牛客小白月赛13 E（图、矩阵幂）

AC通道

如果建立第一天某点到某点有几条路的矩阵，做k次矩阵乘就是第k天某点到某点有几条路。统计即可。

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

typedef long long ll;
const int maxn = 101, mod = 1e9 + 7;
int N, M, K, S, ans;

struct Matrix {
    int v[maxn][maxn], n;

    Matrix(int n) { memset(v, 0, sizeof v); this->n = n; }

    Matrix operator * (const Matrix &A) const {
        Matrix ret(n);
        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++)
                for (int k = 0; k < n; k++)
                    ret.v[i][j] = ((ll)ret.v[i][j] + (ll)v[i][k] * A.v[k][j] % mod) % mod;
        return ret;
    }

    Matrix operator ^ (int b) const {
        Matrix ret(n);
        Matrix A = *this;
        for (int i = 0; i < n; i++)
            ret.v[i][i] = 1;
        for (; b; b >>= 1) {
            if (b & 1)    ret = ret * A;
            A = A * A;
        }
        return ret;
    }
};

int main() {
    scanf("%d %d %d %d", &N, &M, &K, &S);
    Matrix A(N);
    for (int i = 0; i < M; i++) {
        int u, v;
        scanf("%d %d", &u, &v);
        A.v[--u][--v]++;
    }
    A = A ^ K;
    S--;
    for (int i = 0; i < N; i++) {
        if (i != S) {
            ans = ((ll)ans + A.v[S][i]) % mod;
        }
    }
    printf("%d\n", ans);
    return 0;
}