Find minimum difference between any two elements

1.3

Given an unsorted array, find the minimum difference between any pair in given array.

Examples :

Input  : {1, 5, 3, 19, 18, 25};
Output : 1
Minimum difference is between 18 and 19

Input  : {30, 5, 20, 9};
Output : 4
Minimum difference is between 5 and 9

Input  : {1, 19, -4, 31, 38, 25, 100};
Output : 5
Minimum difference is between 1 and -4

Method 1 (Simple: O(n2)
A simple solution is to use two loops.

C/C++

// C++ implementation of simple method to find
// minimum difference between any pair
#include <bits/stdc++.h>
using namespace std;

// Returns minimum difference between any pair
int findMinDiff(int arr[], int n)
{
   // Initialize difference as infinite
   int diff = INT_MAX;

   // Find the min diff by comparing difference
   // of all possible pairs in given array
   for (int i=0; i<n-1; i++)
      for (int j=i+1; j<n; j++)
          if (abs(arr[i] - arr[j]) < diff)
                diff = abs(arr[i] - arr[j]);

   // Return min diff
   return diff;
}

// Driver code
int main()
{
   int arr[] = {1, 5, 3, 19, 18, 25};
   int n = sizeof(arr)/sizeof(arr[0]);
   cout << "Minimum difference is " << findMinDiff(arr, n);
   return 0;
}

Java

// Java implementation of simple method to find
// minimum difference between any pair

class GFG
{
	// Returns minimum difference between any pair
	static int findMinDiff(int[] arr, int n)
	{
		// Initialize difference as infinite
		int diff = Integer.MAX_VALUE;
	
		// Find the min diff by comparing difference
		// of all possible pairs in given array
		for (int i=0; i<n-1; i++)
			for (int j=i+1; j<n; j++)
				if (Math.abs((arr[i] - arr[j]) )< diff)
					diff = Math.abs((arr[i] - arr[j]));
	
		// Return min diff	
		return diff;
	}

	// Driver method to test the above function
	public static void main(String[] args)
	{
		int arr[] = new int[]{1, 5, 3, 19, 18, 25};
		System.out.println("Minimum difference is "+
		                      findMinDiff(arr, arr.length));
	
	}
}

Python

# Python implementation of simple method to find
# minimum difference between any pair

# Returns minimum difference between any pair
def findMinDiff(arr, n):
    # Initialize difference as infinite
    diff = 10**20
    
    # Find the min diff by comparing difference
    # of all possible pairs in given array
    for i in range(n-1):
        for j in range(i+1,n):
            if abs(arr[i]-arr[j]) < diff:
                diff = abs(arr[i] - arr[j])

    # Return min diff
    return diff

# Driver code
arr = [1, 5, 3, 19, 18, 25]
n = len(arr)
print("Minimum difference is " + str(findMinDiff(arr, n)))

# This code is contributed by Pratik Chhajer


Output :
Minimum difference is 1

 
Method 2 (Efficient: O(n Log n)
The idea is to use sorting. Below are steps.
1) Sort array in ascending order. This step takes O(n Log n) time.
2) Initialize difference as infinite. This step takes O(1) time.
3) Compare all adjacent pairs in sorted array and keep track of minimum difference. This step takes O(n) time.

Below is implementation of above idea.

C++

// C++ program to find minimum difference between
// any pair in an unsorted array
#include <bits/stdc++.h>
using namespace std;

// Returns minimum difference between any pair
int findMinDiff(int arr[], int n)
{
   // Sort array in non-decreasing order
   sort(arr, arr+n);

   // Initialize difference as infinite
   int diff = INT_MAX;

   // Find the min diff by comparing adjacent
   // pairs in sorted array
   for (int i=0; i<n-1; i++)
      if (arr[i+1] - arr[i] < diff)
          diff = arr[i+1] - arr[i];

   // Return min diff
   return diff;
}

// Driver code
int main()
{
   int arr[] = {1, 5, 3, 19, 18, 25};
   int n = sizeof(arr)/sizeof(arr[0]);
   cout << "Minimum difference is " << findMinDiff(arr, n);
   return 0;
}

Java

// Java program to find minimum difference between
// any pair in an unsorted array

import java.util.Arrays;

class GFG
{
	// Returns minimum difference between any pair
	static int findMinDiff(int[] arr, int n)
	{
		   // Sort array in non-decreasing order
		   Arrays.sort(arr);
		 
		   // Initialize difference as infinite
		   int diff = Integer.MAX_VALUE;
		 
		   // Find the min diff by comparing adjacent
		   // pairs in sorted array
		   for (int i=0; i<n-1; i++)
		      if (arr[i+1] - arr[i] < diff)
		          diff = arr[i+1] - arr[i];
		 
		   // Return min diff
		   return diff;
	}

	// Driver method to test the above function
	public static void main(String[] args)
	{
		int arr[] = new int[]{1, 5, 3, 19, 18, 25};
		System.out.println("Minimum difference is "+
		                      findMinDiff(arr, arr.length));
	
	}
}

Python

# Python program to find minimum difference between
# any pair in an unsorted array

# Returns minimum difference between any pair
def findMinDiff(arr, n):

    # Sort array in non-decreasing order
    arr = sorted(arr)

    # Initialize difference as infinite
    diff = 10**20

    # Find the min diff by comparing adjacent
    # pairs in sorted array
    for i in range(n-1):
        if arr[i+1] - arr[i] < diff:
            diff = arr[i+1] - arr[i]

    # Return min diff
    return diff

# Driver code
arr = [1, 5, 3, 19, 18, 25]
n = len(arr)
print("Minimum difference is " + str(findMinDiff(arr, n)))

# This code is contributed by Pratik Chhajer


Output :
Minimum difference is 1

Asked in: Amazon

This article is contributed by Harshit Agrawal. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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