PAT 甲级 1013. Battle Over Cities

原题传送门

• 题意：从一个无向图里，取出一个顶点，至少要补几条边能够使得它联通。

• 思路：就相当于求它的连通分量x，需要连x-1条边。

#include <iostream>#include <string.h>#include <vector>using namespace std;const int MAX = 1000 + 5;int attack;int visit[MAX];vector<int> G[MAX];void dfs(int cur) {    visit[cur] = 1;    for(auto at : G[cur]) {        if(visit[at]==0 && at!=attack )            dfs(at);    }}int main(int argc, const char * argv[]) {    int N, M, K;    cin >> N >> M >> K; // 城市数量、道路数量、要关注的城市数量    while(M--) {    // 建立无向图        int city1, city2;        cin >> city1 >> city2;        G[city1].push_back(city2);        G[city2].push_back(city1);    }    while(K--) {        int concern;        cin >> concern;        attack = concern;        memset(visit, 0, sizeof(visit));        int count = 0;  // 连通分量        for(int i=1; i<=N; ++i) {            if(i==attack || visit[i])   //如果被攻占或者已经dfs则跳过                continue;            dfs(i);            count++;        }        printf("%d\n", count-1);    // 连通分量count需要连count-1条边    }    return 0;}

附原题：

It is vitally important to have all the cities connected by highways in a war. If a city is occupied by the enemy, all the highways from/toward that city are closed. We must know immediately if we need to repair any other highways to keep the rest of the cities connected. Given the map of cities which have all the remaining highways marked, you are supposed to tell the number of highways need to be repaired, quickly.

For example, if we have 3 cities and 2 highways connecting city1-city2 and city1-city3. Then if city1 is occupied by the enemy, we must have 1 highway repaired, that is the highway city2-city3.

• Input

Each input file contains one test case. Each case starts with a line containing 3 numbers N (<1000), M and K, which are the total number of cities, the number of remaining highways, and the number of cities to be checked, respectively. Then M lines follow, each describes a highway by 2 integers, which are the numbers of the cities the highway connects. The cities are numbered from 1 to N. Finally there is a line containing K numbers, which represent the cities we concern.

• Output

For each of the K cities, output in a line the number of highways need to be repaired if that city is lost.

• Sample Input
  3 2 3
  1 2
  1 3
  1 2 3
• Sample Output
  1
  0
  0