph))

38
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class Node(object):
def __init__(self, value, left=None, right=None):
self.value = value
self.left = left
self.right = right
def insert_left(self, value):
self.left = Node(value)
return self.left
def insert_right(self, value):
self.right = Node(value)
return self.right
tree = Node(
50,
Node(
17,
Node(
12,
Node(9),
Node(14),
),
Node(
23,
Node(19),
),
),
Node(
72,
Node(
54,
None,
Node(67)
),
Node(76),
),
)

13
scratch/facebook/nth-fibonacci.py Normal file
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# 0, 1, 1, 2, 3, 5
def fib(n):
if n < 0:
raise Exception("Need to supply an index that's >= 0. Not: {}".format(n))
elif n in {0, 1}:
return n
state = [0, 1]
for i in range(1, n):
state[0], state[1] = state[1], state[0] + state[1]
return state[-1]
for i in range(10):
print("fib({}) => {}".format(i, fib(i)))

22
scratch/facebook/onsite.txt Normal file
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** Behavior Interview **
- Can I work in an unstructured environment?
- Do I have a growth mindset?
- How do I handle conflict?
- Am I empathic?
- Am I a self-starter?
- What is my communication style?
- Do I persevere?
- <forgot to write this one down>
** Design Interview **
- requirement gathering, problem exploring
- component analysis
- quantitative analysis
- trade-offs
- bottlenecks, weaknesses
- securing data (e.g. PII)
Consider:
- pagination
- push/pull requests
- API design

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from parser import Parser
# As an exercise to stress-test my understanding of recursive descent parsers,
# I'm attempting to write a JSON parser without referencing any existing BNF
# descriptions of JSON or existing JSON parser implementations.
#
# I'm only parsing a subset of JSON: enough to parse `sample`. Here is the BNF
# that I wrote to describe my expected input:
#
# expression -> object
# object -> '{' ( STRING ':' expression ) ( ',' STRING ':' expression )* '}'
# | array
# array -> '[' expression ( ',' expression )* ']'
# | literal
# literal -> STRING | INT
def tokenize(xs):
"""
Return a list of tokens from the string input, `xs`.
"""
result = []
i = 0
while i < len(xs):
# single characters
if xs[i] in ",{}:[]":
result.append(xs[i])
i += 1
# strings
elif xs[i] == "\"":
curr = xs[i]
i += 1
while xs[i] != "\"":
curr += xs[i]
i += 1
curr += xs[i]
result.append(curr)
i += 1
# integers
elif xs[i] in "0123456789":
curr = xs[i]
i += 1
while xs[i] in "0123456789":
curr += xs[i]
i += 1
result.append(int(curr))
# whitespace
elif xs[i] in {" ", "\n"}:
i += 1
return result
def parse_json(x):
"""
Attempt to parse the string, `x`, into JSON.
"""
tokens = tokenize(x)
return parse_object(Parser(tokens))
def parse_object(parser):
if parser.match(['{']):
key = parse_string(parser)
parser.expect([':'])
value = parse_object(parser)
result = [(key, value)]
while parser.match([',']):
key = parse_string(parser)
parser.match([':'])
value = parse_object(parser)
result.append((key, value))
return result
return parse_array(parser)
def parse_array(parser):
if parser.match(['[']):
if parser.match([']']):
return []
result = [parse_object(parser)]
while parser.match([',']):
result.append(parse_object(parser))
parser.expect([']'])
return result
else:
return parse_literal(parser)
def parse_string(parser):
if parser.curr().startswith("\""):
return parser.consume()
else:
raise Exception("Unexpected token: {}".format(parser.curr()))
def parse_literal(parser):
return parser.consume()
sample = """
{
"glossary": {
"title": "example glossary",
"GlossDiv": {
"title": "S",
"GlossList": {
"GlossEntry": {
"ID": "SGML",
"SortAs": "SGML",
"GlossTerm": "Standard Generalized Markup Language",
"Acronym": "SGML",
"Abbrev": "ISO 8879:1986",
"GlossDef": {
"para": "A meta-markup language, used to create markup languages such as DocBook.",
"GlossSeeAlso": [
"GML",
"XML"
]
},
"GlossSee": "markup"
}
}
}
}
}
"""
print(parse_json(sample))

