uva 1267 Network（DFS）

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                                 uva 1267 Network

Consider a tree network with n nodes where the internal nodes correspond to servers and the terminal nodes correspond to clients. The nodes are numbered from 1 ton . Among the servers, there is an original serverS which provides VOD (Video On Demand) service. To ensure the quality of service for the clients, the distance from each client to the VOD serverS should not exceed a certain value k . The distance from a node u to a nodev in the tree is defined to be the number of edges on the path fromu to v . If there is a nonempty subsetC of clients such that the distance from each u in C to S is greater thank , then replicas of the VOD system have to be placed in some servers so that the distance from each client to the nearest VOD server (the original VOD system or its replica) isk or less.

Given a tree network, a server S which has VOD system, and a positive integerk , find the minimum number of replicas necessary so that each client is within distancek from the nearest server which has the original VOD system or its replica.

For example, consider the following tree network.

In the above tree, the set of clients is {1, 6, 7, 8, 9, 10, 11, 13}, the set of servers is {2, 3, 4, 5, 12, 14}, and the original VOD server is located at node 12.

For k = 2 , the quality of service is not guaranteed with one VOD server at node 12 because the clients in {6, 7, 8, 9, 10} are away from VOD server at distance> k . Therefore, we need one or more replicas. When one replica is placed at node 4, the distance from each client to the nearest server of {12, 4} is less than or equal to 2. The minimum number of the needed replicas is one for this example.

Input 

Your program is to read the input from standard input. The input consists of T test cases. The number of test cases ( T ) is given in the first line of the input. The first line of each test case contains an integern(3n1, 000) which is the number of nodes of the tree network. The next line contains two integerss(1sn) and k(k1) wheres is the VOD server and k is the distance value for ensuring the quality of service. In the followingn - 1 lines, each line contains a pair of nodes which represent an edge of the tree network.

Output 

Your program is to write to standard output. Print exactly one line for each test case. The line should contain an integer that is the minimum number of the needed replicas.

Sample Input 

2 14 12 2 1 2 2 3 3 4 4 5 5 6 7 5 8 5 4 9 10 3 2 12 12 14 13 14 14 11 14 3 4 1 2 2 3 3 4 4 5 5 6 7 5 8 5 4 9 10 3 2 12 12 14 13 14 14 11

Sample Output 

1 0

題目大意：給出n，s，k，即有n台用戶端和伺服器，然後給出n-1條邊，串連n台主機，現在在序號為s的伺服器上有一個資源，為了方便所有使用者瀏覽（訪問路徑長度不超過k），要在較少的伺服器上複製資源，問說最少再在幾個伺服器上複製資源。

解題思路：首先現將無根圖轉化成樹，以資源所在的伺服器s為根，然後dfs建樹，建樹的過程中將所有葉子節點按照深度記錄。其二就是枚舉需要複製資源的伺服器，從節點深度最大的葉子節點開始，向上尋找父親節點k次，即為當前的最有策略，然後將距離該伺服器不超過k的終端全部標記。

#include<stdio.h>#include<vector>#include<string.h>using namespace std;int n, s, k, fa[1005], vis[1005];vector<int> gra[1005], node[1005];void Tra(int u, int f, int d) {//轉換為樹fa[u] = f;int n = gra[u].size();if (n == 1 && d > k) node[d].push_back(u);for (int i = 0; i < n; i++) {int v = gra[u][i];if (v != f) Tra(v, u, d + 1);}}void DFS(int u, int f, int d) { vis[u] = 1;int n = gra[u].size();for (int i = 0; i < n; i++) {int v = gra[u][i];if (v != f && d < k) DFS(v, u, d + 1); //距離不超過k}}int solve() {int ans = 0;memset(vis, 0, sizeof(vis));for (int d = n - 1; d > k; d--) {for (int i = 0; i < node[d].size(); i++) {int u = node[d][i];if (vis[u]) continue;int v = u;for (int j = 0; j < k; j++) v = fa[v];//v是u的k級祖先，所以在v處放伺服器，是最優的DFS(v, -1, 0);ans++;}}return ans;}int main() {intT;scanf("%d", &T);while (T--) {scanf("%d\n%d %d", &n, &s, &k);for (int i = 1; i <= n; i++) {gra[i].clear();node[i].clear();}int a, b;for (int i = 0; i < n - 1; i++) {scanf("%d %d", &a, &b);gra[a].push_back(b);gra[b].push_back(a);}Tra(s, -1, 0);printf("%d\n", solve());}return 0;}

uva 1267 Network（DFS）