Given a directed graph G with N vertices and M edges. The task is to find the length of the longest directed path in Graph.
Note: Length of a directed path is the number of edges in it.
Input: N = 4, M = 5
The directed path 1->3->2->4
Input: N = 5, M = 8
Simple Approach: A naive approach is to calculate the length of the longest path from every node using DFS.
The time complexity of this approach is O(N2).
Let dp[i] be the length of the longest path starting from the node i. Initially all positions of dp will be 0. We can call the DFS function from every node and traverse for all its children. The recursive formula will be:
dp[node] = max(dp[node], 1 + max(dp[child1], dp[child2], dp[child3]..))
At the end check for the maximum value in dp array, which will be the longest path in the DAG.
Below is the implementation of the above approach:
Time Complexity: O(N)
Auxiliary Space: O(N)
- Longest Path in a Directed Acyclic Graph | Set 2
- Longest Path in a Directed Acyclic Graph
- Shortest Path in Directed Acyclic Graph
- Clone a Directed Acyclic Graph
- All Topological Sorts of a Directed Acyclic Graph
- Assign directions to edges so that the directed graph remains acyclic
- Number of paths from source to destination in a directed acyclic graph
- Convert the undirected graph into directed graph such that there is no path of length greater than 1
- Find if there is a path between two vertices in a directed graph
- Shortest path with exactly k edges in a directed and weighted graph
- Shortest path with exactly k edges in a directed and weighted graph | Set 2
- Longest subsequence with a given OR value : Dynamic Programming Approach
- DFS for a n-ary tree (acyclic graph) represented as adjacency list
- Calculate number of nodes between two vertices in an acyclic Graph by Disjoint Union method
- Detect Cycle in a Directed Graph using BFS
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