28
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class Parser(object):
def __init__(self, tokens):
self.tokens = tokens
self.i = 0
def prev(self):
return self.tokens[self.i - 1]
def curr(self):
return self.tokens[self.i]
def consume(self):
if not self.exhausted():
self.i += 1
return self.prev()
def match(self, xs):
if not self.exhausted() and self.curr() in xs:
self.consume()
return True
return False
def expect(self, xs):
if not self.match(xs):
raise Exception("Expected token \"{}\" but received \"{}\"".format(xs, self.curr()))
def exhausted(self):
return self.i >= len(self.tokens)

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# Writing a small proof-of-concept...
# - lexer
# - parser
# - compiler
# ...for regex.
from parser import Parser
import string
################################################################################
# Top-Level API
################################################################################
def tokenize(xs):
"""
Transform `xs` into a list of tokens.
Also: expand shorthand symbols using the following table:
- ? -> {0,1}
- * -> {0,}
- + -> {1,}
"""
result = []
i = 0
shorthand = {
"?": ["{", 0, ",", 1, "}"],
"*": ["{", 0, ",", "}"],
"+": ["{", 1, ",", "}"],
}
while i < len(xs):
if xs[i] in shorthand:
for c in shorthand[xs[i]]:
result.append(c)
i += 1
elif xs[i] == "{":
result.append(xs[i])
i += 1
curr = ""
while xs[i] in string.digits:
curr += xs[i]
i += 1
result.append(int(curr))
assert xs[i] == ","
result.append(",")
i += 1
curr = ""
while xs[i] in string.digits:
curr += xs[i]
i += 1
result.append(int(curr))
else:
result.append(xs[i])
i += 1
return result
def parse(expr):
"""
Tokenize `expr` and convert it into a parse-tree.
"""
tokens = tokenize(expr)
return parse_tokens(tokens)
def compile(xs):
"""
Transform `xs`, a parse-tree representing a regex, into a function that
accepts a string, and returns the substring that the regex matches.
"""
def fn(input):
match = ""
i = 0
for x in xs:
matches, q = x[1], x[2]
lo, hi = q[1], q[2]
for j in range(lo):
if i < len(input) and input[i] in matches:
match += input[i]
i += 1
else:
print("Failed to match {} with {}".format(input[i], matches))
return None
if hi == float('inf'):
while i < len(input) and input[i] in matches:
match += input[i]
i += 1
else:
for j in range(hi - lo):
if i < len(input) and input[i] in matches:
match += input[i]
i += 1
return match
return fn
################################################################################
# Helper Functions
################################################################################
def parse_tokens(tokens):
result = []
parser = Parser(tokens)
while not parser.exhausted():
result.append(parse_expression(parser))
return result
def parse_expression(parser):
if parser.curr() == "[":
return parse_character_class(parser)
else:
return parse_character(parser)
def parse_character_class(parser):
parser.expect("[")
beg = parser.consume()
parser.expect("-")
end = parser.consume()
parser.expect("]")
if parser.curr() == "{":
q = parse_quantifier(parser)
return char_class(xs=expand_range(beg, end), q=q)
def parse_quantifier(parser):
parser.expect("{")
if parser.match([","]):
end = parser.consume()
parser.expect("}")
return quantifier(beg=0, end=end)
else:
beg = parser.consume()
parser.expect(",")
if parser.match(["}"]):
return quantifier(beg=beg)
else:
end = parser.consume()
parser.expect("}")
return quantifier(beg=beg, end=end)
def parse_character(parser):
c = parser.consume()
q = None
if parser.curr() == "{":
q = parse_quantifier(parser)
return char_class(xs={c}, q=q)
def char_class(xs=set(), q=None):
if not q:
q = quantifier(beg=1, end=1)
return ["CHARACTER_CLASS", xs, q]
def expand_range(beg, end):
# TODO: Implement this
return {string.printable[i]
for i in range(string.printable.index(beg),
string.printable.index(end) + 1)}
def quantifier(beg=0, end=float('inf')):
return ['QUANTIFIER', beg, end]
################################################################################
# Tests
################################################################################
xs = [
("[a-c]*[0-9]{2,3}", ["dog"]),
("ca+t?", ["cat", "caaaat", "ca", "dog"]),
]
for re, inputs in xs:
print("Regex: {}".format(re))
print("Tokens: {}".format(tokenize(re)))
print("Parsed: {}".format(parse(re)))
print("\nTESTS")
for input in inputs:
print("Attempting to match \"{}\"...".format(input))
parser = compile(parse(re))
print("Result: \"{}\"\n".format(parser(input)))

