Hdu-3926 Hand in Hand(同构图)

原博客：http://blog.csdn.net/niushuai666/article/details/6916764

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3926

题目大意：给你2个图，最大度为2.问两个图是否相似

解题思路：

本质是并查集，但是细节是在是恶心死人了。。。

1.最大度为2.说明这个图可能有多个连通分量，每个连通分量要么是环，要么是链。

2.然后遍历每个连通分量，记录该连通分量的结点个数，以及该连通分量是环还是链。

3.将第一个图按照结点个数排序（若子结点个数相同，则对链先排序）

4.将第二个图按照步骤三排序

5.比较排序后，2个图是否每个元素都相等。若相等，则相似。

代码如下：

#include<iostream>#include<cstdio>#include<cstring>#include<string>#include<climits>#include<algorithm>using namespace std;#define MAXN 10010int pre1[MAXN], pre2[MAXN]; //父节点int num1, num2;struct graph //图的子结点数目，是否为环{int son;bool ring;};graph g1[MAXN], g2[MAXN];bool cmb(const graph &g1, const graph &g2) //子结点优先+先链后环排序{if(g1.son < g2.son)return true;else if(g1.son == g2.son && g1.ring < g2.ring)return true;elsereturn false;}int find(int x, int pre[]) //查找根结点+路径压缩{return x == pre[x] ? x : find(pre[x], pre);}void join(int x, int y, int pre[],graph g1[]) //合并{int root1, root2;root1 = find(x, pre);root2 = find(y, pre);if(root1 == root2)g1[root1].ring = true; //为环else{if(g1[root1].son >= g1[root2].son) //结点相加{pre[root2] = root1;g1[root1].son += g1[root2].son;}else{pre[root1] = root2;g1[root2].son += g1[root1].son;}}}bool cmp(int num, graph g1[], graph g2[]) //判断图是否同构{sort(g1 + 1, g1 + num + 1, cmb); //排序sort(g2 + 1, g2 + num + 1, cmb);for(int i = 1; i <= num; ++i)if(g1[i].son != g2[i].son || (g1[i].son == g2[i].son && g1[i].ring != g2[i].ring))return false;return true;}int main(){int ncase, T = 0;int link1, link2;int hand1, hand2;int ans1, ans2;bool flag;scanf("%d", &ncase);while(ncase--){flag = true;scanf("%d%d", &num1, &link1);for(int i = 1; i < MAXN; ++i) //初始化{pre1[i] = i;pre2[i] = i;g1[i].son = 1;g2[i].son = 1;g1[i].ring = false;g2[i].ring = false;}for(int i = 1; i <= link1; ++i){scanf("%d%d", &hand1, &hand2);join(hand1, hand2, pre1, g1);}scanf("%d%d", &num2, &link2);if(link2 != link1) //边数不同跳出flag = false;for(int i = 1; i <= link2; ++i){scanf("%d%d", &hand1, &hand2);if(flag == false)continue;elsejoin(hand1, hand2, pre2, g2);}flag = cmp(num2, g1, g2);if(flag == false)printf("Case #%d: NO\n", ++T);else{if(flag)printf("Case #%d: YES\n", ++T);elseprintf("Case #%d: NO\n", ++T);}}return 0;}