UVa 193 - Graph Coloring

193 - Graph Coloring10946

22.52%

2634

58.39%

题目链接：

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=108&page=show_problem&problem=129

原题：

You are to write a program that tries to find an optimal coloring for a given graph. Colors are applied to the nodes of the graph and the only available colors are black and white. The coloring of the graph is called optimal if a maximum of nodes is black. The coloring is restricted by the rule that no two connected nodes may be black.

   
Figure: An optimal graph with three black nodes

题目大意：

给一张图染色， 只能染白色或黑色， 不能让相连的两个点都是染成黑色（白色的可以）。 求这张图能染黑色的最多点数

分析与总结：

其实就是对于每一个点，染黑，或者不染黑的问题。直接暴力搜索即可。

参考：王晓东的《计算机算法设计与分析第三版》P163页 ”图的m着色问题“。

代码：

#include<iostream>#include<cstdio>#include<algorithm>#include<cstring>#define MAXN 102using namespace std;int n,k, G[MAXN][MAXN], maxVal;int color[MAXN], ans[MAXN];// 判断与这个点相连的是否有黑色的inline bool isOk(int u){    for(int i=1; i<=n; ++i)        if(G[u][i] && color[i])return false;    return true;}void search(int u, int num){    if(u > n){        if(num > maxVal){             maxVal = num;            memcpy(ans, color, sizeof(ans)) ;        }        return;    }    if(num + n - u + 1 <= maxVal) return;// 减枝    if(isOk(u)){        color[u] = 1;        search(u+1, num+1);        color[u] = 0;    }    search(u+1, num);}int main(){#ifdef LOCAL    freopen("input.txt","r",stdin);#endif    int T, u, v;    scanf("%d",&T);    while(T--){        scanf("%d %d", &n, &k);        memset(G, 0, sizeof(G));        for(int i=0; i<k; ++i){            scanf("%d %d", &u, &v);            G[u][v] = G[v][u] = 1;        }        maxVal = -2147483646;        memset(color, 0, sizeof(color));        search(1, 0);        printf("%d\n", maxVal);        bool flag=true;        for(int i=1; i<=n; ++i)if(ans[i]){            if(flag){ printf("%d",i);  flag=false;}            else printf(" %d",i);        }        printf("\n");    }    return 0;}

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     原创 http://blog.csdn.net/shuangde800 ， By   D_Double  (转载请标明)