From b90583dc840bc42cdfad792d297a541cbb3598b7 Mon Sep 17 00:00:00 2001
From: Edson Neto <72220739+emn2@users.noreply.github.com>
Date: Tue, 5 Oct 2021 08:39:27 -0300
Subject: [PATCH] Maximum Flow Algorithm

---
 Graphs/edmonds_karp.cpp | 47 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)
 create mode 100644 Graphs/edmonds_karp.cpp

diff --git a/Graphs/edmonds_karp.cpp b/Graphs/edmonds_karp.cpp
new file mode 100644
index 0000000..63627ed
--- /dev/null
+++ b/Graphs/edmonds_karp.cpp
@@ -0,0 +1,47 @@
+int n;
+vector<vector<int> > capacity;
+vector<vector<int> > adj;
+
+int bfs(int s, int t, vector<int>& parent) {
+    fill(parent.begin(), parent.end(), -1);
+    parent[s] = -2;
+    queue<pair<int, int> > q;
+    q.push(make_pair(s, INF));
+
+    while (!q.empty()) {
+        int cur = q.front().first;
+        int flow = q.front().second;
+        q.pop();
+
+        for (int next : adj[cur]) {
+            if (parent[next] == -1 && capacity[cur][next]) {
+                parent[next] = cur;
+                int new_flow = min(flow, capacity[cur][next]);
+                if (next == t)
+                    return new_flow;
+                q.push(make_pair(next, new_flow));
+            }
+        }
+    }
+
+    return 0;
+}
+
+int maxflow(int s, int t) {
+    int flow = 0;
+    vector<int> parent(n);
+    int new_flow;
+
+    while (new_flow = bfs(s, t, parent)) {
+        flow += new_flow;
+        int cur = t;
+        while (cur != s) {
+            int prev = parent[cur];
+            capacity[prev][cur] -= new_flow;
+            capacity[cur][prev] += new_flow;
+            cur = prev;
+        }
+    }
+
+    return flow;
+}