Work Scheduling URAL - 1099 一般图最大匹配带花树

Posted 2021-03-07 qingyuyyyyy

#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <string>
using namespace std;
const int MAXN = 250;
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
",Count);
    for(int u = 1; u <= N; u++)
        if(u < Match[u])
            printf("%d %d
",u,Match[u]);
}
int main() {
    CreateGraph();//建图
    Edmonds();//进行匹配
    PrintMatch();//输出匹配数和匹配
    return 0;
}