2018牛客多校第一场，D

最新推荐文章于 2019-08-04 18:26:51 发布

原创最新推荐文章于 2019-08-04 18:26:51 发布 · 281 阅读

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本文介绍了一种解决图同构问题的算法实现，通过深度优先搜索（DFS）找到两个图之间的所有可能映射，并利用集合来避免重复计数，最终输出第一个图在第二个图中的同构子图数量。

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大致意思是从第二个图的子图中找与第一个图的同构的图，输出数量。

#include <vector>
#include <set>
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <algorithm>

using namespace std;

int tu1[10][10] = {{0}}, tu2[10][10] = {{0}}, tmp_tu[10][10] = {{0}};

int init_tu[10][10] = {{0}}, vnode[10] = {0};

int n,m1,m2;
int real_n;
int ans = 0;

int x[10] = {0};
bool vis[10] = {false};

set< set< pair<int,int> > > ans_set;


void dfs(int num,int bj)
{
    if (bj == real_n - 1)
    {
//        for (int i = 0; i < bj; ++i)
//        {
//
//            cout << x[i] << ',';
//        }cout << endl;

        for (int i = 0; i < 10; ++i)
        {
            for (int j = 0; j < 10; ++j)
            {
                tmp_tu[i][j] = 0;
            }
        }

        for (int i = 0; i < real_n; ++i)
        {
            for (int j = 0; j < real_n; ++j)
            {
                if (init_tu[i][j])
                {
                    //cout << "i:" << i << " j:" << j << endl;
                    //cout << "xi:" << x[i] << " xj:" << x[j] << endl;
                    tmp_tu[ x[i] - 1 ][ x[j] - 1 ] = tmp_tu[ x[j] - 1 ][ x[i] - 1 ] = 1;

                }
            }
        }

        int yes = 1;
        for (int i = 0; i < n; ++i)
        {
            int flag = 1;
            for (int j = 0; j < n; ++j)
            {
                if (tmp_tu[i][j] )
                {
                    if (!tu2[i][j])
                    {
                        //cout << "error:" <<i << "-->" << j << endl;
                        flag = 0;
                        break;
                    }
                    
                }
            }
            if (!flag)
            {
                yes = 0;
                break;
            }
        }

        if (yes)
        {
            set< pair<int,int> > t_set;
            for (int i = 0; i < n; ++i)
            {
                for (int j = 0; j < n; ++j)
                {
                    if (tmp_tu[i][j] )
                    {
                        int a,b;
                        if (i < j)
                        {
                            a = i;
                            b = j;
                        }
                        else
                        {
                            a = j;
                            b = i;
                        }
                        t_set.insert( make_pair(a,b) );
                    }
                }
            }

            set< set< pair<int,int> > >::iterator it = ans_set.find( t_set );

            if (it == ans_set.end())
            {
                ans_set.insert( t_set );
                ++ans;                
            }
        }


        //cout << endl;

        return;
    }

    for (int i = 1; i <= n; ++i)
    {
        if (!vis[i])
        {
            vis[i] = true;
            x[bj] = i;
            dfs(i,bj+1);
            vis[i] = false;
        }
    }
}

int main(int argc, char* argv[])
{   
    while (~scanf("%d%d%d",&n,&m1,&m2))
    {
        ans_set.clear();
        for (int i = 0; i < 10; ++i)
        {
            for (int j = 0; j < 10; ++j)
            {
                tu1[i][j] = tu2[i][j] = init_tu[i][j] = 0;
            }
        }

        ans = 0;
        for (int i = 0; i < m1; ++i)
        {
            int a,b;
            scanf("%d%d",&a,&b);
            tu1[a-1][b-1] = tu1[b-1][a-1] = 1;
        }

        int bj = 0;
        
        for (int i = 0; i < 10; ++i)
        {
            vnode[i] = -1;
        }
        for (int i = 0; i < n; ++i)
        {
            for (int j = 0; j < n; ++j)
            {
                if (tu1[i][j])
                {
                    if (vnode[i] == -1)
                    {
                        vnode[i] = bj++;;
                    }
                    if (vnode[j] == -1)
                    {
                        vnode[j] = bj++;
                    }
                }
            }
        }

        real_n = bj + 1;

        for (int i = 0; i < n; ++i)
        {
            for (int j = 0; j < n; ++j)
            {
                if (tu1[i][j])
                {
                    init_tu[ vnode[i] ][ vnode[j] ] = init_tu[ vnode[j] ][ vnode[i] ] = 1;
                }
            }
        }

        for (int i = 0; i < m2; ++i)
        {
            int a,b;
            scanf("%d%d",&a,&b);
            tu2[a-1][b-1] = tu2[b-1][a-1] = 1;
        }

        dfs(0,0);

        printf("%d\n",ans);

    }

    return 0;
}