poj1419Graph Coloring(一般图最大独立集或着最大团)

一般图的最大独立集和最大团是等效的。图G = (V, E)，其补图G’。G的最大独立集等价于G’的最大团。度娘
一般的做法就是搜索。

// 最大独立集做法
vector<vector<int> > G;
int n, m;
int color[123];
vector<int> rec;
int maxnum;
void dfs(int u,int _count) {
    if (_count > maxnum) {//更新答案
        maxnum = _count;
        rec.clear();
        for (int i = 1;i <= n;++i) {
            if (color[i]) rec.push_back(i);
        }
    }
    if (u == n + 1) return ;
    //用于判断是否可以染成黑色
    bool ok = true;
    for (int i = 0;i < G[u].size();++i) {
        if (color[G[u][i]]) ok = false;
    }

    if (ok) {//u节点可以染成黑色
        color[u] = 1;
        dfs(u + 1, _count + 1);
        color[u] = 0;
    }
    dfs(u + 1, _count);//u染成白色－>跳过


}
int main(int argc, const char * argv[])
{    
    // freopen("in.txt","r",stdin);
    // freopen("out.txt","w",stdout);
    // clock_t _ = clock();

    int t, u, v;
    cin >> t;
    while(t--) {
        scanf("%d%d", &n, &m);
        G.clear();
        G.resize(n + 2);
        while(m--) {
            scanf("%d%d", &u, &v);
            G[u].push_back(v);
            G[v].push_back(u);
        }
        memset(color, 0,sizeof color);
        maxnum = 0;
        dfs(1, 0);
        printf("%d\n", maxnum);
        for (int i = 0;i < rec.size();++i)
            printf("%d%c", rec[i], i == maxnum - 1?'\n':' ');
    }

    // printf("\nTime cost: %.2fs\n", 1.0 * (clock() - _) / CLOCKS_PER_SEC);
    return 0;
}

//最大团做法
int mp[123][123];
int rec[123];
int tmp[123];
int cnt, ans;
int n, m;
void dfs(int u) {
    if (u == n + 1) {
        if (cnt > ans)
            ans = cnt;
            memcpy(rec, tmp, sizeof tmp);
        return ;
    }
//判断u是否可以划入到这个团中去
    bool ok = true;
    for (int i = 1;i < u;++i) {
        if (tmp[i] && mp[i][u]) {
            ok = false;
            break;
        }
    }

    if (ok) {
        tmp[u] = 1;cnt++;
        dfs(u + 1);
        tmp[u] = 0;cnt--;
    }
//跳过u节点后判断下可行性
    if (n + cnt - u > ans) 
        dfs(u + 1);
}
int main(int argc, const char * argv[])
{    
    // freopen("in.txt","r",stdin);
    // freopen("out.txt","w",stdout);
    // clock_t _ = clock();

    int t;
    cin >> t;
    while(t--) {
        scanf("%d%d", &n, &m);
        memset(mp, 0,sizeof mp);
        memset(tmp, 0,sizeof tmp);
        int u, v;
        for (int i = 1;i <= m;++i) {
            scanf("%d%d", &u, &v);
            mp[u][v] = mp[v][u] = 1;
        }
        cnt = ans = 0;
        dfs(1);
        printf("%d\n", ans);
        bool first = true;
        for (int i = 1;i <= n;++i) {
            if (rec[i]) {
                if (first) printf("%d", i);
                else printf(" %d", i);
                first = false;
            }
        }
        printf("\n");
    }

    // printf("\nTime cost: %.2fs\n", 1.0 * (clock() - _) / CLOCKS_PER_SEC);
    return 0;
}