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from collections import Counter
def is_palindrome(x):
return len([count for _, count in Counter(x).items() if count % 2 == 1]) <= 1
xs = [("civic", True),
("ivicc", True),
("civil", False),
("livci", False)]
for x, expected in xs:
result = is_palindrome(x)
print(x)
print(result)
assert result == expected
print("Success!")

33
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from random import randint
from math import floor
# loop {forwards, backwards, up, down}
# through a table of values, [[a]].
def product(xs):
n = len(xs)
lhs = [1] * (n + 1)
for i in range(1, n):
lhs[i] = lhs[i - 1] * xs[i - 1]
rhs = [1] * (n + 1)
for i in range(n - 1, 0, -1):
rhs[i] = rhs[i + 1] * xs[i]
result = []
for i in range(n):
result.append(lhs[i] * rhs[i + 1])
return result
def computed_expected(xs):
product = 1
for x in xs:
product *= x
return [floor(product / x) for x in xs]
xs = [randint(1, 10) for _ in range(5)]
expected = computed_expected(xs)
result = product(xs)
print(xs, result, expected)
assert result == expected
print("Success!")
print(product([2, 4, 3, 10, 5]))

20
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from stack import Stack
class Queue(object):
def __init__(self):
self.lhs = Stack()
self.rhs = Stack()
def enqueue(self, x):
self.rhs.push(x)
def dequeue(self, x):
y = self.rhs.pop()
while y:
self.lhs.push(y)
y = self.rhs.pop()
result = self.lhs.pop()
y = self.lhs.pop()
while y:
self.rhs.push(y)
return result

33
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from math import floor
def find_magic_index_brute(xs):
for i in range(len(xs)):
if xs[i] == i:
return i
return -1
def mid(lo, hi):
return lo + floor((hi - lo) / 2)
def find_magic_index(xs):
lo, hi = 0, len(xs) - 1
return do_find_magic_index(xs, 0, len(xs) - 1)
def do_find_magic_index(xs, lo, hi):
pass
xss = [
[],
[-1,0,2,4,5,6],
[1,1,1,1,1,5],
[-2,-2,-2,-2,4],
[1,2,3,4,5],
]
for xs in xss:
print(xs)
a = find_magic_index_brute(xs)
b = find_magic_index(xs)
print(a, b)
assert a == b
print("Success!")

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# Given an infinite supply of:
# - quarters
# - dimes
# - nickels
# - pennies
# Write a function to count the number of ways to make change of n.
def get(table, row, col):
"""
Defensively get cell `row`, `col` from `table`.
"""
if row < 0 or row >= len(table):
return 0
if col < 0 or col >= len(table[0]):
return 0
return table[row][col]
def print_table(table):
print('\n'.join([
','.join([str(col) for col in table[row]])
for row in range(len(table))]))
def init_table(rows=0, cols=0, default=0):
result = []
for row in range(rows):
r = []
for col in range(cols):
r.append(default)
result.append(r)
return result
def make_change(n):
coins = [1, 5, 10, 25]
table = init_table(rows=len(coins), cols=n)
for row in range(len(table)):
for col in range(len(table[row])):
curr_coin = coins[row]
curr_n = col + 1
# a
a = get(table, row - 1, col)
# b
b = get(table, row, curr_n - curr_coin - 1)
# c
c = 1 if curr_coin <= curr_n else 0
# commit
if curr_coin == curr_n:
table[row][col] = a + c
else:
table[row][col] = a + b * c
# debug
print_table(table)
print()
return table[-1][-1]
print(make_change(7))

