Augmenting Path Algorithm : 一般图最大匹配
2024-09-02 05:04:05
算法原理详见 http://www.csie.ntnu.edu.tw/~u91029/Matching.html
orz 带花树很神奇,挖坑最大权匹配
#include <iostream>
#include <cstring>
#include <cstdio>
#include <deque>
using namespace std;
const int maxn = ;
deque<int> p[maxn]; //树根到x的交错路径
bool adj[maxn][maxn];
int m[maxn]; //记录匹配情况
int d[maxn]; //记录奇点和偶点
int q[maxn], *qf, *qb; //记录可延伸的偶点
int n; void label_one_side(int x, int y, int bi){
for(int i = bi+; i < p[x].size(); i++){
int z = p[x][i];
if(d[z] == ){
p[z] = p[y];
p[z].insert(p[z].end(), p[x].rbegin(), p[x].rend()-i);
d[z] = ;
*qb++ = z;
}
}
} bool BFS(int r){
for(int i = ; i < n; i++) p[i].clear();
p[r].push_back(r);
for(int i = ; i < n; i++) d[i] = -;
d[r] = ;
qf = qb = q;
*qb++ = r;
while(qf < qb){
for(int x = *qf++, y = ; y < n; y++){
if(adj[x][y] && m[y] != y){
if(d[y] == -){
if(m[y] == -){
for(int i = ; i+ < p[x].size(); i += ){
m[p[x][i]] = p[x][i+];
m[p[x][i+]] = p[x][i];
}
m[x] = y; m[y] = x;
return true;
} else {
int z = m[y];
p[z] = p[x];
p[z].push_back(y);
p[z].push_back(z);
d[y] = ; d[z] = ;
*qb++ = z;
}
} else if(d[y] == ) {
int bi = ;
while(bi < p[x].size() && bi < p[y].size() && p[x][bi] == p[y][bi]) bi++;
bi--;
label_one_side(x, y, bi);
label_one_side(y, x, bi);
}
}
}
}
return false;
} int match(){
for(int i = ; i < n; i++) m[i] = -;
int c = ;
for(int i = ; i < n; i++){
if(m[i] == -)
if(BFS(i)) c++;
else m[i] = i;
}
return c;
} int main(){
cin>>n;
int x, y;
while(cin>>x>>y) adj[x][y] = adj[y][x] = true;
match();
}
这个是缩点版本的
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
const int N = ;
int n;
bool adj[N][N];
int p[N];
int m[N];
int d[N];
int c1[N], c2[N];
int q[N], *qf, *qb; int pp[N];
int f(int x) { return x == pp[x] ? x : pp[x] = f(pp[x]); }
void u(int x, int y) { pp[x] = y; }
int v[N]; void path(int r, int x){
if(r == x) return;
if(d[x] == ){
path(r, p[p[x]]);
int i = p[x], j = p[p[x]];
m[i] = j; m[j] = i;
} else if(d[x] == ){
path(m[x], c1[x]);
path(r, c2[x]);
int i = c1[x], j = c2[x];
m[i] = j; m[j] = i;
}
} int lca(int x, int y, int r){
int i = f(x), j = f(y);
while(i != j && v[i] != && v[j] != ){
v[i] = ; v[j] = ;
if(i != r) i = f(p[i]);
if(j != r) j = f(p[j]);
}
int b = i, z = j; if(v[j] == ) swap(b, z);
for(int i = b; i != z; i = f(p[i])) v[i] = -;
v[z] = -;
return b;
} void contract_one_side(int x, int y, int b){
for(int i = f(x); i != b; i = f(p[i])){
u(i, b);
if(d[i] == ) c1[i] = x, c2[i] = y, *qb++ = i;
}
} bool BFS(int r){
for(int i = ; i < n; i++) pp[i] = i;
for(int i = ; i < n; i++) v[i] = d[i] = -;
d[r] = ;
qf = qb = q;
*qb++ = r;
while(qf < qb){
for(int x = *qf++, y = ; y < n; y++){
if(!adj[x][y] || m[y] == y || f(x) == f(y)) continue;
if(d[y] == -){
if(m[y] == -){
path(r, x);
m[x] = y; m[y] = x;
return true;
} else {
p[y] = x; p[m[y]] = y;
d[y] = ; d[m[y]] = ;
*qb++ = m[y];
}
} else if(d[f(y)] == ){
int b = lca(x, y, r);
contract_one_side(x, y, b);
contract_one_side(y, x, b);
}
}
}
return false;
} int main(){ }
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