Question

I need pseudocode based on the depth-first search to find the longest path in a DAG, assuming all edges have the same weight.

Answer 1

Pseudo Code:

/* We will use dynamic programming using dfs. Let dp[node] be the longest path distance from node
@params:
int node: current node
vector<int> adj[]: Adjacency list of graph
int dp[]: array to store longest path distance
bool vis[]: visited array*/

void dfs(node,adj,dp,vis):
START
vis[node] <- true //mark node as visited
for i = 0 to adj[node].size():
v <- adj[node][i] //neighbour node
if(vis[v]=false):
dfs(v, adj, dp, vis)
if(1 + dp[v]>dp[node]):
dp[node] <- 1 + dp[v]
END
  
/*@params
vector<int> adj[]: Adjacency list of graph
int n: number of nodes
int wt = weight of each edge*/
  
void findLongestPath(vector<int> adj[], int n, int wt):
START
   // Dp array initialized to 0
   dp[n + 1] <- {0}
// visited array initialized to false
   vis[n + 1] <- {false}
   for i = 1 to n+1:
       if (vis[i]=false) :
           dfs(i, adj, dp, vis);
   ans //to store number of edges in longest path
   max //to store the vertex from which the longest path will start
   // find the maximum of all dp[i]
   for i = 1 to n+1:
       if(dp[i]>ans):
       ans = dp[i]
       max = i
  
   print "The longest path contain "+ans+" edges. It syarts from node "+max+". Total cost: "+ans*wt
END