比赛的时候刚开始看这题还以为是二分图匹配，后来才发现根本不是，因为该题存在长度为奇数的圈 。 比如1->2，2->3，3->1 。 所以该题要用一般图匹配，即带花树算法 。
比赛时抄的模板有地方抄错了，上述样例出现了死循环 。 赛后补题的时候用map去重却得不到正确答案，不知为何，暂放 ，下面给出一种正确解法。
细节参见代码：
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<vector>
#include<map>
#include<list>
#include<cmath>
#include<set>
#include<queue>
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<node,int> p;
void PrintMatch() {
cnt = getMatch();
vector<int> ans;
int g[maxn][maxn];
memcpy(g,Graph,sizeof(g));
for(int i=0;i<m;i++) {
memcpy(Graph,g,sizeof(g));
int u = e[i].a, v = e[i].b;
for(int j = 1; j <= n; j++)
Graph[j][u] = Graph[u][j] = Graph[j][v] = Graph[v][j] = false;
int cur = getMatch();
if(cur == cnt - 1) ;
else ans.push_back(i+1);
}
int sz = ans.size();
printf("%d\n",sz);
for(int i = 0;i < sz;i++)
{
printf("%d",ans[i]);
if(i < sz-1)printf(" ");
}
printf("\n");
}
int main() {
while(~scanf("%d%d",&n,&m)) {
memset(Graph,0,sizeof(Graph));
for(int i=0; i<m; i++) {
scanf("%d%d",&e[i].a,&e[i].b);
Graph[e[i].a][e[i].b]=Graph[e[i].b][e[i].a]=true;
}
Edmonds();
PrintMatch();
}
return 0;
}
版权声明：本文为博主原创文章，未经博主允许不得转载。
HDU 4687 Boke and Tsukkomi（一般图匹配|带花树）
原文地址：http://blog.csdn.net/weizhuwyzc000/article/details/48009923
