URAL 1099 Work Scheduling (一般图匹配带花树)

最新推荐文章于 2020-01-12 14:31:36 发布

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最新推荐文章于 2020-01-12 14:31:36 发布

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分类专栏：一般图匹配带花树 ACM算法图论匹配问题文章标签：匹配问题

本文链接：https://blog.youkuaiyun.com/wzazzy/article/details/83756716

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一般图匹配带花树

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本文详细解析了KuangBin模版题的代码实现，包括最大匹配算法的Edmonds算法，通过创建图、寻找增广路径、进行匹配等步骤，展示了如何解决二分图的最大匹配问题。

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kuangbin模版题

//
//  main.cpp
//  wzazzy
//
//  Created by apple on 2018/10/23.
//  Copyright © 2018年 apple. All rights reserved.
//

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<cmath>
#include<cstring>
#include<string.h>
#include<queue>
#include<stack>
#include<list>
#include<map>
#include<set>
#include<vector>
using namespace std;
typedef long long int ll;
const int maxn =250;
const int maxm=10000;
const int mod =1e8+7;
const int INF=0x3f3f3f3f;
//**********************************
int N; //点的个数，点的编号从1到N
bool Graph[maxn][maxn];
int Match[maxn];
bool InQueue[maxn],InPath[maxn],InBlossom[maxn];
int Head,Tail;
int Queue[maxn];
int Start,Finish;
int NewBase;
int Father[maxn],Base[maxn];
int Count;//匹配数，匹配对数是Count/2
void CreateGraph()
{
    int u,v;
    memset(Graph,false,sizeof(Graph));
    scanf("%d",&N);
    while(scanf("%d%d",&u,&v) == 2)
    {
        Graph[u][v] = Graph[v][u] = true;
    }
}
void Push(int u)
{
    Queue[Tail] = u;
    Tail++;
    InQueue[u] = true;
}
int Pop()
{
    int res = Queue[Head];
    Head++;
    return res;
}
int FindCommonAncestor(int u,int v)
{
    memset(InPath,false,sizeof(InPath));
    while(true)
    {
        u = Base[u];
        InPath[u] = true;
        if(u == Start) break;
        u = Father[Match[u]];
    }
    while(true)
    {
        v = Base[v];
        if(InPath[v])break;
        v = Father[Match[v]];
    }
    return v;
}
void ResetTrace(int u)
{
    int v;
    while(Base[u] != NewBase)
    {
        v = Match[u];
        InBlossom[Base[u]] = InBlossom[Base[v]] = true;
        u = Father[v];
        if(Base[u] != NewBase) Father[u] = v;
    }
}
void BloosomContract(int u,int v)
{
    NewBase = FindCommonAncestor(u,v);
    memset(InBlossom,false,sizeof(InBlossom));
    ResetTrace(u);
    ResetTrace(v);
    if(Base[u] != NewBase) Father[u] = v;
    if(Base[v] != NewBase) Father[v] = u;
    for(int tu = 1; tu <= N; tu++)
        if(InBlossom[Base[tu]])
        {
            Base[tu] = NewBase;
            if(!InQueue[tu]) Push(tu);
        }
}
void FindAugmentingPath()
{
    memset(InQueue,false,sizeof(InQueue));
    memset(Father,0,sizeof(Father));
    for(int i = 1;i <= N;i++)
        Base[i] = i;
    Head = Tail = 1;
    Push(Start);
    Finish = 0;
    while(Head < Tail)
    {
        int u = Pop();
        for(int v = 1; v <= N; v++)
            if(Graph[u][v] && (Base[u] != Base[v]) && (Match[u] != v))
            {
                if((v == Start) || ((Match[v] > 0) && Father[Match[v]] > 0))
                    BloosomContract(u,v);
                else if(Father[v] == 0)
                {
                    Father[v] = u;
                    if(Match[v] > 0)
                        Push(Match[v]);
                    else
                    {
                        Finish = v;
                        return;
                    }
                }
            }
    }
}
void AugmentPath()
{
    int u,v,w;
    u = Finish;
    while(u > 0)
    {
        v = Father[u];
        w = Match[v];
        Match[v] = u;
        Match[u] = v;
        u = w;
    }
}
void Edmonds()
{
    memset(Match,0,sizeof(Match));
    for(int u = 1; u <= N; u++)
        if(Match[u] == 0)
        {
            Start = u;
            FindAugmentingPath();
            if(Finish > 0)AugmentPath();
        }
}
void PrintMatch()
{
    Count = 0;
    for(int u = 1; u <= N;u++)
        if(Match[u] > 0)
            Count++;
    printf("%d\n",Count);
    for(int u = 1; u <= N; u++)
        if(u < Match[u])
            printf("%d %d\n",u,Match[u]);
}
int main()
{
    CreateGraph();//建图
    Edmonds();//进行匹配
    PrintMatch();//输出匹配数和匹配
    return 0;
}