Minimize difference between maximum and minimum element of all possible subarrays (original) (raw)

Last Updated : 10 Sep, 2021

Given an array arr[ ] of size N, the task is to find the minimum difference between maximum and minimum elements of all possible sized subarrays of arr[ ].

Examples:

Input: arr[] ={ 5, 14, 7, 10 }
Output: 3
Explanation: {7, 10} is the subarray having max element = 10 & min element = 7, and their difference = 10 - 7 = 3

Input: arr[] = { 2, 6, 15, 7, 6 }
Output: 1
Explanation: {7, 6} is the subarray having max element = 7 & min element = 6, and their difference = 7 - 6 = 1

Approach: The simple idea is to use two loops and check for every subarray, the minimum difference between the maximum and the minimum element. Keep track of the differences and return the minimum possible difference. Time Complexity for this approach would be Quadratic.

Efficient Approach: The idea is to use the fact that we can get minimum difference by iterating over only the subarrays of size two.
Suppose we have two elements in our subarray. Let the difference between maximum and minimum element be x. Now if we include an element from either the right side or left side to our subarray, the maximum element or minimum element might get updated. This change will ultimately make our difference x increase, as either max or min element is getting updated.

Follow the below steps to implement the above approach:

Iterate the array and keep track of the minimum adjacent difference
Print this min difference as the result.

Below is the implementation of the above approach:

C++ `

// C++ program for the above approach #include <bits/stdc++.h> using namespace std;

// Function to get the min difference // between max and min element of all // possible subarrays int getMinDifference(int arr[], int n) { // To store the adjacent difference int diff;

// To compare with min difference
int mn = INT_MAX;

for (int i = 1; i < n; i++) {

    // Storing adjacent difference
    diff = abs(arr[i] - arr[i - 1]);

    // Updating the min difference
    mn = min(diff, mn);
}

// Returning min difference
return mn;

}

// Driver code int main() {

int arr[] = { 2, 6, 15, 7, 6 };
int N = sizeof(arr) / sizeof(arr[0]);
cout << getMinDifference(arr, N);
return 0;

}

Java

// Java program for the above approach import java.io.*;

class GFG{

// Function to get the min difference // between max and min element of all // possible subarrays static int getMinDifference(int []arr, int n) { // To store the adjacent difference int diff = 0;

// To compare with min difference
int mn = Integer.MAX_VALUE;

for (int i = 1; i < n; i++) {

    // Storing adjacent difference
    diff = Math.abs(arr[i] - arr[i - 1]);

    // Updating the min difference
    mn = Math.min(diff, mn);
}

// Returning min difference
return mn;

}

// Driver code public static void main (String[] args) {

int []arr = {2, 6, 15, 7, 6 };
int N = arr.length;
System.out.println(getMinDifference(arr, N));

} }

// This code is contributed by shivanisinghss2110

Python3

Python3 program for the above approach

import sys,math

Function to get the min difference

between max and min element of all

possible subarrays

def getMinDifference(arr, n) :

INT_MAX = sys.maxsize;

# To compare with min difference
mn = INT_MAX;

for i in range(1, n):

    # Storing adjacent difference
    diff = abs(arr[i] - arr[i - 1]);

    # Updating the min difference
    mn = min(diff, mn);

# Returning min difference
return mn;

Driver code

if name == "main" :

arr = [ 2, 6, 15, 7, 6 ];
N = len(arr);
print(getMinDifference(arr, N));

# This code is contributed by AnkThon

C#

// C# program for the above approach using System; using System.Collections.Generic;

class GFG{

// Function to get the min difference // between max and min element of all // possible subarrays static int getMinDifference(int []arr, int n) { // To store the adjacent difference int diff = 0;

// To compare with min difference
int mn = Int32.MaxValue;

for (int i = 1; i < n; i++) {

    // Storing adjacent difference
    diff = Math.Abs(arr[i] - arr[i - 1]);

    // Updating the min difference
    mn = Math.Min(diff, mn);
}

// Returning min difference
return mn;

}

// Driver code public static void Main() {

int []arr = {2, 6, 15, 7, 6 };
int N = arr.Length;
Console.Write(getMinDifference(arr, N));

} }

// This code is contributed by SURENDRA_GANGWAR.

JavaScript