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from collection import deque
def fill(point, canvas, color):
if x not in canvas:
return
elif y not in canvas[x]:
return
x, y = point
if canvas[y][x] == color:
return
canvas[y][x] = color
fill((x + 1, y), canvas, color)
fill((x - 1, y), canvas, color)
fill((x, y + 1), canvas, color)
fill((x, y - 1), canvas, color)
def fill_bfs(point, canvas, color):
x, y = point
if x not in canvas:
return None
if y not in canvas[x]:
return None
xs = deque()
xs.append((x, y))
while xs:
x, y = xs.popleft()
canvas[y][x] = color
for x2, y2 in [(x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1)]:
if x2 not in canvas:
continue
elif y2 not in canvas[x2]:
continue
if canvas[y2][x2] != color:
xs.append((x2, y2))
return None

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# BNF
# expression -> bool ( ( '|' | '&' | '^' ) bool )*
# bool -> '0' | '1'
def tokenize(xs):
result = []
for c in xs:
if c == '0':
result.append(0)
elif c == '1':
result.append(1)
elif c in "&|^":
result.append(c)
else:
raise Exception("Unexpected token, \"{}\"".format(c))
return result
class Parser(object):
def __init__(self, tokens):
self.tokens = tokens
self.i = 0
def prev(self):
return self.tokens[self.i - 1]
def curr(self):
return self.tokens[self.i]
def match(self, xs):
if self.exhausted():
return False
if (self.curr() in xs):
self.consume()
return True
return False
def consume(self):
result = self.curr()
self.i += 1
return result
def exhausted(self):
return self.i >= len(self.tokens)
def recursive_descent(tokens):
parser = Parser(tokens)
return parse_expression(parser)
def parse_expression(parser):
lhs = parse_bool(parser)
while parser.match(['|', '&', '^']):
op = parser.prev()
rhs = parse_expression(parser)
lhs = [op, lhs, rhs]
return lhs
def parse_bool(parser):
if parser.curr() == 0:
parser.consume()
return False
elif parser.curr() == 1:
parser.consume()
return True
else:
raise Exception("Unexpected token: {}".format(parser.curr()))
def f(expr, result):
tokens = tokenize(expr)
tree = recursive_descent(tokens)
return do_f(tree, result)
def do_f(tree, result):
if type(tree) == bool:
if tree == result:
return 1
else:
return 0
op, lhs, rhs = tree[0], tree[1], tree[2]
truth_tables = {
True: {
'|': [
(True, True),
(True, False),
(False, True),
],
'&': [
(True, True),
],
'^': [
(True, False),
(False, True),
],
},
False: {
'|': [
(False, False),
],
'&': [
(False, False),
(True, False),
(False, True),
],
'^': [
(True, True),
(False, False),
],
}
}
return sum([do_f(lhs, x) * do_f(rhs, y) for x, y in truth_tables[result][op]])
print(f("1^0|0|1", False))
print(f("1|0|1|1", False))

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def char_and_rest(i, xs):
return xs[i], xs[:i] + xs[i+1:]
# perms :: String -> [String]
def perms(xs):
if len(xs) == 1:
return [xs]
result = []
for c, rest in [char_and_rest(i, xs) for i in range(len(xs))]:
result += [c + perm for perm in perms(rest)]
return result
print(perms("cat"))

