topsort cycle check added

Author: zarif98sjs

Algorithm/41.2 Cycle Check Directed 2.cpp

@@ -0,0 +1,164 @@
+
+/**
+
+Cycle check (Directed Graph)
+===========
+
+Here the idea is to use TOP SORT .
+After top sort , let the topological order be like this
+
+A -> B -> C -> D
+
+if there is an edge from A to D (i.e from lower position to higher position in topological order) , it won't create a cycle .
+BUT if there is an edge from D to A (i.e from higher position to lower position in topological order) , it WILL create a cycle .
+
+This is the core idea behind cycle checking here .
+
+Idea
+====
+
+For each edge we check if it connects from higher position to lower position in topological order .
+If we find one like this , there is a cycle
+
+Complexity : O(V+E)
+
+**/
+
+/**Which of the favors of your Lord will you deny ?**/
+
+#include<bits/stdc++.h>
+using namespace std;
+
+#define LL long long
+#define PII pair<int,int>
+#define PLL pair<LL,LL>
+#define MP make_pair
+#define F first
+#define S second
+#define INF INT_MAX
+
+#define ALL(x) (x).begin(), (x).end()
+#define DBG(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << endl
+
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+using namespace __gnu_pbds;
+
+template<class TIn>
+using indexed_set = tree<
+                    TIn, null_type, less<TIn>,
+                    rb_tree_tag, tree_order_statistics_node_update>;
+
+/**
+
+PBDS
+-------------------------------------------------
+1) insert(value)
+2) erase(value)
+3) order_of_key(value) // 0 based indexing
+4) *find_by_order(position) // 0 based indexing
+
+**/
+
+inline void optimizeIO()
+{
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+}
+
+const int nmax = 2e5+7;
+const LL LINF = 1e17;
+
+string to_str(LL x)
+{
+    stringstream ss;
+    ss<<x;
+    return ss.str();
+}
+
+vector<vector<int>>adj;
+
+vector<bool>vis;
+vector<int>stk;
+vector<int>pos;
+
+void dfs(int u)
+{
+    vis[u] = true;
+
+    for(int v:adj[u])
+    {
+        if(vis[v])
+            continue;
+
+        dfs(v);
+    }
+
+    stk.push_back(u);
+}
+
+bool hasCycle(int n,const vector<PII> &dir_edges)
+{
+    fill(ALL(vis),0);
+
+    for(int i=1; i<=n; i++)
+        if(!vis[i])
+            dfs(i);
+
+    int cnt = 0;
+
+    while(!stk.empty())
+    {
+        int now = stk.back();
+        stk.pop_back();
+        pos[now] = ++cnt;
+    }
+
+    for(auto e:dir_edges)
+    {
+        int u = e.F , v = e.S;
+
+        if(pos[u]>pos[v]) /** edge is from RIGHT to LEFT in the topological order and that's why creating cycle **/
+            return true;
+    }
+
+    return false;
+}
+
+void RESIZE(int n)
+{
+    adj = vector<vector<int>>(n);
+    vis = vector<bool>(n);
+    pos = vector<int>(n);
+    stk.clear();
+}
+
+int main()
+{
+    optimizeIO();
+
+    int n,m;
+    cin>>n>>m;
+
+    RESIZE(n+1);
+
+    vector<PII>dir_ed;
+
+    for(int i=0;i<m;i++)
+    {
+        int a,b;
+        cin>>a>>b;
+
+        adj[a].push_back(b);
+        dir_ed.push_back({a,b});
+    }
+
+    bool cycle = hasCycle(n,dir_ed);
+
+    if(cycle) cout<<"Has Cycle"<<endl;
+    else cout<<"No Cycle"<<endl;
+
+    return 0;
+}
+
+