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;
}