From 573fd55940b4c23b28de2d0349592050db6a54d0 Mon Sep 17 00:00:00 2001
From: Adarsh <46349391+4d4r5h@users.noreply.github.com>
Date: Mon, 10 Oct 2022 21:02:28 +0530
Subject: [PATCH] Create Download Speed.cpp

Edmonds-Karp Algorithm
---
 cses/Download Speed.cpp | 80 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 cses/Download Speed.cpp

diff --git a/cses/Download Speed.cpp b/cses/Download Speed.cpp
new file mode 100644
index 0000000..d79cc02
--- /dev/null
+++ b/cses/Download Speed.cpp	
@@ -0,0 +1,80 @@
+// The Edmonds-Karp algorithm is an implementation of the Ford-Fulkerson method for computing a maximal flow in a flow network.
+
+#include<bits/stdc++.h>
+#define int long long
+using namespace std;
+ 
+int c[501][501];
+int flowPassed[501][501];
+vector <int> g[501];
+int parList[501];
+ 
+bool bfs(int sNode, int eNode)
+{
+    memset(parList,-1,sizeof(parList));
+    queue <int> q;
+    q.push(sNode);
+    parList[sNode]=-1;
+    while(!q.empty())
+    {
+        int currNode=q.front();
+        q.pop();
+        for(int i=0; i<g[currNode].size(); i++)
+        {
+            int to=g[currNode][i];
+            if(parList[to]==-1 && c[currNode][to]>flowPassed[currNode][to])
+            {
+                parList[to]=currNode;
+                if(to==eNode)
+                {
+                    return true;
+                }
+                q.push(to);
+            }
+        }
+    }
+    return false;
+}
+
+int edmondsKarp(int sNode, int eNode)
+{
+    int maxFlow=0;
+    while(bfs(sNode, eNode))
+    {
+        int flow=LONG_LONG_MAX;
+        int currNode=eNode;
+        while(currNode!=sNode)
+        {
+            int prevNode=parList[currNode];
+            flow=min(flow, c[prevNode][currNode]-flowPassed[prevNode][currNode]);
+            currNode=prevNode;
+        }
+        maxFlow+=flow;
+        currNode=eNode;
+        while(currNode!=sNode)
+        {
+            int prevNode=parList[currNode];
+            flowPassed[prevNode][currNode]+=flow;
+            flowPassed[currNode][prevNode]-=flow;
+            currNode=prevNode;
+        }
+    }
+    return maxFlow;
+}
+ 
+signed main()
+{
+    int n,m;
+    cin>>n>>m;
+    int source=1, sink=n;
+    for(int i=0; i<m; i++)
+    {
+        int u,v,cap;
+        cin>>u>>v>>cap;
+        c[u][v]+=cap;
+        g[u].push_back(v);
+        g[v].push_back(u);
+    }
+    int maxFlow=edmondsKarp(source,sink);
+    cout<<maxFlow<<endl;
+}