Find minimum difference between any two elements (pair) in given array

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

Examples :

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

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

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

Naive Approach: To solve the problem follow the below idea:

A simple solution is to use two loops two generate every pair of elements and compare them to get the minimum difference

Below is the implementation of the above approach:

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]);

    // Function call
    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 code
    public static void main(String[] args)
    {
        int arr[] = new int[] { 1, 5, 3, 19, 18, 25 };

        // Function call
        System.out.println("Minimum difference is "
                           + findMinDiff(arr, arr.length));
    }
}

Python3

# 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
if __name__ == "__main__":
    arr = [1, 5, 3, 19, 18, 25]
    n = len(arr)

    # Function call
    print("Minimum difference is " + str(findMinDiff(arr, n)))

# This code is contributed by Pratik Chhajer

C#

// C# implementation of simple method to find
// minimum difference between any pair
using System;

class GFG {

    // Returns minimum difference between any pair
    static int findMinDiff(int[] arr, int n)
    {

        // Initialize difference as infinite
        int diff = int.MaxValue;

        // 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 code
    public static void Main()
    {
        int[] arr = new int[] { 1, 5, 3, 19, 18, 25 };

        // Function call
        Console.Write("Minimum difference is "
                      + findMinDiff(arr, arr.Length));
    }
}

// This code is contributed by nitin mittal.

PHP

<?php
// PHP implementation of simple
// method to find minimum
// difference between any pair

// Returns minimum difference
// between any pair
function findMinDiff($arr, $n)
{
// Initialize difference
// as infinite
$diff = PHP_INT_MAX;

// Find the min diff by comparing
// difference of all possible
// pairs in given array
for ($i = 0; $i < $n - 1; $i++)
    for ($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
$arr = array(1, 5, 3, 19, 18, 25);
$n = sizeof($arr);

// Function call
echo "Minimum difference is " ,
         findMinDiff($arr, $n);

// This code is contributed by ajit
?>

Javascript

<script>

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

    // Returns minimum difference between any pair
    function findMinDiff( arr, n)
    {
        // Initialize difference as infinite
        let diff = Number.MAX_VALUE;

        // Find the min diff by comparing difference
        // of all possible pairs in given array
        for (let i=0; i<n-1; i++)
            for (let 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 Code

        let arr = [1, 5, 3, 19, 18, 25];
        document.write("Minimum difference is "+
                              findMinDiff(arr, arr.length));

</script>

Output

Minimum difference is 1

Time Complexity: O(N²).
Auxiliary Space: O(1)

Find the minimum difference between any two elements using sorting:

The idea is to use sorting and compare every adjacent pair of the array

Follow the given steps to solve the problem:

• Sort array in ascending order
• Initialize difference as infinite
• Compare all adjacent pairs in a sorted array and keep track of the minimum difference

Below is the implementation of the above approach:

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]);

    // Function call
    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 code
    public static void main(String[] args)
    {
        int arr[] = new int[] { 1, 5, 3, 19, 18, 25 };

        // Function call
        System.out.println("Minimum difference is "
                           + findMinDiff(arr, arr.length));
    }
}

Python3

# Python3 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
if __name__ == "__main__":
    arr = [1, 5, 3, 19, 18, 25]
    n = len(arr)

    # Function call
    print("Minimum difference is " + str(findMinDiff(arr, n)))

# This code is contributed by Pratik Chhajer

C#

// C# program to find minimum
// difference between any pair
// in an unsorted array
using System;

class GFG {
    // Returns minimum difference
    // between any pair
    static int findMinDiff(int[] arr, int n)
    {
        // Sort array in
        // non-decreasing order
        Array.Sort(arr);

        // Initialize difference
        // as infinite
        int diff = int.MaxValue;

        // 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
    public static void Main()
    {
        int[] arr = new int[] { 1, 5, 3, 19, 18, 25 };

        // Function call
        Console.WriteLine("Minimum difference is "
                          + findMinDiff(arr, arr.Length));
    }
}

// This code is contributed by anuj_67.

PHP

<?php
// PHP program to find minimum
// difference between any pair
// in an unsorted array

// Returns minimum difference
// between any pair
function findMinDiff($arr, $n)
{

// Sort array in
// non-decreasing order
sort($arr);

// Initialize difference
// as infinite
$diff = PHP_INT_MAX;

// Find the min diff by
// comparing adjacent
// pairs in sorted array
for ($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
$arr = array(1, 5, 3, 19, 18, 25);
$n = sizeof($arr);

// Function call
echo "Minimum difference is " ,
         findMinDiff($arr, $n);

// This code is contributed ajit
?>

Javascript

<script>

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

    // Returns minimum difference
    // between any pair
    function findMinDiff(arr, n)
    {
        // Sort array in
        // non-decreasing order
        arr.sort(function(a, b)
        {return a - b});

        // Initialize difference
        // as infinite
        let diff = Number.MAX_VALUE;

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

        // Return min diff
        return diff;
    }

    let arr = [1, 5, 3, 19, 18, 25];
    document.write("Minimum difference is "
    + findMinDiff(arr, arr.length));

</script>

Output

Minimum difference is 1

Time Complexity: O(N log N)
Auxiliary Space: O(1)

Find the minimum difference between any two elements using Map:

We can solve this problem using a map. We can first sort the array in ascending order and then find the minimum difference by comparing adjacent elements. Alternatively, we can insert all the elements into a map and then iterate through the map, comparing adjacent elements.

