### mkitkat's blog

By mkitkat, history, 2 years ago,

Help with the approach and code in C++. Thanks I have tried Dijkstra by make every edge weights to -1. But I am not able to print the longest path.

• 0

 » 2 years ago, # |   +1 Naive approach : Do BFS from every non visited node and keep track of farthest node which is reachable (let's say it's pathlength as COUNT) & mark every intermediate node visited. take maximum of all COUNT and print path from node(which is giving max COUNT) to Farthest node. I think it should work :)
 » 2 years ago, # |   0 Find a topological sort of the given graph and do dp on it. dp[u] is the length of the longest path which ends in node u. Initially dp[u] = 0 for every u. To calculate this dp go from left to right in topological order and if the current node is u, for every node v such that there is edge from u to v dp[v] = max(dp[v], dp[u] + 1). Then the length of the longest path in the graph is the maximal element in the dp array. To restore the longest path find any u such that dp[u] = max and go through reverse edges of the graph to any v such that dp[v] = dp[u] — 1, until dp[u] is not zero and add u to your answer array. Reverse the answer and it will be one of the possible longest paths in the given DAG. Complexity is O(N + M).
•  » » 2 years ago, # ^ |   0 Hi, Thanks got it
•  » » 7 weeks ago, # ^ |   0 can you just share the implement part of reverse going in dp[u]-1 --> dp[u]-2 -->0
 » 2 years ago, # |   +1 You can practice the same concept on atcoder — https://atcoder.jp/contests/dp/tasks/dp_g
 » 19 months ago, # |   0 do simple dfs on nodes and store longest path in a dp Spoiler...import sys sys.setrecursionlimit(10**9)def dfs (edges , e , visited ,dp): visited[e] = True for i in edges[e]: if not visited[i]: dfs(edges,i,visited,dp) dp[e] = max(dp[e],dp[i]+1) return dp[e]n,m = map(int, input().split()) edges = [[] for i in range(n + 1)] for i in range(m): u,v = map(int, input().split()) edges[u].append(v) dp = [0] * (n + 1) visited = [False] * (n + 1) for i in range(1,n+1): if not visited[i]: dp[i] = dfs(edges,i,visited,dp) if len(dp) > 0 : print(max(dp)) else : print(0)