一般图极大团个数,最大团顶点数

Posted 2021-01-18 Aragaki

极大团个数:POJ 2989

#include <cstdio>
#include <cstring>
using namespace std;
const int maxn = 130;
bool mp[maxn][maxn];
int some[maxn][maxn], none[maxn][maxn], all[maxn][maxn];
int n, m, ans;
void dfs(int d, int an, int sn, int nn)
{
    if(!sn && !nn) ++ans;
    int u = some[d][0];
    for(int i = 0; i < sn; ++i)
    {
        int v = some[d][i];
        if(mp[u][v]) continue;
        for(int j = 0; j < an; ++j)
        all[d+1][j] = all[d][j];
        all[d+1][an] = v;
        int tsn = 0, tnn = 0;
        for(int j = 0; j < sn; ++j)
        if(mp[v][some[d][j]])
        some[d+1][tsn++] = some[d][j];
        for(int j = 0; j < nn; ++j)
        if(mp[v][none[d][j]])
        none[d+1][tnn++] = none[d][j];
        dfs(d+1, an+1, tsn, tnn);
        some[d][i] = 0, none[d][nn++] = v;
    }
}
int work()
{
    ans = 0;
    for(int i = 0; i < n; ++i) some[1][i] = i+1;
    dfs(1, 0, n, 0);
    return ans;
}
int main()
{
    while(~scanf("%d %d", &n, &m))
    {
        memset(mp, 0, sizeof mp);
        for(int i = 1; i <= m; ++i)
        {
            int u, v;
            scanf("%d %d", &u, &v);
            mp[u][v] = mp[v][u] = 1;
        }
        int tmp = work();
        printf("%d
", tmp);
    }
    return 0;
}

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最大团顶点数:ZOJ 1492

#include <bits/stdc++.h>
using namespace std;
const int maxn = 55;
bool mp[maxn][maxn];
int best, n, num[maxn];
bool dfs(int *adj, int total, int cnt)
{
    int t[maxn], k;
    if (total == 0) {
        if (cnt > best) {
            best = cnt;
            return true;    //剪枝4
        }
        return false;
    }
    for (int i = 0; i < total; ++i) {
        if (cnt + total - i <= best) {
            return false;    //剪枝1
        }
        if (cnt + num[adj[i]] <= best) {
            return false;    //剪枝3
        }
        k = 0;
        for (int j = i + 1; j < total; ++j)
            if (mp[adj[i]][adj[j]]) {
                t[k++] = adj[j];
            }
        //扫描与u相连的顶点中与当前要选中的adj[i]相连的顶点adj[j]并存储到数组t[]中，数量为k
        if (dfs(t, k, cnt + 1)) {
            return true;
        }
    }
    return false;
}
int MaximumClique()
{
    int adj[maxn], k;
    best = 0;
    for (int i = n; i >= 1; --i) {
        k = 0;
        for (int j = i + 1; j <= n; ++j)
            if (mp[i][j]) {
                adj[k++] = j;
            }
        //得到当前点i的所有相邻点存入adj
        dfs(adj, k, 1); //每次dfs相当于必选当前i点看是否能更新best
        num[i] = best;
    }
    return best;
}
int main()
{
    while (scanf("%d", &n) != -1 && n) {
        for (int i = 1; i <= n; ++i)
            for (int j = 1; j <= n; ++j) {
                scanf("%d", &mp[i][j]);
            }
        printf("%d
", MaximumClique());
    }
    return 0;
}

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