2014蓝桥杯B组c/c++预赛 第九题地宫取宝 (四维线性dp)

#include <cstdio>
#include <cstring>
#define MOD 1000000007
int dp[55][55][15][15];
int val[55][55];

int main()
{
    int n, m, k;
    scanf("%d %d %d", &n, &m, &k);
    for(int i = 1; i <= n; i++)
    {
        for(int j = 1; j <= m; j++)
        {
            scanf("%d", &val[i][j]);
            val[i][j] ++;
        }
    }
    memset(dp, 0, sizeof(dp));
    dp[1][1][val[1][1]][1] = 1;
    dp[1][1][0][0] = 1;
    for(int i = 1; i <= n; i++)
    {
        for(int j = 1; j <= m; j++)
        {
            if(i == 1 && j == 1)
                continue;
            for(int num = 0; num <= k; num++)
            {
                for(int ma = 0; ma <= 13; ma++)
                {
                    if(ma < val[i][j])
                    {
                        dp[i][j][val[i][j]][num + 1] = (dp[i][j][val[i][j]][num + 1] + dp[i - 1][j][ma][num]) % MOD;
                        dp[i][j][val[i][j]][num + 1] = (dp[i][j][val[i][j]][num + 1] + dp[i][j - 1][ma][num]) % MOD;    
                    }
                    dp[i][j][ma][num] = (dp[i][j][ma][num] + dp[i - 1][j][ma][num]) % MOD;
                    dp[i][j][ma][num] = (dp[i][j][ma][num] + dp[i][j - 1][ma][num]) % MOD;
                }
            }
        }
    }
    int ans = 0;
    for(int i = 0; i < 13; i++)
        ans = (ans + dp[n][m][i][k]) % MOD;
    printf("%d\n", ans);
}