Below is the implementation of the above approach:

C++

#include <bits/stdc++.h>
using namespace std;

int findMinDiff(int arr[], int n) {
    map<int, int> mp;
    int minDiff = INT_MAX;
    for (int i = 0; i < n; i++) {
        auto it = mp.lower_bound(arr[i]); // Find the first element that is greater than or equal to arr[i]
        if (it != mp.end()) {
            minDiff = min(minDiff, it->first - arr[i]); // Check difference between current element and the next element in map
        }
        if (it != mp.begin()) {
            it--;
            minDiff = min(minDiff, arr[i] - it->first); // Check difference between current element and the previous element in map
        }
        mp[arr[i]] = i; // Insert element into map
    }
    return minDiff;
}

int main() {
    int arr[] = {1, 5, 3, 19, 18, 25};
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << findMinDiff(arr, n) << endl;


    return 0;
}

Python3

import bisect

def findMinDiff(arr, n):
    mp = {}
    minDiff = float('inf')
    for i in range(n):
        it = bisect.bisect_left(list(mp.keys()), arr[i]) # Find the first element that is greater than or equal to arr[i]
        if it != len(mp):
            minDiff = min(minDiff, list(mp.keys())[it] - arr[i]) # Check difference between current element and the next element in map
        if it != 0:
            minDiff = min(minDiff, arr[i] - list(mp.keys())[it-1]) # Check difference between current element and the previous element in map
        mp[arr[i]] = i # Insert element into map
    return minDiff

arr = [1, 5, 3, 19, 18, 25]
n = len(arr)
print(findMinDiff(arr, n))

Java

import java.util.*;

public class Main {
    public static int findMinDiff(int[] arr, int n) {
        TreeMap<Integer, Integer> mp = new TreeMap<>();
        int minDiff = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++) {
            Map.Entry<Integer, Integer> entry = mp.ceilingEntry(arr[i]); // Find the first element that is greater than or equal to arr[i]
            if (entry != null) {
                minDiff = Math.min(minDiff, entry.getKey() - arr[i]); // Check difference between current element and the next element in map
            }
            entry = mp.lowerEntry(arr[i]);
            if (entry != null) {
                minDiff = Math.min(minDiff, arr[i] - entry.getKey()); // Check difference between current element and the previous element in map
            }
            mp.put(arr[i], i); // Insert element into map
        }
        return minDiff;
    }

    public static void main(String[] args) {
        int[] arr = {1, 5, 3, 19, 18, 25};
        int n = arr.length;
        System.out.println(findMinDiff(arr, n));
    }
}

Output

1

Time Complexity: O(N)

Auxiliary Space: O(N)

Find the minimum difference between any two elements using Merge Sort:

The merge Helper function always compares two elements between each other. We can do this in O(nlogn) time instead of sorting and then again traversing the sorted array.

• Take a variable minDiff and store the minimum difference and compare with each recursive stack of the merge helper function.

C++

// C++ code
#include <bits/stdc++.h>
using namespace std;

class Solution {

public:
    // Function to find minimum difference between any pair
    // of elements in an array.
    int MinimumDifference(int arr[], int n)
    {
        if (n < 2)
            return INT_MAX;
        int mid = n / 2;
        int left[mid];
        int right[n - mid];

        for (int i = 0; i < mid; i++) {
            left[i] = arr[i];
        }

        for (int i = mid; i < n; i++) {
            right[i - mid] = arr[i];
        }

        int ls = MinimumDifference(left, mid);
        int rs = MinimumDifference(right, n - mid);
        int mg
            = mergeHelper(left, right, arr, mid, n - mid);

        return min(mg, min(ls, rs));
    }

private:
    int mergeHelper(int left[], int right[], int arr[],
                    int n1, int n2)
    {
        int i = 0;
        int j = 0;
        int k = 0;
        int minDiff = INT_MAX;

        while (i < n1 && j < n2) {
            if (left[i] <= right[j]) {
                minDiff = min(minDiff, right[j] - left[i]);
                arr[k] = left[i];
                i++;
            }
            else {
                minDiff = min(minDiff, left[i] - right[j]);
                arr[k] = right[j];
                j++;
            }
            k++;
        }

        while (i < n1) {
            arr[k] = left[i];
            i++;
            k++;
        }
        while (j < n2) {
            arr[k] = right[j];
            j++;
            k++;
        }

        return minDiff;
    }
};

int main()
{

    // Code
    int arr[] = { 1, 5, 3, 19, 18, 25 };
    int n = sizeof(arr) / sizeof(arr[0]);

    // Function call
    Solution sln;
    int minDiff = sln.MinimumDifference(arr, n);
    cout << "Minimum difference is " << minDiff << endl;
    return 0;
}

