Add solution for challenge #46

Author: Mauricio Klein

README.md

@@ -45,3 +45,4 @@
 - [x] [Challenge 43: Contiguous Subarray with Maximum Sum](challenge-43/)
 - [x] [Challenge 44: Find the k-th Largest Element in a List](challenge-44/)
 - [x] [Challenge 45: Occurrences of a number in a sorted array](challenge-45/)
+- [x] [Challenge 46: Sudoku solver](challenge-46/)

challenge-46/Makefile

@@ -0,0 +1,4 @@
+test:
+	python test_*.py
+
+.PHONY: test

challenge-46/README.md

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+# Sudoku solver
+
+## Description
+
+Given a partially filled 9×9 2D array `grid[9][9]`, the goal is to assign digits (from 1 to 9) to the empty cells (denoted by the number `zero`) so that every row, column, and subgrid of size 3×3 contains exactly one instance of the digits from 1 to 9.
+
+## Example
+```
+Input:
+  [
+    [3, 0, 6, 5, 0, 8, 4, 9, 0],
+    [5, 2, 0, 0, 0, 0, 0, 0, 0],
+    [0, 8, 7, 0, 0, 0, 0, 3, 1],
+    [0, 0, 3, 0, 1, 0, 0, 8, 0],
+    [9, 0, 0, 8, 6, 3, 0, 0, 5],
+    [0, 5, 0, 0, 9, 0, 6, 0, 0],
+    [1, 3, 0, 0, 0, 0, 2, 5, 0],
+    [0, 0, 0, 0, 0, 0, 0, 7, 4],
+    [0, 0, 5, 2, 0, 6, 3, 0, 0]
+  ]
+
+Output: a valid Sudoku board
+```

challenge-46/__init__.py

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+def sudoku(board, rows, columns):
+  return helper(board, 0, 0, columns, rows)
+
+def helper(board, r, c, rows, columns):
+  def inbound(r, c):
+    return (0 <= r < rows) and (0 <= c < columns)
+
+  # Out of bounds:
+  # We filled all blank cells and, thus, a valid solution
+  if not inbound(r, c):
+    return True
+
+  nr, nc = next_pos(r, c, rows, columns)
+
+  if board[r][c] != 0:
+    # This is a pre-filled cell, so skip
+    # for the next one
+    return helper(board, nr, nc, rows, columns)
+
+  for i in range(1, 10):
+    if valid_placement(board, r, c, rows, columns, i):
+      # "i" can be place in the cell without breaking
+      # the sudoku rules. So, it's a canditate for solution.
+      # Mark the cell with the value and try to solve
+      # recursively for the remaining blank cells
+      board[r][c] = i
+
+      if helper(board, nr, nc, rows, columns):
+        return True
+      else:
+        # No solution found for the search branch:
+        # reset the cell for the future attemps
+        board[r][c] = 0
+
+  return False
+
+def next_pos(r, c, rows, columns):
+  if c + 1 == columns:
+    return (r + 1, 0)
+  else:
+    return (r, c + 1)
+
+def valid_placement(board, r, c, rows, columns, v):
+  # Check conflict with row
+  if v in board[r]:
+    return False
+
+  # Check conflict with column
+  for i in range(0, rows):
+    if v == board[i][c]:
+      return False
+
+  # Check conflict with the subgrid
+  row_offset = r - r % 3
+  col_offset = c - c % 3
+
+  for i in range(3):
+    for j in range(3):
+      if board[i + row_offset][j + col_offset] == v:
+        return False
+
+  return True

challenge-46/solver.py

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+import unittest, pprint
+from solver import sudoku
+
+class TestSolver(unittest.TestCase):
+  def test_sudoku(self):
+    pp = pprint.PrettyPrinter(indent=4)
+
+    board = [
+      [3, 0, 6, 5, 0, 8, 4, 9, 0],
+      [5, 2, 0, 0, 0, 0, 0, 0, 0],
+      [0, 8, 7, 0, 0, 0, 0, 3, 1],
+      [0, 0, 3, 0, 1, 0, 0, 8, 0],
+      [9, 0, 0, 8, 6, 3, 0, 0, 5],
+      [0, 5, 0, 0, 9, 0, 6, 0, 0],
+      [1, 3, 0, 0, 0, 0, 2, 5, 0],
+      [0, 0, 0, 0, 0, 0, 0, 7, 4],
+      [0, 0, 5, 2, 0, 6, 3, 0, 0]
+    ]
+
+    solved = sudoku(board, 9, 9)
+
+    pp.pprint(board)
+    self.assertTrue(solved)
+
+if __name__ == "__main__":
+    unittest.main()