Unable to use MODULO operation correctly in C++ for SAFECRAC SPOJ?

Question

I'm trying to solve problem http://www.spoj.com/problems/SAFECRAC.

I figured that it can easily be solved using dynamic programming but since the final answer is very large we have to output the answer MODULO 1000000007. It seems that I am unable to use the MODULO operation properly since I get correct output for length = 3 but for length = 25 output differs from sample.

Here is my code:

#include <iostream>

using namespace std;

#define MOD 1000000007
typedef long long int ll;

ll dp[100001][10];

int t, n;       

void precompute()
{
    for (int j = 0; j < 10; j++)
        dp[1][j] = 1;

    for (int i = 2; i <= 100000; i++) {
        for (int j = 0; j < 10; j++) {
            if (j == 0) dp[i][j] = dp[i-1][7] % MOD;
            if (j == 1) dp[i][j] = ( dp[i-1][2] + dp[i-1][4] ) % MOD;
            if (j == 2) dp[i][j] = ( dp[i-1][1] + ( dp[i-1][3] + dp[i-1][5] ) % MOD ) % MOD;
            if (j == 3) dp[i][j] = ( dp[i-1][2] + dp[i-1][6] ) % MOD;
            if (j == 4) dp[i][j] = ( dp[i-1][1] + ( dp[i-1][5] + dp[i-1][7] ) % MOD ) % MOD;
            if (j == 5) dp[i][j] = ( ( dp[i-1][2] + dp[i-1][4] ) % MOD + ( dp[i-1][6] + dp[i-1][8] ) % MOD ) % MOD;
            if (j == 6) dp[i][j] = ( dp[i-1][3] + ( dp[i-1][5] + dp[i-1][9] ) % MOD ) % MOD;
            if (j == 7) dp[i][j] = ( dp[i-1][4] + ( dp[i-1][8] + dp[i-1][0] ) % MOD ) % MOD;
            if (j == 8) dp[i][j] = ( dp[i-1][5] + ( dp[i-1][7] + dp[i-1][9] ) % MOD ) % MOD;
            if (j == 9) dp[i][j] = ( dp[i-1][6] + dp[i-1][8] ) % MOD;
        }
    }
}

int main()
{
    precompute();

    cin >> t;

    while (t--) {
        cin >> n;

        ll sum = 0;

        for (int i = 0; i < 10; i++) {
            sum += dp[n][i];
        }

        cout << sum << endl;
    }
}

Answer 1

Check your for loop in the main(). dp[n][i] is always less than MOD, but this is not guaranteed for sum. So, try changing sum += dp[n][i]; to sum = (sum + dp[n][i]) % MOD;.