Create Edmonds-karp.cpp

ps/Graph/network_flow/Edmonds-karp.cpp

@@ -0,0 +1,40 @@
+int Edmond_Karp(){
+    int n, p; cin >> n >> p;
+    int st = 1, ed = 2;
+    vector<vector<int>> cap(n + 1, vector<int>(n + 1));
+    vector<vector<int>> flow(n + 1, vector<int>(n + 1));
+    vector<int> edge[n + 1];
+    while (p--){
+        int u, v, w = 1; cin >> u >> v;// >> w
+        cap[u][v] += w; edge[u].emplace_back(v); edge[v].emplace_back(u);
+    }
+    int answer = 0;
+    int parent[n + 1];
+
+    while (true){
+        queue<int> q; q.push(st);
+        memset(parent, -1, sizeof(parent));
+        //bfs로 다음 경로 구하기
+        while (!q.empty()){
+            int now = q.front(); q.pop();
+            for (int nxt: edge[now]){
+                if (cap[now][nxt] - flow[now][nxt] > 0 && parent[nxt] == -1){
+                    q.push(nxt); parent[nxt] = now;
+                    if (nxt == ed)  break;
+                }
+            }
+        }
+        //만약 더 이상 augmenting path가 존재하지 않으면 maximum flow
+        if (parent[ed] == -1)   break;
+
+
+        int mn = 1e9;
+        for (int i = ed; i != st; i = parent[i])    mn = min(mn, cap[parent[i]][i] - flow[parent[i]][i]);
+        for (int i = ed; i != st; i = parent[i]) {
+            flow[parent[i]][i] += mn; //잔여 네트워크에서 flow 흘림
+            flow[i][parent[i]] -= mn; 
+        }
+        answer += mn;
+    }
+    return answer;
+}