Bzoj 1211: Count of [HNOI2004] trees (combinatorial mathematics)

Know Prufer sequence can write ... is to find the permutation of a re-set ... First the strange situation, then the answer is (N-2)!/π (d[i]-1)!

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#include <cstdio>#include <algorithm>#include <cstring>using namespace std;typedef long Long ll;const int MAXN = n; int D[MAXN], N, m;int P[MAXN], PN, CNT[MAXN];bool F[MAXN];void Init () {pn = 0;memset (f, 0, sizeof f);for (int i = 2; i < MAXN; i++) {if (! F[i])p[pn++] = i;For (int j = 0; J < pn && I * p[j] < MAXN; J + +) {f[i * P[j]] = true;if (i% p[j] = = 0) break;}}}void Calculate (int t, bool Typ) {if (T < 2) return;for (int i = 2; I <= t; i++)for (int j = 0, v = i; j < pn && V! = 1; j + +)for (; v% p[j] = = 0; v/= p[j], Typ cnt[j]++: cnt[j]--);} ll Power (ll x, int t) {LL ret = 1;for (; t; t >>= 1, x *= x)if (T & 1) RET *= x;return ret;}int main () {Init ();m = 0;scanf ("%d", &n);for (int i = 0; i < N; i++) {scanf ("%d", D + i);m + = d[i]-1;}if (m! = N-2) {puts ("0"); return 0;}if (N = = 1 &&!d[0]) {puts ("1"); return 0;}for (int i = 0; i < N; i++) if (!d[i]) {puts ("0"); return 0;}memset (CNT, 0, sizeof CNT);Calculate (M, 1);for (int i = 0; i < N; i++)Calculate (D[i]-1, 0);ll ans = 1;for (int i = 0; i < pn; i++)if (Cnt[i]) ans *= Power (LL (P[i]), cnt[i]);printf ("%lld\n", ans);return 0;}

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1211: Count of [HNOI2004] tree time limit: ten Sec Memory Limit: 162 MB
Submit: 1752 Solved: 578
[Submit] [Status] [Discuss] Description

A tree with n nodes, with its nodes of V1, v2, ..., vn, known as the degree of the I node VI as DI, asking how many different trees meet such conditions. Given N,D1, D2, ..., DN, programming needs to output the number of trees that meet the D (vi) =di.

Input

The first line is a positive integer n, which indicates that the tree has n nodes. The second line has n numbers, and the number of I represents Di, which is the degree of the first node of the tree. Where 1<=n<=150, the input data ensures that the tree that satisfies the criteria does not exceed 10^17.

Output

How many trees are available for the output to meet the criteria.

Sample Input4
2 1 2 1
Sample Output2HINT

Source

Combinatorial mathematics

Bzoj 1211: Count of [HNOI2004] trees (combinatorial mathematics)