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.
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.
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
5 10
0 1
1 2
1 3
1 4
0 2
2 3
0 4
0 3
3 4
2 4
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.
一开始没个输入都遍历一遍,结果超时了。。。。只能逆着来。。。
#include <bits/stdc++.h>
using namespace std;
int pre[100010];
int find(int x){
if(pre[x]==x)
return x;
return pre[x]=find(pre[x]);
}
int init(int a,int b){
int x=find(a),y=find(b);
if(x!=y){
pre[x]=y;
return 1;
}
else
return 0;
}
int main(){
int n,m;
while(~scanf("%d %d",&n,&m)){
for(int i=0;i<=n;i++)
pre[i]=i;
int a[100010],b[100010],c[100010];
for(int i=1;i<=m;i++)
scanf("%d %d",&a[i],&b[i]);
c[m]=n;
for(int i=m;i>=1;i--){
c[i-1]=c[i]-init(a[i],b[i]);
}
for(int i=1;i<=m;i++)
printf("%d\n",c[i]);
}
}
本文探讨了一个关于图论的问题:一个名为Luxer的恶棍破坏了一个包含N个点和M条边的城市的每一条边后,剩余的连通块数量。通过逆向思维,文章提供了一种高效的解决方案。
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