28
scratch/facebook/recursion-and-dynamic-programming/robot-grid-traversal.py Normal file
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import random
def factorial(n):
result = 1
for i in range(1, n + 1):
result *= i
return result
def travel(a, b):
if a == b:
return 1
ax, ay = a
bx, by = b
if ax > bx or ay > by:
return 0
return sum([travel((ax + 1, ay), b), travel((ax, ay + 1), b)])
def travel_compute(a, b):
bx, by = b
return int(factorial(bx + by) / (factorial(bx) * factorial(by)))
a = (0, 0)
b = (random.randint(1, 10), random.randint(1, 10))
print("Travelling to {}, {}".format(b[0], b[1]))
print(travel(a, b))
print(travel_compute(a, b))

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scratch/facebook/recursion-and-dynamic-programming/staircase.py Normal file
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# accidentally deleted my solution... TBI (again)

41
scratch/facebook/recursion-and-dynamic-programming/subsets.py Normal file
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# take-aways:
# - Use integers as lists of boolean values
# - Use 1 << n to compute 2^n where n = len(xs)
def set_from_int(xs, n):
result = []
for i in range(len(xs)):
if n & (1 << i) != 0:
result.append(xs[i])
return result
# subsets :: Set a -> List (Set a)
def subsets(xs):
n = len(xs)
return [set_from_int(xs, i) for i in range(1 << n)]
# 0 1 2
# 0 N Y Y
# 1 _ N Y
# 2 _ _ N
# For my interview, be able to compute *permutations* and *combinations*
# This differs from permutations because this is about finding combinations...
#
# bottom-up
# 0 => { }
# 1 => {3} {4} {3}
# 2 => {5,4} {5,3} {4,3}
xs = [
([], [[]]),
([5], [[], [5]]),
([5,4], [[],[5],[4],[5,4]]),
]
for x, expected in xs:
result = subsets(x)
print("subsets({}) => {} == {}".format(x, result, expected))
assert result == expected
print("Success!")

50
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def valid_parens(n):
if n == 0:
return []
if n == 1:
return ["()"]
result = set()
for x in valid_parens(n - 1):
result.add("({})".format(x))
result.add("(){}".format(x))
result.add("{}()".format(x))
return result
def valid_parens_efficient(n):
result = []
curr = [''] * n**2
do_valid_parens_efficient(result, curr, 0, n, n)
return result
def do_valid_parens_efficient(result, curr, i, lhs, rhs):
if lhs == 0 and rhs == 0:
result.append(''.join(curr))
else:
if lhs > 0:
curr[i] = '('
do_valid_parens_efficient(result, curr, i + 1, lhs - 1, rhs)
if rhs > lhs:
curr[i] = ')'
do_valid_parens_efficient(result, curr, i + 1, lhs, rhs - 1)
# Avoids recursion by using either a stack or a queue. I think this version is
# easier to understand.
def valid_parens_efficient_2(n):
result = []
xs = []
xs.append(('', n, n))
while xs:
curr, lhs, rhs = xs.pop()
print(curr)
if lhs == 0 and rhs == 0:
result.append(''.join(curr))
if lhs > 0:
xs.append((curr + '(', lhs - 1, rhs))
if rhs > lhs:
xs.append((curr + ')', lhs, rhs - 1))
return result
# print(valid_parens(4))
print(valid_parens_efficient(3))
print(valid_parens_efficient_2(3))

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scratch/facebook/recursive-string-permutations.py Normal file
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# permutations: no repeat characters
def char_and_rest(i, xs):
return xs[i], xs[0:i] + xs[i + 1:]
def permutations(xs):
if len(xs) == 1:
return [xs]
result = []
for c, rest in [char_and_rest(i, xs) for i in range(len(xs))]:
result += [c + perm for perm in permutations(rest)]
return result
expected = ["cat", "cta", "act", "atc", "tca", "tac"]
result = permutations("cat")
print(result, expected)
assert len(result) == len(expected)
assert result == expected
print("Success!")

