From 7672049e1cc25b2848245c565329240c95d2e96d Mon Sep 17 00:00:00 2001
From: William Carroll <wpcarro@gmail.com>
Date: Fri, 13 Nov 2020 16:56:02 +0000
Subject: [PATCH] Solve N queens

After a five year hiatus, I decided to attempt to solve the famous N queens
problem again. This time, instead of modeling the chess board using a
`[[Bool]]`, I'm using `[Integer]` where the `Integer` indicates which column has
a queen. This is a bit lighter in RAM.
---
 scratch/facebook/n-queens.py | 46 ++++++++++++++++++++++++++++++++++++
 1 file changed, 46 insertions(+)
 create mode 100644 scratch/facebook/n-queens.py

diff --git a/scratch/facebook/n-queens.py b/scratch/facebook/n-queens.py
new file mode 100644
index 000000000..fc9326886
--- /dev/null
+++ b/scratch/facebook/n-queens.py
@@ -0,0 +1,46 @@
+def print_board(board):
+    result = []
+    for row in range(8):
+        r = []
+        for col in range(8):
+            r.append("X" if col == board[row] else "-")
+        result.append(" ".join(r))
+    print("\n".join(result))
+    print()
+
+def can_place(board, row, col):
+    column_occupied = not any([board[i] == col for i in range(row)])
+
+    diagonals_clear = True
+    for r in range(row):
+        w = abs(col - board[r])
+        h = abs(r - row)
+        if w == h:
+            diagonals_clear = False
+            break
+
+    return all([column_occupied, diagonals_clear])
+
+def init_board():
+    board = []
+    for row in range(8):
+        board.append(None)
+    return board
+
+def copy_board(board):
+    return board[:]
+
+def n_queens():
+    do_n_queens(init_board(), 0, 0)
+
+def do_n_queens(board, row, col):
+    if row == 8:
+        print_board(board)
+        return
+    for i in range(col, 8):
+        if can_place(board, row, i):
+            copy = copy_board(board)
+            copy[row] = i
+            do_n_queens(copy, row + 1, 0)
+
+n_queens()