二分图染色问题
2017-04-15 20:52
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A. NP-Hard Problem
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Recently, Pari and Arya did some research about NP-Hard problems and they found the minimum vertex cover problem very interesting.
Suppose the graph G is given. Subset A of
its vertices is called a vertex cover of this graph, if for each edge uv there
is at least one endpoint of it in this set, i.e.
or
(or
both).
Pari and Arya have won a great undirected graph as an award in a team contest. Now they have to split it in two parts, but both of them want their parts of the graph to be a vertex cover.
They have agreed to give you their graph and you need to find two disjoint subsets of its vertices A and B,
such that both A and B are
vertex cover or claim it's impossible. Each vertex should be given to no more than one of the friends (or you can even keep it for yourself).
Input
The first line of the input contains two integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) —
the number of vertices and the number of edges in the prize graph, respectively.
Each of the next m lines contains a pair of integers ui and vi (1 ≤ ui, vi ≤ n),
denoting an undirected edge between ui and vi.
It's guaranteed the graph won't contain any self-loops or multiple edges.
Output
If it's impossible to split the graph between Pari and Arya as they expect, print "-1" (without quotes).
If there are two disjoint sets of vertices, such that both sets are vertex cover, print their descriptions. Each description must contain two lines. The first line contains a single integer k denoting
the number of vertices in that vertex cover, and the second line contains kintegers — the indices of vertices. Note that because of m ≥ 1,
vertex cover cannot be empty.
Examples
input
output
input
output
Note
In the first sample, you can give the vertex number 2 to Arya and vertices numbered 1 and 3 to
Pari and keep vertex number 4 for yourself (or give it someone, if you wish).
In the second sample, there is no way to satisfy both Pari and Arya.
这道题用广搜染色,然后进行判断。用的数据结构是vector,很适合这道题。
#include<bits/stdc++.h>
using namespace std;
int n,m;
vector<int> G[100001];
int color[100001]; //保存点的颜色
int bfs(int pos,int c)
{
int i,j;
color[pos]=c;
for(i=0;i<G[pos].size();i++)
{
if(color[G[pos][i]]==c)
return 0;
if(color[G[pos][i]]==0 && !bfs(G[pos][i],-c))
return 0;
}
return 1;
}
int solve()
{
int i,j;
for(i=1;i<=n;i++)
{
if(color[i]==0)
{
if(bfs(i,1)==0)
return 0;
}
}
return 1;
}
int main()
{
int i,j;
int u,v;
while(~scanf("%d %d",&n,&m))
{
//不要忘记初始化vector数组
memset(color,0,sizeof(color));
for(i=1;i<=n;i++)
G[i].clear();
for(i=0;i<m;i++)
{
cin>>u>>v;
G[u].push_back(v);
G[v].push_back(u);
}
if(solve())
{
int a[100000];
int b[100000];
int t=0;
int tt=0;
for(i=1;i<=n;i++)
{
if(color[i]==1)
{
a[t++]=i;
}
else if(color[i]==-1)
{
b[tt++]=i;
}
}
printf("%d\n",t);
for(i=0;i<t;i++)
printf("%d ",a[i]);
printf("\n");
printf("%d\n",tt);
for(i=0;i<tt;i++)
printf("%d ",b[i]);
printf("\n");
}
else
printf("-1\n");
}
return 0;
}
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Recently, Pari and Arya did some research about NP-Hard problems and they found the minimum vertex cover problem very interesting.
Suppose the graph G is given. Subset A of
its vertices is called a vertex cover of this graph, if for each edge uv there
is at least one endpoint of it in this set, i.e.
or
(or
both).
Pari and Arya have won a great undirected graph as an award in a team contest. Now they have to split it in two parts, but both of them want their parts of the graph to be a vertex cover.
They have agreed to give you their graph and you need to find two disjoint subsets of its vertices A and B,
such that both A and B are
vertex cover or claim it's impossible. Each vertex should be given to no more than one of the friends (or you can even keep it for yourself).
Input
The first line of the input contains two integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) —
the number of vertices and the number of edges in the prize graph, respectively.
Each of the next m lines contains a pair of integers ui and vi (1 ≤ ui, vi ≤ n),
denoting an undirected edge between ui and vi.
It's guaranteed the graph won't contain any self-loops or multiple edges.
Output
If it's impossible to split the graph between Pari and Arya as they expect, print "-1" (without quotes).
If there are two disjoint sets of vertices, such that both sets are vertex cover, print their descriptions. Each description must contain two lines. The first line contains a single integer k denoting
the number of vertices in that vertex cover, and the second line contains kintegers — the indices of vertices. Note that because of m ≥ 1,
vertex cover cannot be empty.
Examples
input
4 2 1 2 2 3
output
1 2 2 1 3
input
3 3 1 2 2 3 1 3
output
-1
Note
In the first sample, you can give the vertex number 2 to Arya and vertices numbered 1 and 3 to
Pari and keep vertex number 4 for yourself (or give it someone, if you wish).
In the second sample, there is no way to satisfy both Pari and Arya.
这道题用广搜染色,然后进行判断。用的数据结构是vector,很适合这道题。
#include<bits/stdc++.h>
using namespace std;
int n,m;
vector<int> G[100001];
int color[100001]; //保存点的颜色
int bfs(int pos,int c)
{
int i,j;
color[pos]=c;
for(i=0;i<G[pos].size();i++)
{
if(color[G[pos][i]]==c)
return 0;
if(color[G[pos][i]]==0 && !bfs(G[pos][i],-c))
return 0;
}
return 1;
}
int solve()
{
int i,j;
for(i=1;i<=n;i++)
{
if(color[i]==0)
{
if(bfs(i,1)==0)
return 0;
}
}
return 1;
}
int main()
{
int i,j;
int u,v;
while(~scanf("%d %d",&n,&m))
{
//不要忘记初始化vector数组
memset(color,0,sizeof(color));
for(i=1;i<=n;i++)
G[i].clear();
for(i=0;i<m;i++)
{
cin>>u>>v;
G[u].push_back(v);
G[v].push_back(u);
}
if(solve())
{
int a[100000];
int b[100000];
int t=0;
int tt=0;
for(i=1;i<=n;i++)
{
if(color[i]==1)
{
a[t++]=i;
}
else if(color[i]==-1)
{
b[tt++]=i;
}
}
printf("%d\n",t);
for(i=0;i<t;i++)
printf("%d ",a[i]);
printf("\n");
printf("%d\n",tt);
for(i=0;i<tt;i++)
printf("%d ",b[i]);
printf("\n");
}
else
printf("-1\n");
}
return 0;
}
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