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edmonds-karp.cpp
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edmonds-karp.cpp
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#include <bits/stdc++.h>
using namespace std;
int n,u,v,w;
int s=0,t=1; // source, sink target index
int f;
const int INF = 1e8;
vector<int> pars;
vector<map<int,int>> graph;
void augment(int u, int mn) {
if(u==s) {
f = mn;
} else if(pars[u] != -1) {
int p = pars[u];
augment(p, min(mn, graph[p][u]));
graph[p][u] -= f;
graph[u][p] += f;
}
}
// O(V*E^2)
int maxFlow() {
int mf = 0;
while(1) {
vector<bool> vis(n);
pars.assign(n, -1);
queue<int> q;
q.push(s);
while(!q.empty()) {
u = q.front(); q.pop();
if(u==t) break;
for(auto& edge : graph[u]) {
tie(v, w) = edge;
if(!vis[v] && w>0) {
vis[v] = 1;
pars[v] = u;
q.push(v);
}
}
}
f = 0;
augment(t, INF);
if(f==0) break;
mf += f;
}
return mf;
}
int main()
{
n = 4;
graph.assign(n, map<int, int>());
auto add = [&](int u, int v, int w) {
graph[u][v] = w;
};
add(s,2,3);
add(s,3,2);
add(2,t,1);
add(3,t,2);
cout << maxFlow(); // 3
}