CodeForces 161D Distance in Tree 树形DP
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现在做题都是翻status看到有人A了D题才做。。
给出一棵树,求距离为k的点对有多少。
令f[i][j]表示i的子树中距离i为j的点有多少个。
显然有f[i][j+1]=sum{f[son[i]][j]}
那么i子树中的符合题意的点对数就是sum{f[son[i]][j-1]*(f[i][k-j]-f[son[i]][k-j-1])}
即son[i]中距离i为j的点数*不在son[i]中距离为k-j的点数。
注意到5W*5W会爆int,要开long long。
#include <cstdio>typedef long long ll;const int N = 50001, M = N * 2;int head[N] = {0}, next[M], to[M], cnt = 0, n, k;void add(int u, int v) { next[++cnt] = head[u]; head[u] = cnt; to[cnt] = v; }ll ans, f[N][502] = {0};void dfs(int u, int fa) { f[u][0] = 1; int i, j; for(i = head[u]; i; i = next[i]) if(to[i] != fa) { dfs(to[i], u); for (j = 0; j <= k; j++) f[u][j + 1] += f[to[i]][j]; } ans += f[u][k]; ll tmp = 0; for(i = head[u]; i; i = next[i]) if(to[i] != fa) for (j = 1; j < k; j++) tmp += f[to[i]][j - 1] * (f[u][k - j] - f[to[i]][k - j - 1]); ans += tmp / 2;}int main() { int x, y, i; scanf("%d%d", &n, &k); for (i = 1; i < n; i ++) { scanf("%d%d", &x, &y); add(x, y); add(y, x); } dfs(1, 1); printf("%I64d", ans); return 0;}
A tree is a connected graph that doesn't contain any cycles.
The distance between two vertices of a tree is the length (in edges) of the shortest path between these vertices.
You are given a tree with n vertices and a positive number k. Find the number of distinct pairs of the vertices which have a distance of exactly k between them. Note that pairs (v, u) and (u, v) are considered to be the same pair.
The first line contains two integers n and k (1 ≤ n ≤ 50000, 1 ≤ k ≤ 500) — the number of vertices and the required distance between the vertices.
Next n - 1 lines describe the edges as "ai bi" (without the quotes) (1 ≤ ai, bi ≤ n, ai ≠ bi), where ai and bi are the vertices connected by the i-th edge. All given edges are different.
Print a single integer — the number of distinct pairs of the tree's vertices which have a distance of exactly k between them.
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
5 21 22 33 42 5
4
5 31 22 33 44 5
2
In the first sample the pairs of vertexes at distance 2 from each other are (1, 3), (1, 5), (3, 5) and (2, 4).
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