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++ program for the above approach #include <bits/stdc++.h> 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 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<ArrayList<Integer> > 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<ArrayList<Integer>> 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 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# 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<List< int >> 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<List< int >> Adj = new List<List< int >>();
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. |
<script> // Javascript program for the above approach var ans = 0;
// Function to perform DFS // Traversal on the given graph function DFS(src, Adj, arr, currentMin, 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
Adj[src].forEach(child => {
// Recursively call
// for the child node
DFS(child, Adj,arr,
currentMin, currentMax);
});
} // Function to calculate maximum absolute // difference between a node and its ancestor function getMaximumDifference(Edges, arr, N, M)
{ // Stores the adjacency list of graph
var Adj = Array.from(Array(N+1), ()=> Array());
// Create Adjacency list
for ( var i = 0; i < M; i++) {
var u = Edges[i][0];
var v = Edges[i][1];
// Add a directed edge
Adj[u].push(v);
}
// Perform DFS Traversal
DFS(1, Adj, arr,
arr[0], arr[0]);
// Print the maximum
// absolute difference
document.write( ans);
} // Driver Code var N = 5, M = 4;
var Edges
= [ [ 1, 2 ], [ 2, 3 ],
[ 4, 5 ], [ 1, 3 ] ];
var arr = [13, 8, 3, 15, 18];
getMaximumDifference(Edges, arr, N, M); </script> |
10
Time Complexity: O(N + M)
Auxiliary Space: O(N)