Sudoku Solver - Amazon Top Interview Questions


Problem Statement :


Sudoku is a puzzle where you're given a partially-filled 9 by 9 grid with digits. The objective is to fill the grid with the constraint that every row, column, and box (3 by 3 subgrid) must contain all of the digits from 1 to 9.

Implement an efficient sudoku solver that takes in an incomplete board and solves it. In the given board, the incomplete spaces will be 0.

Constraints

n = 9 where n is the number of rows and columns in matrix

Example 1

Input

matrix = [
    [0, 2, 0, 5, 0, 1, 0, 9, 0],
    [8, 0, 0, 2, 0, 3, 0, 0, 6],
    [0, 3, 0, 0, 6, 0, 0, 7, 0],
    [0, 0, 1, 0, 0, 0, 6, 0, 0],
    [5, 4, 0, 0, 0, 0, 0, 1, 9],
    [0, 0, 2, 0, 0, 0, 7, 0, 0],
    [0, 9, 0, 0, 3, 0, 0, 8, 0],
    [2, 0, 0, 8, 0, 4, 0, 0, 7],
    [0, 1, 0, 9, 0, 7, 0, 6, 0]
]

Output

[
    [4, 2, 6, 5, 7, 1, 3, 9, 8],
    [8, 5, 7, 2, 9, 3, 1, 4, 6],
    [1, 3, 9, 4, 6, 8, 2, 7, 5],
    [9, 7, 1, 3, 8, 5, 6, 2, 4],
    [5, 4, 3, 7, 2, 6, 8, 1, 9],
    [6, 8, 2, 1, 4, 9, 7, 5, 3],
    [7, 9, 4, 6, 3, 2, 5, 8, 1],
    [2, 6, 5, 8, 1, 4, 9, 3, 7],
    [3, 1, 8, 9, 5, 7, 4, 6, 2]
]


Solution :



title-img 




                        Solution in C++ :

bool isValid(vector<vector<int>>& matrix, int x, int y, int val) {
    for (int j = 0; j < 9; j++) {
        if (matrix[x][j] == val) return false;
    }

    for (int i = 0; i < 9; i++) {
        if (matrix[i][y] == val) return false;
    }

    int smi = x / 3 * 3;
    int smj = y / 3 * 3;

    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            if (matrix[smi + i][smj + j] == val) return false;
        }
    }

    return true;
}

bool solveSudoku(vector<vector<int>>& matrix, int i, int j) {
    if (i == 9) {
        return true;
    }

    int ni = 0, nj = 0;
    if (j == 8) {
        ni = i + 1;
        nj = 0;
    } else {
        ni = i;
        nj = j + 1;
    }

    if (matrix[i][j] != 0) {
        if (solveSudoku(matrix, ni, nj)) return true;
    } else {
        for (int po = 1; po <= 9; po++) {
            if (isValid(matrix, i, j, po)) {
                matrix[i][j] = po;
                if (solveSudoku(matrix, ni, nj)) return true;
                matrix[i][j] = 0;
            }
        }
    }

    return false;
}

vector<vector<int>> solve(vector<vector<int>>& matrix) {
    solveSudoku(matrix, 0, 0);
    return matrix;
}
                    


                        Solution in Java :

import java.util.*;

class Solution {
    public int[][] solve(int[][] matrix) {
        if (matrix == null || matrix.length == 0) {
            return matrix;
        }
        helper(matrix);
        return matrix;
    }
    public boolean helper(int[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            for (int j = 0; j < matrix[0].length; j++) {
                if (matrix[i][j] == 0) {
                    for (int num = 1; num < 10; num++) {
                        if (isvalid(matrix, i, j, num)) {
                            matrix[i][j] = num;
                            if (helper(matrix))
                                return true;
                            else
                                matrix[i][j] = 0;
                        }
                    }
                    return false;
                }
            }
        }
        return true;
    }
    public boolean isvalid(int[][] matrix, int i, int j, int num) {
        // check column
        for (int row = 0; row < 9; row++) {
            if (matrix[row][j] == num)
                return false;
        }
        // check column
        for (int col = 0; col < 9; col++) {
            if (matrix[i][col] == num)
                return false;
        }
        // check borad
        for (int row = (i / 3) * 3; row < (i / 3) * 3 + 3; row++)
            for (int col = (j / 3) * 3; col < (j / 3) * 3 + 3; col++)
                if (matrix[row][col] == num)
                    return false;

        return true;
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, matrix):
        if not matrix or not matrix[0]:
            return

        self.solve_board(matrix)

        return matrix

    def solve_board(self, matrix) -> bool:
        for i in range(9):
            for j in range(9):
                if matrix[i][j] == 0:
                    # for every possible number value, try and see if it works
                    for k in range(1, 10):
                        if self.is_valid(matrix, i, j, k):
                            matrix[i][j] = k

                            if self.solve_board(matrix):
                                return True
                            else:
                                matrix[i][j] = 0

                    # we went through every number and nothing worked
                    return False

        return True

    def is_valid(self, matrix, row, col, value):
        box_row = (row // 3) * 3
        box_col = (col // 3) * 3

        # check row
        for i in range(9):
            if matrix[i][col] == value:
                return False

        # check col
        for i in range(9):
            if matrix[row][i] == value:
                return False

        # check box subgrid
        for i in range(9):
            resolved_row = box_row + (i % 3)
            resolved_col = box_col + (i // 3)

            if matrix[resolved_row][resolved_col] == value:
                return False

        return True


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