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HDU 4687 Boke and Tsukkomi（一般圖匹配|帶花樹）

編輯：關於C++

比賽的時候剛開始看這題還以為是二分圖匹配，後來才發現根本不是，因為該題存在長度為奇數的圈。比如1->2，2->3，3->1 。所以該題要用一般圖匹配，即帶花樹算法。

比賽時抄的模板有地方抄錯了，上述樣例出現了死循環。賽後補題的時候用map去重卻得不到正確答案，不知為何，暫放，下面給出一種正確解法。

細節參見代碼：

#include
#include
#include
#include
#include
#include
#include
#include
#include
#include
using namespace std;
const int maxn = 55;
int n,m,Match[maxn],Head,Tail,Queue[maxn],Start,Finish,NewBase,Father[maxn],Base[maxn],cnt,Count;
bool InQueue[maxn],InPath[maxn],InBlossom[maxn],Graph[maxn][maxn];
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();
        }
}
int getMatch() {
    Edmonds();
    Count = 0;
    for(int u = 1; u <= n; u++)
        if(Match[u] > 0)
            Count++;
    return Count/2;
}
struct node {
    int a,b;
    node(int a=0,int b=0): a(a),b(b) {}
    bool operator < (const node& rhs) const {
        return a < rhs.a || (a == rhs.a && b < rhs.b);
    }
    bool operator == (const node& rhs)const {
        return a == rhs.a && b == rhs.b;
    }
} e[155],ee[155];
map p;
void PrintMatch() {
    cnt = getMatch();
vector ans;
    int g[maxn][maxn];
    memcpy(g,Graph,sizeof(g));
    for(int i=0;i