Largest gap in an array
Given an unsorted array of length N, and we have to find the largest gap between any two elements of the array. In simple words, find max(|Ai-Aj|) where 1 ? i ? N and 1 ? j ? N.
Examples:
Input : arr = {3, 10, 6, 7} Output : 7 Explanation : Here, we can see largest gap can be found between 3 and 10 which is 7 Input : arr = {-3, -1, 6, 7, 0} Output : 10 Explanation : Here, we can see largest gap can be found between -3 and 7 which is 10
Simple Approach:
A simple solution is, we can use a naive approach. We will check the absolute difference of every pair in the array, and we will find the maximum value of it. So we will run two loops one is for i and one is for j complexity of this method is O(N^2)
Implementation:
C++
// A C++ program to find largest gap // between two elements in an array. #include<bits/stdc++.h> using namespace std; // function to solve the given problem int solve( int a[], int n) { int max1 = INT_MIN; for ( int i = 0; i < n; i++) { for ( int j = 0; j < n; j++) { if ( abs (a[i] - a[j]) > max1) { max1 = abs (a[i] - a[j]); } } } return max1; } // Driver Code int main() { int arr[] = { -1, 2, 3, -4, -10, 22 }; int size = sizeof (arr) / sizeof (arr[0]); cout << "Largest gap is : " << solve(arr, size); return 0; } // This code is contributed // by Akanksha Rai |
C
// A C program to find largest gap // between two elements in an array. #include <limits.h> #include <stdio.h> #include <stdlib.h> // function to solve the given problem int solve( int a[], int n) { int max1 = INT_MIN; for ( int i = 0; i < n; i++) { for ( int j = 0; j < n; j++) { if ( abs (a[i] - a[j]) > max1) { max1 = abs (a[i] - a[j]); } } } return max1; } int main() { int arr[] = { -1, 2, 3, -4, -10, 22 }; int size = sizeof (arr) / sizeof (arr[0]); printf ( "Largest gap is : %d" , solve(arr, size)); return 0; } |
Java
// A Java program to find // largest gap between // two elements in an array. import java .io.*; class GFG { // function to solve // the given problem static int solve( int []a, int n) { int max1 = Integer.MIN_VALUE ; for ( int i = 0 ; i < n; i++) { for ( int j = 0 ; j < n; j++) { if (Math.abs(a[i] - a[j]) > max1) { max1 = Math.abs(a[i] - a[j]); } } } return max1; } // Driver Code static public void main (String[] args) { int []arr = {- 1 , 2 , 3 , - 4 , - 10 , 22 }; int size = arr.length; System.out.println( "Largest gap is : " + solve(arr, size)); } } // This code is contributed // by anuj_67. |
Python3
# A Python 3 program to find largest gap # between two elements in an array. import sys # function to solve the given problem def solve(a, n): max1 = - sys.maxsize - 1 for i in range ( 0 , n, 1 ): for j in range ( 0 , n, 1 ): if ( abs (a[i] - a[j]) > max1): max1 = abs (a[i] - a[j]) return max1 # Driver Code if __name__ = = '__main__' : arr = [ - 1 , 2 , 3 , - 4 , - 10 , 22 ] size = len (arr) print ( "Largest gap is :" , solve(arr, size)) # This code is contributed by # Sanjit_Prasad |
C#
// A C# program to find // largest gap between // two elements in an array. using System; class GFG { // function to solve // the given problem static int solve( int []a, int n) { int max1 = int .MinValue ; for ( int i = 0; i < n; i++) { for ( int j = 0; j < n; j++) { if (Math.Abs(a[i] - a[j]) > max1) { max1 = Math.Abs(a[i] - a[j]); } } } return max1; } // Driver Code static public void Main () { int []arr = {-1, 2, 3, -4, -10, 22}; int size = arr.Length; Console.WriteLine( "Largest gap is : " + solve(arr, size)); } } // This code is contributed // by anuj_67. |
PHP
<?php // A PHP program to find // largest gap between // two elements in an array. // function to solve // the given problem function solve( $a , $n ) { $max1 = PHP_INT_MIN; for ( $i = 0; $i < $n ; $i ++) { for ( $j = 0; $j < $n ; $j ++) { if ( abs ( $a [ $i ] - $a [ $j ]) > $max1 ) { $max1 = abs ( $a [ $i ] - $a [ $j ]); } } } return $max1 ; } // Driver Code $arr = array (-1, 2, 3, -4, -10, 22); $size = count ( $arr ); echo "Largest gap is : " , solve( $arr , $size ); // This code is contributed // by anuj_67. ?> |
Javascript
<script> // A Javascript program to find // largest gap between // two elements in an array. // function to solve // the given problem function solve(a,n) { let max1 = Number.MIN_VALUE ; for (let i = 0; i < n; i++) { for (let j = 0; j < n; j++) { if (Math.abs(a[i] - a[j]) > max1) { max1 = Math.abs(a[i] - a[j]); } } } return max1; } // Driver Code let arr=[-1, 2, 3, -4, -10, 22]; let size = arr.length; document.write( "Largest gap is : " + solve(arr, size)); // This code is contributed by rag2127 </script> |
Largest gap is : 32
Time Complexity: O(N2)
Space Complexity: O(1)
Better Approach:
Now we will see a better approach it is a greedy approach that can solve this problem in O(N). We will find the maximum and minimum element of the array which can be done in O(N) and then we will return the value of (maximum-minimum).
