Map Coloring
Time limit: 1.0 second
Memory limit: 64 MB
Memory limit: 64 MB
We consider a geographical map with N countries numbered from 1 to N (0 < N < 99).
For every country we know the numbers of other countries which are
connected with its border. From every country we can reach to any other
one, eventually crossing some borders. Write a program which determines
whether it is possible to color the map only in two colors — red and
blue in such a way that if two countries are connected their colors are
different. The color of the first country is red. Your program must
output one possible coloring for the other countries, or show, that such
coloring is impossible.
For every country we know the numbers of other countries which are
connected with its border. From every country we can reach to any other
one, eventually crossing some borders. Write a program which determines
whether it is possible to color the map only in two colors — red and
blue in such a way that if two countries are connected their colors are
different. The color of the first country is red. Your program must
output one possible coloring for the other countries, or show, that such
coloring is impossible.
Input
On the first line is written the number N. On the following N lines, the i-th line contains the countries to which the i-th country is connected. Every integer on this line is bigger than i, except the last one which is 0 and marks that no more countries are listed for country i. If a line contains 0, that means that the i-th country is not connected to any other country, which number is larger than i.
Output
The output contains exactly one line. If the coloring is
possible, this line must contain a list of zeros and ones,
without any separators between them. The i-th digit
in this sequence is the color of the i-th country. 0 corresponds to red color, and one — to blue color. If a coloring is not possible, output the integer −1.
possible, this line must contain a list of zeros and ones,
without any separators between them. The i-th digit
in this sequence is the color of the i-th country. 0 corresponds to red color, and one — to blue color. If a coloring is not possible, output the integer −1.
Sample
| input | output |
|---|---|
3 |
010 |
Problem Author: Emil Kelevedzhiev
【分析】一个很简单的图染色问题。
#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <stack>
#include <queue>
#include <vector>
#define inf 0x3f3f3f3f
#define met(a,b) memset(a,b,sizeof a)
#define pb push_back
typedef long long ll;
using namespace std;
const int N = ;
const int M = ;
int n,m,k,l,tot=;
int parent[N],pre[N],vis[N],color[N];
vector<int>vec[N];
bool ok=true;
void dfs(int u){
vis[u]=;
for(int i=;i<vec[u].size();i++){
int v=vec[u][i];
if(!vis[v]){
color[v]=(color[u]+)%;
dfs(v);
}
else if(vis[v]&&color[v]==color[u]){
ok=false;return;
}
}
}
int main() {
int u,v;
scanf("%d",&n);
for(int i=;i<=n;i++){
while(){
scanf("%d",&v);
if(!v)break;
vec[i].pb(v);vec[v].pb(i);
}
}
for(int i=;i<=n;i++){
if(!vis[i]){
color[i]=;
dfs(i);
}
}
if(ok)for(int i=;i<=n;i++)printf("%d",color[i]);
else printf("-1");
printf("\n"); return ;
}