bzoj2302: [HAOI2011]Problem c

bzoj2302: [HAOI2011]Problem c

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OI题有三种从一般到特殊，从暴力到优化，换角度思考 −WerkeyTom_FTD
这道题让我认识到了从题目到充要条件的转换这种解题思路
这道题我们可以看出他的充要条件为
∀j,∑ni=1[ai>=j]<=n−j+1
现在我们要求的便为满足这个条件的序列的合法方案数，这个东西就很好dp了
f[i][j]表示>=i的a有j个的合法方案数,r[i]表示被钦定为a(a=i)的人有多少个
m[i]表示被钦定为a(a>i)的人有多少个
f[i][j]=∑j−r[i]k=0f[i+1][k]∗Cj−k−r[i]n−k−m[i]+l[j<=n−i+1]

#include<cstdio>
#include<algorithm>
#include<cstring>

const int N = 310;

int C[N][N], p[N], n, m, k, a1, a2, P, f[N][N], r[N];

void Solve () {
    memset (f, 0, sizeof f);
    scanf ("%d%d%d", &n, &m, &P);
    memset (C, 0, sizeof C);
    C[0][0] = 1;
    for (int i = 1; i <= 300; ++i) {
        C[i][0] = 1;
        for (int j = 1; j <= i; ++j) C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % P;
    }
    for (int i = 1; i <= n; ++i) p[i] = -1, r[i] = 0;
    for (int i = 1; i <= m; ++i) scanf ("%d%d", &a1, &a2), ++r[a2];
    for (int i = n, l = 0; i; --i) {
         l += r[i];
        if (n - i + 1 < l) {
            puts ("NO");
            return ;
        }
    }
    f[n + 1][0] = 1;
    for (int i = n, l = 0; i; --i) {
        for (int j = l; j <= n - i + 1; ++j)
            for (int k = 0; k <= j - r[i]; ++k)
                f[i][j] = (f[i][j] + 1ll * f[i + 1][k] * C[n - k + l - m][j - k - r[i]] % P) % P;
        l += r[i];
    }
    printf ("YES %d\n", f[1][n]);
}


int main () {
    int T; scanf ("%d", &T);
    while (T--) Solve ();
    return 0;
}