# Maximum difference between node and its ancestor in a Directed Acyclic Graph ( DAG )

Last Updated : 14 Sep, 2021

Given a 2D array Edges[][], representing a directed edge between the pair of nodes in a Directed Acyclic Connected Graph consisting of N nodes valued from [1, N] and an array arr[] representing weights of each node, the task is to find the maximum absolute difference between the weights of any node and any of its ancestors.

Examples:

Input: N = 5, M = 4, Edges[][2] = {{1, 2}, {2, 3}, {4, 5}, {1, 3}}, arr[] = {13, 8, 3, 15, 18}
Output: 10
Explanation:

From the above graph, it can be observed that the maximum difference between the value of any node and any of its ancestors is 18 (Node 5) – 8 (Node 2) = 10.

Input: N = 4, M = 3, Edges[][2] = {{1, 2}, {2, 4}, {1, 3}}, arr[] = {2, 3, 1, 5}
Output: 3

Approach: The idea to solve the given problem is to perform DFS Traversal on the Graph and populate the maximum and minimum values from each node to its child node and find the maximum absolute difference.
Follow the steps below to solve the given problem:

• Initialize a variable, say ans as INT_MIN to store the required maximum difference.
• Perform DFS traversal on the given graph to find the maximum absolute difference between the weights of a node and any of its ancestors by performing the following operations:
• For each source node, say src, update the value of ans to store the maximum of the absolute difference between the weight of src and currentMin and currentMax respectively.
• Update the value of currentMin as the minimum of currentMin and the value of the source node src.
• Update the value of currentMax as the maximum of currentMax and the value of the source node src.
• Now, recursively traverse the child nodes of src and update values of currentMax and currentMin as DFS(child, Adj, ans, currentMin, currentMax).
• After completing the above steps, print the value of ans as the resultant maximum difference.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ` `using` `namespace` `std;`   `// Function to perform DFS` `// Traversal on the given graph` `void` `DFS(``int` `src, vector<``int``> Adj[],` `         ``int``& ans, ``int` `arr[],` `         ``int` `currentMin, ``int` `currentMax)` `{`   `    ``// Update the value of ans` `    ``ans = max(` `        ``ans, max(``abs``(` `                     ``currentMax - arr[src - 1]),` `                 ``abs``(currentMin - arr[src - 1])));`   `    ``// Update the currentMin and currentMax` `    ``currentMin = min(currentMin,` `                     ``arr[src - 1]);`   `    ``currentMax = min(currentMax,` `                     ``arr[src - 1]);`   `    ``// Traverse the adjacency` `    ``// list of the node src` `    ``for` `(``auto``& child : Adj[src]) {`   `        ``// Recursively call` `        ``// for the child node` `        ``DFS(child, Adj, ans, arr,` `            ``currentMin, currentMax);` `    ``}` `}`   `// Function to calculate maximum absolute` `// difference between a node and its ancestor` `void` `getMaximumDifference(``int` `Edges[][2],` `                          ``int` `arr[], ``int` `N,` `                          ``int` `M)` `{`   `    ``// Stores the adjacency list of graph` `    ``vector<``int``> Adj[N + 1];`   `    ``// Create Adjacency list` `    ``for` `(``int` `i = 0; i < M; i++) {` `        ``int` `u = Edges[i][0];` `        ``int` `v = Edges[i][1];`   `        ``// Add a directed edge` `        ``Adj[u].push_back(v);` `    ``}`   `    ``int` `ans = 0;`   `    ``// Perform DFS Traversal` `    ``DFS(1, Adj, ans, arr,` `        ``arr[0], arr[0]);`   `    ``// Print the maximum` `    ``// absolute difference` `    ``cout << ans;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `N = 5, M = 4;` `    ``int` `Edges[][2]` `        ``= { { 1, 2 }, { 2, 3 },` `            ``{ 4, 5 }, { 1, 3 } };` `    ``int` `arr[] = { 13, 8, 3, 15, 18 };`   `    ``getMaximumDifference(Edges, arr, N, M);`   `    ``return` `0;` `}`

