Hdu 5378 Leader in the Tree land (dp+ inverse)

Title Link: Hdu 5378 Leader in Tree land

The problem can be understood as a tree of n nodes, with the probability of K ministers, and finally by n!. The probability that each node is ministers is 1/son (the number of nodes in the subtree that the node is the root node), and the probability of not being Ministers is (son-1)/son. So there is no need to consider the structure of the tree, direct root sentence node number transfer dp[i][j]

DP[I][J] = dp[i-1][j-1] * 1/son[u]

DP[I][J] = dp[i-1][j] * (son[u]-1])/son[u]

The part of the modulo can be used as an inverse element.

#include <cstdio> #include <cstring> #include <vector> #include <algorithm>using namespace std; typedef long LONG ll;const int mod = 1000000007;const int maxn = 1005;int fac[maxn];int N, K, Son[maxn];ll DP[MAXN][MAXN];  vector<int> g[maxn];void dfs (int u, int f) {Son[u] = 1;for (int i = 0; i < g[u].size (); i++) {int v = g[u][i];if (v = = f) Continue;dfs (V, u); son[u] + = Son[v];}}  void Init () {scanf ("%d%d", &n, &k); for (int i = 1; I <= N; i++) g[i].clear (); int u, v;for (int i = 1; i < n; i++) {scanf ("%d%d", &u, &v); G[u].push_back (v); G[v].push_back (u);} DFS (1, 0);} void Exgcd (ll A, ll B, ll& D, ll& x, Ll&y) {if (!b) d = A, x = 1, y = 0;else {exgcd (b, a%b, D, y, x); y-= x * (A/b);}} LL INV (ll a) {ll d, X, Y;EXGCD (A, mod, d, X, y); return d = = 1? (x + MoD)% mod:-1;} int solve () {memset (DP, 0, sizeof (DP));DP [0][0] = 1;for (int i = 1; I <= N; i++) {for (int j = 0; J <= K; j + +) {if (Dp[i-1][j] = = 0) continue;dp[i][j] = (Dp[i][j]+ dp[i-1][j] * (Son[i]-1)% mod * INV (son[i]))% mod;dp[i][j+1] = (dp[i][j+1] + dp[i-1][j] * INV (son[i]))% MoD;} return dp[n][k] * fac[n]% MoD;} int main () {fac[1] = 1;for (int i = 2; I <=; i++) Fac[i] = 1LL * i * fac[i-1]% mod;int cas;scanf ("%d", &cas); for (int kcas = 1; kcas <= cas; kcas++) {init ();p rintf ("Case #%d:%d\n", Kcas, Solve ());} return 0;}

Copyright NOTICE: This article for Bo Master original article, without Bo Master permission not reproduced.

Hdu 5378 Leader in the Tree land (dp+ inverse)