HDU4496_D-City(并查集删边/逆向)

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探讨了在一个给定的图中，通过按顺序删除边来计算剩余连通块数量的问题，并提供了一种使用并查集实现的有效算法。

D-City

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65535/65535 K (Java/Others)
Total Submission(s): 1315 Accepted Submission(s): 496

Problem Description

Luxer is a really bad guy. He destroys everything he met.
One day Luxer went to D-city. D-city has N D-points and M D-lines. Each D-line connects exactly two D-points. Luxer will destroy all the D-lines. The mayor of D-city wants to know how many connected blocks of D-city left after Luxer destroying the first K D-lines in the input.
Two points are in the same connected blocks if and only if they connect to each other directly or indirectly.

Input

First line of the input contains two integers N and M.
Then following M lines each containing 2 space-separated integers u and v, which denotes an D-line.
Constraints:
0 < N <= 10000
0 < M <= 100000
0 <= u, v < N.

Output

Output M lines, the ith line is the answer after deleting the first i edges in the input.

Sample Input

Sample Output

  
   1 
1 
1 
2 
2 
2 
2 
3 
4 
5

   
    
     Hint
    
The graph given in sample input is a complete graph, that each pair of vertex has an edge connecting them, so there's only 1 connected block at first. 
The first 3 lines of output are 1s  because  after  deleting  the  first  3  edges  of  the  graph,  all  vertexes  still  connected together. 
But after deleting the first 4 edges of the graph, vertex 1 will be disconnected with other vertex, and it became an independent connected block. 
Continue deleting edges the disconnected blocks increased and finally it will became the number of vertex, so the last output should always be N.

Source

2013 ACM-ICPC吉林通化全国邀请赛——题目重现

解题报告

给定一个图，N个点，M条边，求按顺序删边后剩下的多少联通块。

一般我们都是用并查集来加边，删边也可以用并查集，删除第1条边等于加上m-1条边。。。

#include <iostream>
#include <cstdio>
#include <cstring>
#define M 100000+10
#define N 10000+10
using namespace std;
int n,m;
struct node
{
    int u,v;
} edge[M];
int B[N],ans[M];
int fine(int x)
{
    if(B[x]!=x)
    B[x]=fine(B[x]);
    return B[x];
}
int main()
{
    int i;
    while(~scanf("%d%d",&n,&m))
    {
    memset(ans,0,sizeof(ans));
    memset(edge,0,sizeof(edge));
        for(i=0;i<n;i++)
        B[i]=i;
        for(i=0; i<m; i++)
        {
            scanf("%d%d",&edge[i].u,&edge[i].v);
        }
        int sum=n;
        for(i=m-1;i>=0;i--)
        {
            ans[i]=sum;
            int xx=fine(edge[i].u);
            int yy=fine(edge[i].v);
            if(xx!=yy)
            {
                sum--;
                B[xx]=yy;
            }
        }
        for(i=0;i<m;i++)
        printf("%d\n",ans[i]);
    }
    return 0;
}