## Java

 `// Java program for the above approach` `import` `java.util.*;`   `class` `GFG{` `    `  `static` `int` `ans;`   `// Function to perform DFS` `// Traversal on the given graph` `static` `void` `DFS(``int` `src,` `                ``ArrayList > Adj,` `                ``int` `arr[], ``int` `currentMin,` `                ``int` `currentMax)` `{` `    `  `    ``// Update the value of ans` `    ``ans = Math.max(ans,` `          ``Math.max(Math.abs(currentMax - arr[src - ``1``]),` `                   ``Math.abs(currentMin - arr[src - ``1``])));`   `    ``// Update the currentMin and currentMax` `    ``currentMin = Math.min(currentMin, arr[src - ``1``]);`   `    ``currentMax = Math.min(currentMax, arr[src - ``1``]);`   `    ``// Traverse the adjacency` `    ``// list of the node src` `    ``for``(Integer child : Adj.get(src))` `    ``{` `        `  `        ``// Recursively call` `        ``// for the child node` `        ``DFS(child, Adj, arr, currentMin, currentMax);` `    ``}` `}`   `// Function to calculate maximum absolute` `// difference between a node and its ancestor` `static` `void` `getMaximumDifference(``int` `Edges[][],` `                                 ``int` `arr[], ``int` `N,` `                                 ``int` `M)` `{` `    ``ans = ``0``;` `    `  `    ``// Stores the adjacency list of graph` `    ``ArrayList> Adj = ``new` `ArrayList<>();`   `    ``for``(``int` `i = ``0``; i < N + ``1``; i++)` `        ``Adj.add(``new` `ArrayList<>());`   `    ``// Create Adjacency list` `    ``for``(``int` `i = ``0``; i < M; i++) ` `    ``{` `        ``int` `u = Edges[i][``0``];` `        ``int` `v = Edges[i][``1``];`   `        ``// Add a directed edge` `        ``Adj.get(u).add(v);` `    ``}`   `    ``// Perform DFS Traversal` `    ``DFS(``1``, Adj, arr, arr[``0``], arr[``0``]);`   `    ``// Print the maximum` `    ``// absolute difference` `    ``System.out.println(ans);` `}`   `// Driver code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `N = ``5``, M = ``4``;` `    ``int` `Edges[][] = { { ``1``, ``2` `}, { ``2``, ``3` `}, ` `                      ``{ ``4``, ``5` `}, { ``1``, ``3` `} };` `    ``int` `arr[] = { ``13``, ``8``, ``3``, ``15``, ``18` `};`   `    ``getMaximumDifference(Edges, arr, N, M);` `}` `}`   `// This code is contributed by offbeat`

