From 4245cec44059454a3d4c8f8f3d9d29ee6748870a Mon Sep 17 00:00:00 2001
From: piyushsehgal21 <44509954+piyushsehgal21@users.noreply.github.com>
Date: Sat, 27 Oct 2018 02:12:19 +0530
Subject: [PATCH] Single Source Shortest Path in a DAG

---
 SSSP_in_a_DAG.cpp | 86 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 86 insertions(+)
 create mode 100644 SSSP_in_a_DAG.cpp

diff --git a/SSSP_in_a_DAG.cpp b/SSSP_in_a_DAG.cpp
new file mode 100644
index 0000000..7c61db8
--- /dev/null
+++ b/SSSP_in_a_DAG.cpp
@@ -0,0 +1,86 @@
+    //All trees with directed edges are automatically DAGs as they do not contains any cycle.
+    //Single Source Shortest Path(SSSP) can be solved efficiently on DAG in O(V+E).
+    //SSSP on DAG
+     
+    #include <bits/stdc++.h>
+    using namespace std;
+     
+    #define pb push_back 
+    #define MAX 100001
+    #define INF (1<<20)
+    #define pii pair<int, int>
+     
+    bool visited[MAX];
+    vector<pii> G[MAX];
+    vector<int> topological;
+    int D[MAX];
+     
+    void dfs(int node){
+     
+    	visited[node] = true;
+     
+    	for(int i=0 ; i<G[node].size() ; i++){
+     
+    		int current = G[node][i].first;
+    		if(!visited[current])
+    			dfs(current);
+     
+    	}
+     
+    	topological.pb(node);
+     
+    }
+     
+     
+    void relax(int u, int v, int w){
+    	if(D[v] > D[u] + w){
+    		D[v] = D[u] + w;
+    	}
+    }
+     
+    int main() {
+     
+    	int edges,nodes;
+    	cin>>nodes>>edges;
+     
+    	memset(visited,false,sizeof(visited));
+    	//memset(D,INF,sizeof(D));
+    	for(int i=0 ; i<nodes ; i++)
+    		D[i] = INF;
+     
+    	for(int i=0 ; i<edges ; i++){
+    		int u,v,w;
+    		cin>>u>>v>>w;
+    		G[u].pb(pii(v,w));
+    	}
+     
+     
+    	for(int i=0 ; i<nodes ; i++){
+    		if(!visited[i])
+    			dfs(i);
+    	}
+     
+    	reverse(topological.begin(), topological.end());
+     
+    	for(int i=0 ; i<topological.size() ; i++){
+    		cout<<topological[i]<<" ";
+    	}
+    	cout<<endl;
+     
+    	D[0] = 0;
+    	for(int i=0 ; i<topological.size() ; i++){
+    		int u = topological[i];
+    		for(int j=0 ; j<G[u].size() ; j++){
+    			int v = G[u][j].first;
+    			int w = G[u][j].second;
+    			relax(u, v, w);
+    		}
+    	}
+     
+    	//distance of all nodes from node 0.
+    	for(int i=0 ; i<nodes ; i++){
+    		cout<<D[i]<<" ";
+    	}
+     
+    	return 0;
+    }