POJ 1308 Is It A Tree 解題報告

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題目大意

給一堆邊，判斷這個圖是不是樹。

題解

樹：1、無環。2、是一棵樹，不是森林，只有一個根結點。3、無自環

1、並查集判斷環。
2、根節點數，判斷樹棵。

AC code

#include <iostream>
using namespace std;
 
#define N 105
 
int fa[N];
bool flag[N];
 
int findfa(int x){
	return x == fa[x] ? fa[x]:fa[x] = findfa(fa[x]);
}
void unin(int x,int y){
	int xfa = findfa(x);
	int yfa = findfa(y);
	if ( xfa != yfa )
		fa[ xfa ] = fa[yfa];
}
int main(){
//	freopen("1.txt","r",stdin);	
    int x,y,i,first;
    int t=0;int Case=0; 
    while(cin>>x>>y){
        if(x == -1 && y == -1)
            break;
        else if(x == 0&&y == 0){  //空樹也是一棵樹
////            cout<<"Case "<<t++<<" is a tree."<<endl;
   			printf("Case %d is a tree.\n",++Case);
            continue;
        }
        else {
	        for(i=0;i<N;i++){
	            fa[i] = i;           //初始化
	            flag[i] = false;
	        }
	        flag[x] = flag[y] = true;
	        first = x;
	        bool istree = true;
	        if(x == y)    istree = false;   //自己指向自己，不是一棵樹
	        else{
	            unin(x,y);
	        }
	        while(scanf("%d%d",&x,&y) && x!=0){
	            flag[x] = flag[y] = true;
	            if(findfa(x) == findfa(y))  //有共同祖先，x再指向y,就不是一棵樹
	                istree = false;
	            unin(x,y);
	        }
	        for(i=0;i<N;i++){
	            if(flag[i]&&findfa(i)!=findfa(first)){  //森林不是一棵樹
	                 istree = false;
	            }
	        }
	        if(istree)    	printf("Case %d is a tree.\n",++Case);
//			cout<<"Case "<<t++<<" is a tree."<<endl;
	        else			printf("Case %d is not a tree.\n",++Case);
//	            cout<<"Case "<<t++<<" is not a tree."<<endl;        	
        }

    }
    return 0;
}