## Python3

 `# Python3 program for the above approach` `ans ``=` `0`   `# Function to perform DFS` `# Traversal on the given graph` `def` `DFS(src, Adj, arr, currentMin, currentMax):` `    `  `    ``# Update the value of ans` `    ``global` `ans` `    ``ans ``=` `max``(ans, ``max``(``abs``(currentMax ``-` `arr[src ``-` `1``]),` `                       ``abs``(currentMin ``-` `arr[src ``-` `1``])))`   `    ``# Update the currentMin and currentMax` `    ``currentMin ``=` `min``(currentMin, arr[src ``-` `1``])`   `    ``currentMax ``=` `min``(currentMax, arr[src ``-` `1``])`   `    ``# Traverse the adjacency` `    ``# list of the node src` `    ``for` `child ``in` `Adj[src]:` `        `  `        ``# Recursively call` `        ``# for the child node` `        ``DFS(child, Adj, arr, currentMin, currentMax)`   `# Function to calculate maximum absolute` `# difference between a node and its ancestor` `def` `getMaximumDifference(Edges, arr, N, M):` `    `  `    ``global` `ans` `    `  `    ``# Stores the adjacency list of graph` `    ``Adj ``=` `[[] ``for` `i ``in` `range``(N ``+` `1``)]`   `    ``# Create Adjacency list` `    ``for` `i ``in` `range``(M):` `        ``u ``=` `Edges[i][``0``]` `        ``v ``=` `Edges[i][``1``]`   `        ``# Add a directed edge` `        ``Adj[u].append(v)`   `    ``# Perform DFS Traversal` `    ``DFS(``1``, Adj, arr, arr[``0``], arr[``0``])`   `    ``# Print the maximum` `    ``# absolute difference` `    ``print``(ans)`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    `  `    ``N ``=` `5` `    ``M ``=` `4` `    ``Edges ``=` `[[``1``, ``2``], [``2``, ``3``], [``4``, ``5``], [``1``, ``3``]]` `    ``arr ``=`  `[``13``, ``8``, ``3``, ``15``, ``18``]` `    `  `    ``getMaximumDifference(Edges, arr, N, M)`   `# This code is contributed by ipg2016107`

## C#

 `// C# program for the above approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG {` `    `  `    ``static` `int` `ans;` ` `  `    ``// Function to perform DFS` `    ``// Traversal on the given graph` `    ``static` `void` `DFS(``int` `src, List> Adj, ``int``[] arr, ` `                    ``int` `currentMin, ``int` `currentMax)` `    ``{` `         `  `        ``// Update the value of ans` `        ``ans = Math.Max(ans,` `              ``Math.Max(Math.Abs(currentMax - arr[src - 1]),` `                       ``Math.Abs(currentMin - arr[src - 1])));` `     `  `        ``// Update the currentMin and currentMax` `        ``currentMin = Math.Min(currentMin, arr[src - 1]);` `     `  `        ``currentMax = Math.Min(currentMax, arr[src - 1]);` `     `  `        ``// Traverse the adjacency` `        ``// list of the node src` `        ``foreach``(``int` `child ``in` `Adj[src])` `        ``{` `             `  `            ``// Recursively call` `            ``// for the child node` `            ``DFS(child, Adj, arr, currentMin, currentMax);` `        ``}` `    ``}` `     `  `    ``// Function to calculate maximum absolute` `    ``// difference between a node and its ancestor` `    ``static` `void` `getMaximumDifference(``int``[,] Edges, ` `                                     ``int``[] arr, ``int` `N, ``int` `M)` `    ``{` `        ``ans = 0;` `         `  `        ``// Stores the adjacency list of graph` `        ``List> Adj = ``new` `List>();` `     `  `        ``for``(``int` `i = 0; i < N + 1; i++)` `            ``Adj.Add(``new` `List<``int``>());` `     `  `        ``// Create Adjacency list` `        ``for``(``int` `i = 0; i < M; i++)` `        ``{` `            ``int` `u = Edges[i,0];` `            ``int` `v = Edges[i,1];` `     `  `            ``// Add a directed edge` `            ``Adj[u].Add(v);` `        ``}` `     `  `        ``// Perform DFS Traversal` `        ``DFS(1, Adj, arr, arr[0], arr[0]);` `     `  `        ``// Print the maximum` `        ``// absolute difference` `        ``Console.WriteLine(ans);` `    ``}` `    `  `  ``static` `void` `Main() {` `    ``int` `N = 5, M = 4;` `    ``int``[,] Edges = { { 1, 2 }, { 2, 3 },` `                      ``{ 4, 5 }, { 1, 3 } };` `    ``int``[] arr = { 13, 8, 3, 15, 18 };` ` `  `    ``getMaximumDifference(Edges, arr, N, M);` `  ``}` `}`   `// This code is contributed by rameshtravel07.`

## Javascript

 ``

Output:

`10`

Time Complexity: O(N + M)
Auxiliary Space: O(N)

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