From f2b57ac058b8794091f3a6c8afd46213813c1b14 Mon Sep 17 00:00:00 2001
From: Amisha Sahu <58816552+Amisha328@users.noreply.github.com>
Date: Sat, 7 Oct 2023 14:39:05 +0530
Subject: [PATCH] Add Bellman Ford Algorithm in C++

Given a weighted, directed, and connected graph of V vertices and E edges, Find the shortest distance of all the vertices from the source vertex S. If vertices can't be reached from the S then mark the distance as 10^8. Note: If the Graph contains a negative cycle then return an array consisting of only -1.
---
 25-Graph Theory/BellmanFord_Algorithm.cpp | 68 +++++++++++++++++++++++
 1 file changed, 68 insertions(+)
 create mode 100644 25-Graph Theory/BellmanFord_Algorithm.cpp

diff --git a/25-Graph Theory/BellmanFord_Algorithm.cpp b/25-Graph Theory/BellmanFord_Algorithm.cpp
new file mode 100644
index 0000000..138ad83
--- /dev/null
+++ b/25-Graph Theory/BellmanFord_Algorithm.cpp	
@@ -0,0 +1,68 @@
+// Distance from the Source (Bellman-Ford Algorithm) 
+
+#include<bits/stdc++.h>
+using namespace std;
+
+class Solution{
+	public:
+            // TC-> O(V-1) * O(E) | SC-> O(V)
+          vector<int> bellman_ford(int V, vector<vector<int>>& edges, int S) {
+                vector<int> dist(V, 1e8);
+                dist[S] = 0;
+                for(int i = 1; i <= V-1; i++)
+                {
+                    for(auto it: edges){
+                        int u = it[0];
+                        int v = it[1];
+                        int wt = it[2];
+                        
+                        if(dist[u] != 1e8 && dist[u] + wt < dist[v])
+                            dist[v] = dist[u] + wt;
+                    }
+                }
+                
+                // do the last relaxation for Vth time 
+                // to check if negative edge cycle exists
+                for(auto it: edges){
+                        int u = it[0];
+                        int v = it[1];
+                        int wt = it[2];
+                        
+                        if(dist[u] != 1e8 && dist[u] + wt < dist[v])
+                        return {-1};
+                }
+                return dist;
+        }
+};
+
+int main()
+{
+    int t;
+    cin >> t;
+    while (t--) {
+        int V, E;
+        cin >> V >> E;
+        vector<vector<int>> adj;
+        int i=0;
+        while (i++<E) {
+            int u, v, w;
+            cin >> u >> v >> w;
+            vector<int> t1;
+            t1.push_back(u);
+            t1.push_back(v);
+            t1.push_back(w);
+            adj.push_back(t1);
+        }
+        int S;
+        cin>>S;
+        
+        Solution obj;
+    	vector<int> res = obj.bellman_ford(V, adj, S);
+    	
+    	for(int i=0; i<V; i++)
+    	    cout<<res[i]<<" ";
+    	cout<<endl;
+    }
+
+    return 0;
+}