added graph conceptual problems by DevT75

Graph/reviseGraph.cpp

@@ -0,0 +1,63 @@
+#include <bits/stdc++.h>
+using namespace std;
+void dfs(int source,vector<int> adj[],vector<bool>& visited){
+	cout << source << " ";
+	visited[source] = true;
+	for(auto it = adj[source].begin();it != adj[source].end();it++){
+		if(!visited[*it]){
+			dfs(*it,adj,visited);
+		}
+	}
+}
+void bfs(int source,vector<int> adj[],vector<bool>& visited){
+	queue<int> q;
+	q.push(source);
+	while(!q.empty()){
+		int temp = q.front();
+	    cout << temp << " ";
+		q.pop();
+	    for(auto it = adj[temp].begin();it != adj[temp].end(); it++){
+	    	if(!visited[*it]){
+	    		visited[*it] = true;
+	    		q.push(*it);
+	    	}
+	    }
+	}
+}
+
+int main(){
+	int v,e;
+	cin >> v >> e;
+	// 1-based indexing
+	vector<int> adj[v + 1];
+	for(int i = 0;i < e;i++){
+		// Undirected graph
+		int a,b;
+		cin >> a >> b;
+		adj[a].push_back(b);
+		adj[b].push_back(a);
+	}
+	// for(int i = 0;i < v + 1;i++){
+	// 	cout << i << " - ";
+	// 	for(auto it = adj[i].begin();it != adj[i].end();it++){
+	// 		cout << *it << " ";
+	// 	}
+	// 	cout << "\n";
+	// }
+	vector<bool> visited(v + 1,false);
+	int source = 1;
+	// dfs(source,adj,visited);
+	// bfs(source,adj,visited);
+
+	// Number of Components
+	// The number of times dfs is called the number of components
+	int count = 0;
+	for(int i = 1;i <= v;i++){
+		if(!visited[1]) {
+			dfs(i,adj,visited);
+			count++;
+		};
+	}
+	cout << endl << count << endl;
+	return 0;
+}

Graph/reviseGraph1.cpp

@@ -0,0 +1,61 @@
+#include <iostream>
+#include <queue>
+#include <vector>
+using namespace std;
+class Solution{
+public:
+	bool detectCycleBfs(vector<int> adj[],int src,vector<bool>&vis){
+		queue<pair<int,int>> q;
+		q.push({src,-1});
+		vis[src] = true;
+		while(!q.empty()){
+			int dest = q.front().first;
+			int par = q.front().second;
+			q.pop();
+			for(auto i : adj[dest]){
+				if(!vis[i]){
+					vis[i] = true;
+					q.push({i,dest});
+				}
+				else{
+					if(par != i) return true;
+				}
+			}
+		}
+		return false;
+	}
+	bool detectCycleDfs(vector<int>adj[],int src,int par,vector<bool>&vis){
+		vis[src] = true;
+		for(auto i : adj[src]){
+			if(!vis[i]){
+				if(detectCycleDfs(adj,i,src,vis)) return true;
+			}
+			else if(par != i) return true;
+		}
+		return false;
+	}
+	bool isCycle(vector<int> adj[],int v){
+		vector<bool> vis(v + 1,false);
+		for(int i = 0;i <= v;i++){
+			if(!vis[i] && detectCycleBfs(adj,i,vis)) return true;
+		}
+		return false;
+	}
+};
+
+
+int main(){
+	int v,e;
+	cin >> v >> e;
+	vector<int> adj[v + 1];
+	for(int i = 0;i < e;i++){
+		int a,b;
+		cin >> a >> b;
+		adj[a].push_back(b);
+		adj[b].push_back(a);
+	}
+	Solution s;
+	cout << (s.isCycle(adj,v) ? "true" : "false");
+	return 0;
+}
+