25
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from linked_list import Node
def reverse(node):
prev, curr, next = None, node, node.next
while curr:
curr.next = prev
prev = curr
curr = next
next = curr.next if curr else None
return prev
one = Node(1)
two = Node(2)
three = Node(3)
one.next = two
two.next = three
print(one)
result = reverse(one)
print(result)
assert all([result == three,
three.next == two,
two.next == one])
print("Success!")

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# reverse :: [Char] -> ()
def reverse(xs):
i = 0
j = len(xs) - 1
while i < j:
xs[i], xs[j] = xs[j], xs[i]
i += 1
j -= 1
xs = [list("testing"), list("a"), list("to")]
for x in xs:
print(x)
reverse(x)
print(x)

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# reverse_word :: [Char] -> ()
def reverse_words(x):
pass
x = list("This is a test")
print(''.join(x))
reverse_words(x)
print(''.join(result))

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# This is a scratch pad for randomly selected questions
# def char_and_rest(i, xs):
# return xs[i], xs[:i] + xs[i+1:]
# def perms(xs):
# if len(xs) == 1:
# return [xs]
# result = []
# for i in range(len(xs)):
# c, rest = char_and_rest(i, xs)
# for perm in perms(rest):
# result.append(c + ''.join(perm))
# return result
# print(perms(list("woah")))
# def f(take_out, dine_in, served):
# j, k = 0, 0
# for i in range(len(served)):
# if j < len(take_out) and served[i] == take_out[j]:
# j += 1
# elif k < len(dine_in) and served[i] == dine_in[k]:
# k += 1
# else:
# return False
# if j < len(take_out) or k < len(dine_in):
# return False
# return True
# take_out = [17, 8, 24]
# dine_in = [12, 19, 2]
# served = [17, 8, 12, 19, 24, 2]
# print(f(take_out, dine_in, served))
# def match(a, b):
# if a == '{':
# return b == '}'
# if a == '[':
# return b == ']'
# if a == '(':
# return b == ')'
# return False
# def f(xs):
# s = []
# for c in xs:
# if c in {'{', '[', '('}:
# s.append(c)
# elif c in {'}', ']', ')'}:
# opener = s.pop()
# if not match(opener, c):
# return False
# return len(s) == 0
# assert f("{[]()}")
# assert f("{[(])}") == False
# assert f("{[}") == False
# print("Success!")
# def valid_bst(node):
# lhs = max_bst_value(node.left) if node.left else float('-inf')
# rhs = min_bst_value(node.right) if node.right else float('inf')
# return and([
# lhs <= node.value,
# rhs > node.value,
# valid_bst(node.left),
# valid_bst(node.right),
# ])
import random
import math
def shuffle(xs):
n = len(xs)
for i in range(n - 1):
j = random.randint(i + 1, n - 1)
xs[i], xs[j] = xs[j], xs[i]
return xs
def as_card(i):
if i not in range(1, 53):
raise Exception("Not a card")
# 1
suit = ['Hearts', 'Clubs', 'Diamonds', 'Spades'][math.floor((i - 1) / 13)]
n = ['Ace',2,3,4,5,6,7,8,9,10,'Jack','Queen','King'][(i - 1) % 13]
return '{} of {}'.format(n, suit)
xs = list(range(1, 53))
print(xs)
shuffle(xs)
for x in xs:
print(as_card(x))

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from collections import deque
from node import Node, tree
def find_largest(node):
while node.right:
node = node.right
return node.value
def find_second_largest(node):
# parent of the rightmost, when rightmost is leaf
# max(rightmost.left)
prev = None
while node.right:
prev = node
node = node.right
if node.left:
return find_largest(node.left)
else:
return prev.value
assert find_second_largest(tree) == 72
print("Success!")

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from random import randint
def get_random(i, j):
return randint(i, j)
def shuffle(xs):
for i in range(len(xs)):
j = get_random(i, len(xs) - 1)
xs[i], xs[j] = xs[j], xs[i]
xs = list(range(1, 53))
print(xs)
assert len(set(xs)) == 52
shuffle(xs)
assert len(set(xs)) == 52
print(xs)
print("Success!")

