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POJ 1308 Is It A Tree?(并查集)

霍华德 2023-04-20 阅读 55


Is It A Tree?


Time Limit: 1000MS

 

Memory Limit: 10000K

Total Submissions: 23255

 

Accepted: 7977


Description


A tree is a well-known data structure that is either empty (null, void, nothing) or is a set of one or more nodes connected by directed edges between nodes satisfying the following properties. 


There is exactly one node, called the root, to which no directed edges point. 


Every node except the root has exactly one edge pointing to it. 


There is a unique sequence of directed edges from the root to each node. 


For example, consider the illustrations below, in which nodes are represented by circles and edges are represented by lines with arrowheads. The first two of these are trees, but the last is not. 




POJ 1308    Is It A Tree?(并查集)_ide


In this problem you will be given several descriptions of collections of nodes connected by directed edges. For each of these you are to determine if the collection satisfies the definition of a tree or not.


Input


The input will consist of a sequence of descriptions (test cases) followed by a pair of negative integers. Each test case will consist of a sequence of edge descriptions followed by a pair of zeroes Each edge description will consist of a pair of integers; the first integer identifies the node from which the edge begins, and the second integer identifies the node to which the edge is directed. Node numbers will always be greater than zero.


Output


For each test case display the line "Case k is a tree." or the line "Case k is not a tree.", where k corresponds to the test case number (they are sequentially numbered starting with 1).


Sample Input


6 8 5 3 5 2 6 45 6 0 0 8 1 7 3 6 2 8 9 7 5 7 4 7 8 7 6 0 0 3 8 6 8 6 4 5 3 5 6 5 2 0 0 -1 -1


Sample Output


Case 1 is a tree.Case 2 is a tree. Case 3 is not a tree.


Source


North Central North America 1997





  • Source Code

#include<iostream>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#include<stdlib.h>

using namespace std;

bool map[3001][3001];
int num[10010];
int bin[3001];

int findx(int x)
{
    int r = x;
    while(r!=bin[r])
    {
        r = bin[r];
    }
    int k = x,j;
    while(k!=r)
    {
        j = bin[k];
        bin[k] = r;
        k = j;
    }
    return r;
}

void merrg(int x,int y)
{
    int fx = findx(x);
    int fy = findx(y);
    if(fx!=fy)
    {
        bin[fx] = fy;
    }
}

int main()
{
    int x,y;
    int kk = 0;
    while(scanf("%d%d",&x,&y)!=EOF)
    {
        int maxx = 0;
        kk++;
        int cnt = 0;
        int flag = 0;
        if(x == -1 && y == -1)
        {
            break;
        }
        if(x == 0 && y == 0)
        {
           printf("Case %d is a tree.\n",kk);
           continue;
        }
        for(int i=0;i<=3001;i++)
        {
            bin[i] = i;
        }
        memset(map,0,sizeof(map));
        if(x!=0 && y!=0)
        {
            memset(num,0,sizeof(num));
            map[x][y] = 1;
            merrg(x,y);
            if(x == y && x!=0)
            {
                flag = 1;
            }
            num[y]++;
            int p = max(x,y);
            maxx = max(maxx,p);
            while(scanf("%d%d",&x,&y)!=EOF)
            {
                if(x == 0 && y == 0)
                {
                    break;
                }
                if((x == y && x!=0) || map[y][x] == 1)
                {
                    flag = 1;
                }
                merrg(x,y);
                map[x][y] = 1;
                num[y]++;
                p = max(x,y);
                maxx = max(maxx,p);
                if(num[y]>1)
                {
                    flag = 1;
                }
            }
        }
        if(flag == 1)
        {
            printf("Case %d is not a tree.\n",kk);
        }
        else
        {
            for(int i=0;i<=maxx;i++)
            {
                if(num[i]!=0 && bin[i] == i)
                {
                    cnt++;
                    if(cnt>1)
                    {
                        flag = 1;
                        break;
                    }
                }
            }
            for(int i=0;i<=maxx;i++)
            {
                for(int j=0;j<=maxx;j++)
                {
                    for(int k=0;k<=maxx;k++)
                    {
                        if(map[j][i] == 1 && map[i][k] == 1)
                        {
                            map[j][k] = 1;
                        }
                    }
                }
            }
            for(int i=0;i<maxx;i++)
            {
                for(int j=0;j<=maxx;j++)
                {
                    if(map[i][j]== 1 && map[j][i] == 1)
                    {
                        flag = 1;
                        break;
                    }
                }
                if(flag == 1)
                {
                    break;
                }
            }
            if(flag == 0 && cnt == 1)
            {
                printf("Case %d is a tree.\n",kk);
            }
            else
            {
                printf("Case %d is not a tree.\n",kk);
            }
        }
    }
    return 0;
}


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