Graph/reviseGraph2.cpp

@@ -0,0 +1,46 @@
+#include <iostream>
+#include <vector>
+using namespace std;
+int dfs(int n,int src,vector<int> adj[],vector<bool>&vis,vector<int>&ans){
+	vis[src] = true;
+	for(auto i : adj[src]){
+		if(!vis[i]) n = dfs(n,i,adj,vis,ans);
+	}
+	ans[n] = src;
+	return n-1;
+}
+void topsort(int v,vector<int> adj[],vector<bool> &vis){
+	vector<int> ans(v);
+	int n = v - 1;
+	// Unoptimized version
+	// for(int i = 1;i <= v;i++){
+	// 	if(!vis[i]){
+	// 		vector<int> visited;
+	// 		dfs(i,adj,vis,visited);
+	// 		for(auto visi : visited){
+	// 			ans[n] = visi;
+	// 			n--;
+	// 		}
+	// 	}
+	// }
+	// Optimized Version
+	for(int i = 1;i <= v;i++){
+		if(!vis[i]){
+			n = dfs(n,i,adj,vis,ans);
+		}
+	}
+	for(auto i : ans) cout << i << " ";
+}
+int main(){
+	int v,e;
+	cin >> v >> e;
+	vector<int> adj[v + 1];
+	vector<bool> vis(v + 1,false);
+	for(int i = 0;i < e;i++){
+		int a,b;
+		cin >> a >> b;
+		adj[a].push_back(b);
+	}
+	topsort(v,adj,vis);
+	return 0;
+}

Graph/reviseGraph3.cpp

@@ -0,0 +1,46 @@
+#include <iostream>
+#include <vector>
+#include <queue>
+using namespace std;
+// Kahn's Algorithm for Topological Ordering
+
+void topsort(int v,vector<int> adj[],vector<bool> &vis){
+	vector<int> inDegree(v + 1,0);
+	for(int i = 0;i < v; i++){
+		for(auto j : adj[i]){
+			inDegree[j]++;
+		}
+	}
+	queue<int> nodes;
+	for(int i = 0;i < v;i++){
+		if(inDegree[i] == 0) nodes.push(i);
+	}
+	vector<int> ans(v);
+	int i = 0;
+	while(!nodes.empty()){
+		int temp = nodes.front();nodes.pop();
+		ans[i++] = temp;
+		for(auto node : adj[temp]){
+			inDegree[node]--;
+			if(inDegree[node] == 0) nodes.push(node);
+		}
+	}
+	if(i != v){
+		cout << "Cycle Found\n";
+		return;
+	}
+	for(auto i : ans) cout << i << " ";
+}
+int main(){
+	int v,e;
+	cin >> v >> e;
+	vector<int> adj[v];
+	vector<bool> vis(v,false);
+	for(int i = 0;i < e;i++){
+		int a,b;
+		cin >> a >> b;
+		adj[a].push_back(b);
+	}
+	topsort(v,adj,vis);
+	return 0;
+}

Graph/reviseGraph4.cpp

@@ -0,0 +1,64 @@
+#include <iostream>
+#include <vector>
+#include <queue>
+#include <climits>
+using namespace std;
+// Kahn's Algorithm for Topological Ordering
+
+vector<int> topsort(int v,vector<pair<int,int>> adj[],vector<bool> &vis){
+	vector<int> inDegree(v,0);
+	for(int i = 0;i < v; i++){
+		for(auto j : adj[i]){
+			inDegree[j.first]++;
+		}
+	}
+	queue<int> nodes;
+	for(int i = 0;i < v;i++){
+		if(inDegree[i] == 0) nodes.push(i);
+	}
+	vector<int> ans(v);
+	int i = 0;
+	while(!nodes.empty()){
+		int temp = nodes.front();nodes.pop();
+		ans[i++] = temp;
+		for(auto node : adj[temp]){
+			inDegree[node.first]--;
+			if(inDegree[node.first] == 0) nodes.push(node.first);
+		}
+	}
+	return ans;
+}
+
+// Shortest/Longest Path on a DAG
+// for longest path we just need to multiply all the edge values with
+// negative one and then find the minimum distanve that way
+// and return the ans after multiplying with negative one
+
+void sssp_dag(int src,int v,vector<pair<int,int>> adj[],vector<int>&ts,vector<int> &dist){
+	dist[src] = 0;
+	for(int i = 0;i < v;i++){
+		int currNode = ts[i];
+		int d = dist[currNode];
+		for(auto node : adj[currNode]){
+			dist[node.first] = min(dist[node.first],d + node.second);
+		}
+	}
+}
+int main(){
+	int v,e;
+	cin >> v >> e;
+	vector<pair<int,int>> adj[v];
+	vector<bool> vis(v,false);
+	for(int i = 0;i < e;i++){
+		int a,b,w;
+		cin >> a >> b >> w;
+		adj[a].push_back({ b, w });
+	}
+	auto ans = topsort(v,adj,vis);
+	vector<int> dist(v,INT_MAX);
+	for(auto i : ans) cout << char('A' + i) << " ";
+	sssp_dag(0,v,adj,ans,dist);
+	cout << "\n"; 
+	for(auto i : ans) cout << dist[i] << " ";
+	return 0;
+}