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class Stack(object):
def __init__(self):
self.items = []
def __repr__(self):
return self.items.__repr__()
def push(self, x):
self.items.append(x)
def pop(self):
if not self.items:
return None
return self.items.pop()
def peek(self):
if not self.items:
return None
return self.items[-1]
def from_list(xs):
result = Stack()
for x in xs:
result.push(x)
return result

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def max_profit(xs):
buy = xs[0]
profit = xs[1] - xs[0]
for price in xs[1:]:
profit = max(profit, price - buy)
buy = min(buy, price)
return profit
xs = [([10,7,5,8,11,9], 6),
([10,8,7,6,5], -1)]
for x, expected in xs:
result = max_profit(x)
print(x, result)
assert result == expected
print("Success!")

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scratch/facebook/todo.org Normal file
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* Array and string manipulation
** DONE Merging Meeting Times
** DONE Reverse String in Place
** TODO Reverse Words
** DONE Merge Sorted Arrays
** DONE Cafe Order Checker
* Hashing and hash tables
** DONE Inflight Entertainment
** DONE Permutation Palindrome
** DONE Word Cloud Data
** DONE Top Scores
* Greedy Algorithms
** DONE Apple Stocks
** DONE Highest Product of 3
** DONE Product of All Other Numbers
** DONE Cafe Order Checker
** DONE In-Place Shuffle
* Sorting, searching, and logarithms
** DONE Find Rotation Point
** TODO Find Repeat, Space Edition
** DONE Top Scores
** DONE Merging Meeting Times
* Trees and graphs
** DONE Balanced Binary Tree
** DONE Binary Search Tree Checker
** DONE 2nd Largest Item in a Binary Search Tree
** DONE Graph Coloring
** DONE MeshMessage
** DONE Find Repeat, Space Edition BEAST MODE
* Dynamic programming and recursion
** DONE Recursive String Permutations
** DONE Compute nth Fibonacci Number
** DONE Making Change
** DONE The Cake Thief
** DONE Balanced Binary Tree
** DONE Binary Search Tree Checker
** DONE 2nd Largest Item in a Binary Search Tree
* Queues and stacks
** DONE Largest Stack
** DONE Implement A Queue With Two Stacks
** DONE Parenthesis Matching
** DONE Bracket Validator
* Linked lists
** DONE Delete Node
** DONE Does This Linked List Have A Cycle?
** DONE Reverse A Linked List
** DONE Kth to Last Node in a Singly-Linked List
** DONE Find Repeat, Space Edition BEAST MODE
* General programming
** TODO Rectangular Love
** TODO Temperature Tracker
* Bit manipulation
** DONE The Stolen Breakfast Drone
* Combinatorics, probability, and other math
** TODO Which Appears Twice
** TODO Find in Ordered Set
** TODO In-Place Shuffle
** TODO Simulate 5-sided die
** TODO Simulate 7-sided die
** TODO Two Egg Problem

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import random
from collections import deque
def sorted(xs):
result = [0] * 100
for x in xs:
result[x - 1] += 1
answer = deque()
for i in range(len(result)):
x = result[i]
for _ in range(x):
answer.appendleft(i + 1)
return list(answer)
scores = [random.choice(range(70, 100)) for _ in range(20)]
print(scores)
result = sorted(scores)
print(result)