Implementation:
C++
// A C++ program to find largest gap between // two elements in an array. #include<bits/stdc++.h> using namespace std; // function to solve the given problem int solve( int a[], int n) { int min1 = a[0]; int max1 = a[0]; // finding maximum and minimum of an array for ( int i = 0; i < n; i++) { if (a[i] > max1) max1 = a[i]; if (a[i] < min1) min1 = a[i]; } return abs (min1 - max1); } // Driver code int main() { int arr[] = { -1, 2, 3, 4, -10 }; int size = sizeof (arr) / sizeof (arr[0]); cout << "Largest gap is : " << solve(arr, size); return 0; } //This code is contributed by Mukul Singh. |
C
// A C program to find largest gap between // two elements in an array. #include <limits.h> #include <stdio.h> #include <stdlib.h> // function to solve the given problem int solve( int a[], int n) { int min1 = a[0]; int max1 = a[0]; // finding maximum and minimum of an array for ( int i = 0; i < n; i++) { if (a[i] > max1) max1 = a[i]; if (a[i] < min1) min1 = a[i]; } return abs (min1 - max1); } int main() { int arr[] = { -1, 2, 3, 4, -10 }; int size = sizeof (arr) / sizeof (arr[0]); printf ( "Largest gap is : %d" , solve(arr, size)); return 0; } |
Java
// A Java program to find largest gap // between two elements in an array. import java.io.*; class GFG { // function to solve the given // problem static int solve( int a[], int n) { int min1 = a[ 0 ]; int max1 = a[ 0 ]; // finding maximum and minimum // of an array for ( int i = 0 ; i < n; i++) { if (a[i] > max1) max1 = a[i]; if (a[i] < min1) min1 = a[i]; } return Math.abs(min1 - max1); } // Driver code public static void main (String[] args) { int []arr = { - 1 , 2 , 3 , 4 , - 10 }; int size = arr.length; System.out.println( "Largest gap is : " + solve(arr, size)); } } // This code is contributed by anuj_67. |
Python3
# A python 3 program to find largest gap between # two elements in an array. # function to solve the given problem def solve(a, n): min1 = a[ 0 ] max1 = a[ 0 ] # finding maximum and minimum of an array for i in range ( n): if (a[i] > max1): max1 = a[i] if (a[i] < min1): min1 = a[i] return abs (min1 - max1) # Driver code if __name__ = = "__main__" : arr = [ - 1 , 2 , 3 , 4 , - 10 ] size = len (arr) print ( "Largest gap is : " ,solve(arr, size)) # This code is contributed by chitranayal |
C#
// A C# program to find // largest gap between // two elements in an array. using System; class GFG { // function to solve // the given problem static int solve( int []a, int n) { int min1 = a[0]; int max1 = a[0]; // finding maximum and // minimum of an array for ( int i = 0; i < n; i++) { if (a[i] > max1) max1 = a[i]; if (a[i] < min1) min1 = a[i]; } return Math.Abs(min1 - max1); } // Driver code public static void Main () { int []arr = {-1, 2, 3, 4, -10}; int size = arr.Length; Console.WriteLine( "Largest gap is : " + solve(arr, size)); } } // This code is contributed // by anuj_67. |
PHP
<?php // A PHP program to find // largest gap between // two elements in an array. // function to solve // the given problem function solve( $a , $n ) { $min1 = $a [0]; $max1 = $a [0]; // finding maximum and // minimum of an array for ( $i = 0; $i < $n ; $i ++) { if ( $a [ $i ] > $max1 ) $max1 = $a [ $i ]; if ( $a [ $i ] < $min1 ) $min1 = $a [ $i ]; } return abs ( $min1 - $max1 ); } // Driver Code $arr = array (-1, 2, 3, 4, -10); $size = count ( $arr ); echo "Largest gap is : " , solve( $arr , $size ); // This code is contributed // by anuj_67. ?> |
Javascript
<script> // A Javascript program to find largest gap // between two elements in an array. // function to solve the given // problem function solve(a,n) { let min1 = a[0]; let max1 = a[0]; // finding maximum and minimum // of an array for (let i = 0; i < n; i++) { if (a[i] > max1) max1 = a[i]; if (a[i] < min1) min1 = a[i]; } return Math.abs(min1 - max1); } // Driver code let arr=[-1, 2, 3, 4, -10 ]; let size = arr.length; document.write( "Largest gap is : " + solve(arr, size)); // This code is contributed by avanitrachhadiya2155 </script> |
Largest gap is : 14
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