【HDU1325】Is It A Tree?（并查集基础题）

有以下坑点：

1.结束输入不一定-1，题目中的叙述只是说所有权值都为正值。

2.是否构成一棵树不能只判断是否只有一个根节点，没有环路，而且还需要判断每个节点的入度一定是1，不然就不是一棵树。

（无环路也可用树的性质：结点数 = 边树 + 1 来取代）

#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cctype>
#include <cmath>
#include <string>
#include <cstdio>
#include <algorithm>
#include <numeric>
using namespace std;

const int maxn = 25;

int  father[maxn];
int  eage[maxn];
bool vis[maxn], flag = 0;
int sum = 0;

int getFather (int x) {
    while (father[x] != x) {
        x = father[x];
    }
    return x;
}

void Union (int p, int q) {
    int x = getFather (p);
    int y = getFather (q);
    if (x != y) {
        father[y] = x;
        sum ++;
    } else {
        flag = 0;
    }
}

int main () {
    int x, y, cur = 0;
    while (cin >> x >> y) {
        if (x < 0 && y < 0) break;
        if (x == 0 && y == 0) {
            printf("Case %d is a tree.
", ++ cur);
            continue;
        } else {
            flag = 1;
            memset(vis, 0, sizeof(vis));
            memset(eage, 0, sizeof(eage));
            for (int i = 0; i < maxn; ++ i) {
                father[i] = i;
            }
            vis[x] = vis[y] = 1;
            Union(x, y);
            eage[y] ++;
            while (cin >> x >> y) {
                if (x + y == 0) break;
                vis[x] = vis[y] = 1;
                Union(x, y);
                eage[y] ++;
            }
            sort(eage, eage + maxn, greater<int>());
            int xx = 0;
            if (eage[0] > 1) flag = 0;
            for (int i = 1; i < maxn; ++ i) {
                if (vis[i] && father[i] == i) {
                    xx ++;
                    if (xx > 1) {flag = 0; break;}
                }
            }
            /*for (int i = 1 ; i < maxn; ++ i) {
                cout << vis[i] <<  " " ;
            }*/

            if (flag) printf("Case %d is a tree.
", ++ cur);
            else printf("Case %d is not a tree.
", ++ cur);
        }
    }
    return 0;
}