# 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 :

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;
}
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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