Sudoku Solver

0037-Sudoku-Solver.py

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+'''
+Write a program to solve a Sudoku puzzle by filling the empty cells.
+
+A sudoku solution must satisfy all of the following rules:
+
+    Each of the digits 1-9 must occur exactly once in each row.
+    Each of the digits 1-9 must occur exactly once in each column.
+    Each of the the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.
+
+Empty cells are indicated by the character '.'.
+
+
+A sudoku puzzle...
+
+
+...and its solution numbers marked in red.
+
+Note:
+
+    The given board contain only digits 1-9 and the character '.'.
+    You may assume that the given Sudoku puzzle will have a single unique solution.
+    The given board size is always 9x9.
+'''
+class Solution:
+    def solveSudoku(self, board: List[List[str]]) -> None:
+        """
+        Do not return anything, modify board in-place instead.
+        """
+        def is_empty_cell(row, col):
+            return board[row][col] == "."
+
+        def can_place_digit(row, col, digit):
+            return (digit not in rows[row] and
+                    digit not in cols[col] and
+                    digit not in subgrids[row // 3][col // 3])
+
+        def place_digit(row, col, digit):
+            board[row][col] = digit
+            cols[col].add(digit)
+            rows[row].add(digit)
+            subgrids[row // 3][col // 3].add(digit)
+
+        def remove_digit(row, col):
+            cols[col].remove(board[row][col])
+            rows[row].remove(board[row][col])
+            subgrids[row // 3][col // 3].remove(board[row][col])
+            board[row][col] = "."
+
+        def next_empty_row_col(row, col):
+            while row < len(board) and col < len(board[0]) and not is_empty_cell(row,col):
+                if col == len(board[0]) - 1:
+                    row,col = row+1,0
+                else:
+                    row,col = row,col+1
+            return row,col
+
+        def solve(row, col):
+            if row >= len(board):
+                return True
+
+            for digit in [str(num) for num in range(1,10)]:
+                if can_place_digit(row,col,digit):
+                    place_digit(row,col,digit)
+                    next_row,next_col = next_empty_row_col(row,col)
+                    if solve(next_row, next_col):
+                        return True
+                    remove_digit(row,col) #if solution not found, backtrack
+            return False
+
+
+        #Initialize 3 sets with the existing numbers on the board
+        cols = [set() for _ in range(9)]
+        rows = [set() for _ in range(9)]
+        subgrids = [[set() for _ in range(3)] for _ in range(3)]
+
+        for i in range(len(board)):
+            for j in range(len(board)):
+                if not is_empty_cell(i, j):
+                    cols[j].add(board[i][j])
+                    rows[i].add(board[i][j])
+                    subgrids[i // 3][j // 3].add(board[i][j])
+
+        #find the 1st empty cell and start there!
+        start_row, start_col = next_empty_row_col(0,0)       
+        solve(start_row, start_col)