TheAlgorithms-C/misc/sudoku_solver.c

//recursion problem : Sudoku Solver
/*You are given an incomplete N*N Sudoku and asked to solve it using the following recursive algorithm:
(1) Scan the Sudoku from left to right row-wise to search for an empty cell.
(2) If there are no empty cells, print the Sudoku. Go to step 5.
(3) In the empty cell, try putting numbers 1 to N while ensuring that no two numbers in a single row, column, or box are same. Go back to step 1.
(4) Declare that the Sudoku is Invalid.
(5) Exit.*/

#include <stdio.h>

#define M 144
int N, R, C;

int OKrow(int a[M], int x, int y, int v)
{
	int j;
	for (j = 0; j < N; j++)
		if (a[x * N + j] == v)
			return 0;
	return 1;
}
int OKcol(int a[M], int x, int y, int v)
{
	int i;
	for (i = 0; i < N; i++)
		if (a[i * N + y] == v)
			return 0;
	return 1;
}
int OKbox(int a[M], int x, int y, int v)
{
	int bi = x / R, bj = y / C, i, j;
	for (i = 0; i < R; i++)
		for (j = 0; j < C; j++)
			if (a[(i + bi * R) * N + (j + bj * C)] == v)
				return 0;
	return 1;
}
int OK(int a[M], int x, int y, int v)
{
	return OKrow(a, x, y, v) && OKcol(a, x, y, v) && OKbox(a, x, y, v);
}

void print(int a[M])
{
	int i, j;
	for (i = 0; i < N; i++)
		for (j = 0; j < N; j++)
			printf("%d%c", a[i * N + j], (j == N - 1 ? '\n' : ' '));
}

int solve(int a[M])
{
	int i, j, v, rem = 0;
	for (i = 0; i < N; i++)
	{
		for (j = 0; j < N; j++)
		{
			if (a[i * N + j] == 0)
			{
				rem = 1;
				for (v = 1; v <= N; v++)
				{
					if (OK(a, i, j, v))
					{
						a[i * N + j] = v;
						if (solve(a))
							return 1;
						a[i * N + j] = 0;
					}
				}
			}
		}
	}
	if (rem == 0)
		return 1;
	return 0;
}

int main()
{
	scanf("%d%d%d", &N, &R, &C);
	int a[M], i, j;
	for (i = 0; i < N; i++)
		for (j = 0; j < N; j++)
			scanf("%d", &a[i * N + j]);

	if (solve(a))
		print(a);
	else
		printf("Invalid\n");
	return 0;
}