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import random
from heapq import heappush, heappop
from collections import deque
# A topological sort returns the vertices of a graph sorted in an ascending
# order by the number of incoming edges each vertex has.
#
# A few algorithms for solving this exist, and at the time of this writing, I
# know none. I'm going to focus on two:
# 1. Kahn's
# 2. DFS (TODO)
def count_in_edges(graph):
result = {k: 0 for k in graph.keys()}
for xs in graph.values():
for x in xs:
result[x] += 1
return result
# Kahn's algorithm for returning a topological sorting of the vertices in
# `graph`.
def kahns_sort(graph):
result = []
q = deque()
in_edges = count_in_edges(graph)
for x in [k for k, v in in_edges.items() if v == 0]:
q.append(x)
while q:
x = q.popleft()
result.append(x)
for c in graph[x]:
in_edges[c] -= 1
if in_edges[c] == 0:
q.append(c)
return result
graphs = [
{
0: [],
1: [],
2: [3],
3: [1],
4: [0, 1],
5: [0, 2],
},
{
'A': ['C', 'D'],
'B': ['D', 'E'],
'C': [],
'D': ['F', 'G'],
'E': [],
'F': [],
'G': ['I'],
'H': ['I'],
'I': [],
}
]
print("--- Kahn's --- ")
for graph in graphs:
print(kahns_sort(graph))

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from math import floor
# Lists
def cycle_backwards(times, xs):
n = len(xs)
for i in range(n * times):
print(xs[n - 1 - i % n])
def cycle_forwards(times, xs):
n = len(xs)
for i in range(n * times):
print(xs[i % n])
def backwards(xs):
n = len(xs)
for i in range(n):
print(xs[n - 1 - i])
def forwards(xs):
for i in range(len(xs)):
print(xs[i])
xs = [2, 5, 6, 9, 12]
print("Forwards")
forwards(xs)
print("Backwards")
backwards(xs)
print("Cycle forwards")
cycle_forwards(2, xs)
print("Cycle backwards")
cycle_backwards(2, xs)
# Tables
def tblr(table):
for row in range(len(table)):
for col in range(len(table[row])):
print(table[row][col])
def tbrl(table):
for row in range(len(table)):
n = len(table[row])
for col in range(n):
print(table[row][n - 1 - col])
def btlr(table):
n = len(table)
for row in range(n):
for col in range(len(table[row])):
print(table[n - 1 - row][col])
def btrl(table):
rows = len(table)
for row in range(rows):
cols = len(table[row])
for col in range(cols):
print(table[rows - 1 - row][cols - 1 - col])
def special(table):
rows = len(table)
cols = len(table[0])
for col in range(cols):
for row in range(rows):
print(table[row][col])
def double_bonus(table):
rows = len(table)
cols = len(table[0])
for i in range(rows):
row = i
for col in range(cols):
print(table[row][col % cols])
row = (row + 1) % rows
def free(table):
rows = len(table)
cols = len(table[0])
d = rows * cols
for i in range(d):
row = floor((i % d) / cols)
col = i % cols
print(table[row][col])
table = [[1,2,3,4],
[5,6,7,8]]
print("Top->Bottom, Left->Right")
tblr(table)
print("Top->Bottom, Right->Left")
tbrl(table)
print("Bottom->Top, Left->Right")
btlr(table)
print("Bottom->Top, Right->Left")
btrl(table)
print("Special")
special(table)
print("2x Bonus")
double_bonus(table)
print("Free")
free(table)

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def init_table(rows=0, cols=0, default=None):
table = []
for row in range(rows):
x = []
for col in range(cols):
x.append(default)
table.append(x)
return table
def get(table, row, col, default=0):
if row < 0 or col < 0:
return default
return table[row][col]
def print_table(table):
result = []
for row in range(len(table)):
result.append(' '.join([str(cell) for cell in table[row]]))
print('\n'.join(result))

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def normalize(x):
noise = ".,;-"
for y in noise:
if x.endswith(y):
return normalize(x[0:-1])
if x.startswith(y):
return normalize(x[1:])
return x.lower()
def word_cloud(xs):
result = dict()
for x in xs.split(' '):
k = normalize(x)
if k in result:
result[k] += 1
else:
result[k] = 1
return result
result = word_cloud("This is just the beginning. The UK will lockdown again.")
assert result.get('this') == 1
assert result.get('is') == 1
assert result.get('just') == 1
assert result.get('the') == 2
assert result.get('beginning') == 1
assert result.get('uk') == 1
assert result.get('will') == 1
assert result.get('lockdown') == 1
assert result.get('again') == 1
print("Success!")