sudoku.cpp

#include <bits/stdc++.h>
using namespace std;

#define UNASSIGNED 0
#define N 9


void printGrid(int grid[N][N]){
	for(int row = 0; row < N; row++) {
		for (int col = 0; col < N; col++)
			cout<<grid[row][col]<<" ";
		cout << endl;
	}
}



// Searches the grid to find an entry that is still unassigned.
// If found, the reference parameters row, col will be set the location that is unassigned, and true is returned
// If no unassigned entries remain, false is returned
bool FindUnassignedLocation(int grid[N][N], int &row, int &col){
	for(row = 0; row < N; row++)
		for(col = 0; col < N; col++)
			if (grid[row][col] == UNASSIGNED)
				return true;
	return false;
}



bool UsedInRow(int grid[N][N], int row, int num){
	for(int col = 0; col < N; col++)
		if (grid[row][col] == num)
			return true;
	return false;
}


bool UsedInCol(int grid[N][N], int col, int num){
	for(int row = 0; row < N; row++)
		if (grid[row][col] == num)
			return true;
	return false;
}

bool UsedInBox(int grid[N][N], int boxStartRow, int boxStartCol, int num){
	for(int row = 0; row < 3; row++)
		for(int col = 0; col < 3; col++)
			if (grid[row + boxStartRow][col + boxStartCol] == num)
				return true;
	return false;
}


bool isSafe(int grid[N][N], int row, int col, int num){
	// Check if 'num' is not already placed in current row, current column and current 3x3 box
	return !UsedInRow(grid, row, num)
		&& !UsedInCol(grid, col, num)
		&& !UsedInBox(grid, row - row%3, col - col%3, num)
		&& grid[row][col] == UNASSIGNED;
}

bool SolveSudoku(int grid[N][N]){
	int row, col;

	// If there is no unassigned location, we are done
	if (FindUnassignedLocation(grid, row, col) == false)
		return true;

	// Consider digits 1 to 9
	for (int num = 1; num <= 9; num++) {
		if(isSafe(grid, row, col, num)) {
			grid[row][col] = num;

			if (SolveSudoku(grid))
				return true;

			grid[row][col] = UNASSIGNED; // failure, unmake & try again
		}
	}

	return false;  // this triggers backtracking
}


int main(){

	// 0 means unassigned cells
	int grid[N][N] = { { 3, 0, 6, 5, 0, 8, 4, 0, 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 } };

	if(SolveSudoku(grid) == true)
        printGrid(grid);
	else cout<<"No solution exists";

	return 0;
}