code:-

Copyvoid dfs(vector<vector<int>>&adj, int node, stack<int>&st, vector<bool>&vis){
    vis[node]=true;
    for(auto it:adj[node]){
        if(!vis[it]){
            dfs(adj, it, st, vis);
        }
    }
    st.push(node);
}


vector<int>solve(vector<vector<int>>&adj){
    int n = adj.size();
    vector<bool>vis(n, false);
    stack<int>st;
    dfs(adj, )
    for(int i=0;i<n;i++){
        if(!vis[i])dfs(adj, i, st, vis);
    }
    vector<int>ans;
    while(!st.empty()){
        ans.push_back(st.top());
        st.pop();
    }
    return ans;
}

Kahn's Algorithm (BFS):

here we use modified bfs.

1. Indegree:- array containing number of incomming edges to a node. find the source nodes (indegree[i]==0). insert all source nodes to a queue.

cpp code:-

Copyvector<int> topoSort(vector<vector<int>>&edges, int n){
    vector<int>indegree(n, 0);
    vector<vector<int>>adj(n);
    for(auto [u, v]: edges){
        indegree[v]++;
        adj[u].push_back(v);
    }
    queue<int>q;
    for(int i=0;i<n;i++){
        if(indegree[i]==0)q.push(i);
    }
    vector<int>ans;
    while(!q.empty()){
        int node = q.front();
        q.pop();
        ans.push_back(node);
        for(auto it: adj[node]){
            indegree[it]--;
            if(indegree[it]==0)q.push(it);
        }
    }
    reverse(ans.begin(), ans.end());
    return ans;
}

Cycle detection:

kahn's algorithm can also be used to detect cycles in DAGs. because in a cycle there will not be any node whose indegree will become 0. so you just have to check if the size of the topo array is same as number of nodes or not at last. if it is not same then that means there is a cycle in the graph.