// This code is contributed by Aman Kumar

Java

// Java Code
import java.io.*;

public class GFG {

    public static void main(String[] args)
    {

        // Code
        int[] arr = new int[] { 1, 5, 3, 19, 18, 25 };

        // Function call
        var sln = new Solution();
        var minDiff
            = sln.MinimumDifference(arr, arr.length);
        System.out.println("Minimum difference is "
                           + minDiff);
    }
}
class Solution {
    // Function to find minimum difference between any pair
    // of elements in an array.
    public int MinimumDifference(int[] arr, int n)
    {
        // code here
        if (arr.length < 2)
            return Integer.MAX_VALUE;
        int mid = arr.length / 2;
        int[] left = new int[mid];
        int[] right = new int[arr.length - mid];
        int i = 0;
        while (i < mid) {
            left[i] = arr[i];
            i += 1;
        }
        while (i < arr.length) {
            right[i - mid] = arr[i];
            i += 1;
        }
        var ls = MinimumDifference(left, left.length);
        var rs = MinimumDifference(right, right.length);
        var mg = mergeHelper(left, right, arr);
        return Math.min(mg, Math.min(ls, rs));
    }
    private int mergeHelper(int[] left, int[] right,
                            int[] arr)
    {
        int i = 0;
        int j = 0;
        int k = 0;
        int minDiff = Integer.MAX_VALUE;
        while (i < left.length && j < right.length) {
            if (left[i] <= right[j]) {
                minDiff
                    = Math.min(minDiff, right[j] - left[i]);
                arr[k] = left[i];
                i += 1;
            }
            else {
                minDiff
                    = Math.min(minDiff, left[i] - right[j]);
                arr[k] = right[j];
                j += 1;
            }
            k += 1;
        }
        while (i < left.length) {
            arr[k] = left[i];
            i += 1;
            k += 1;
        }
        while (j < right.length) {
            arr[k] = right[j];
            j += 1;
            k += 1;
        }
        return minDiff;
    }
}

// This code is contributed by Pushpesh Raj.

Python3

# Python Code
class Solution:
        # Function to find minimum difference between any pair
    # of elements in an array.
    def MinimumDifference(self, arr, n):
        if n < 2:
            return float('inf')
        mid = n // 2
        left = arr[:mid]
        right = arr[mid:]

        ls = self.MinimumDifference(left, len(left))
        rs = self.MinimumDifference(right, len(right))
        mg = self.mergeHelper(left, right, arr, len(left), len(right))

        return min(mg, min(ls, rs))

    def mergeHelper(self, left, right, arr, n1, n2):
        i, j, k = 0, 0, 0
        minDiff = float('inf')

        while i < n1 and j < n2:
            if left[i] <= right[j]:
                minDiff = min(minDiff, right[j] - left[i])
                arr[k] = left[i]
                i += 1
            else:
                minDiff = min(minDiff, left[i] - right[j])
                arr[k] = right[j]
                j += 1
            k += 1

        while i < n1:
            arr[k] = left[i]
            i += 1
            k += 1
        while j < n2:
            arr[k] = right[j]
            j += 1
            k += 1

        return minDiff


# Driver Code
arr = [1, 5, 3, 19, 18, 25]
n = len(arr)
sln = Solution()

# Function call
minDiff = sln.MinimumDifference(arr, n)
print("Minimum difference is", minDiff)

# This code is contributed by Prasad Kandekar(prasad264)

C#

using System;

public class GFG {

    static public void Main()
    {

        // Code
        int[] arr = new int[] { 1, 5, 3, 19, 18, 25 };

        // Function call
        var sln = new Solution();
        var minDiff
            = sln.MinimumDifference(arr, arr.Length);
        Console.WriteLine("Minimum difference is "
                          + minDiff);
    }
}
class Solution {
    // Function to find minimum difference between any pair
    // of elements in an array.
    public int MinimumDifference(int[] arr, int n)
    {
        // code here
        if (arr.Length < 2)
            return int.MaxValue;
        int mid = arr.Length / 2;
        int[] left = new int[mid];
        int[] right = new int[arr.Length - mid];
        int i = 0;
        while (i < mid) {
            left[i] = arr[i];
            i += 1;
        }
        while (i < arr.Length) {
            right[i - mid] = arr[i];
            i += 1;
        }
        var ls = MinimumDifference(left, left.Length);
        var rs = MinimumDifference(right, right.Length);
        var mg = mergeHelper(left, right, arr);
        return Math.Min(mg, Math.Min(ls, rs));
    }
    private int mergeHelper(int[] left, int[] right,
                            int[] arr)
    {
        int i = 0;
        int j = 0;
        int k = 0;
        int minDiff = int.MaxValue;
        while (i < left.Length && j < right.Length) {
            if (left[i] <= right[j]) {
                minDiff
                    = Math.Min(minDiff, right[j] - left[i]);
                arr[k] = left[i];
                i += 1;
            }
            else {
                minDiff
                    = Math.Min(minDiff, left[i] - right[j]);
                arr[k] = right[j];
                j += 1;
            }
            k += 1;
        }
        while (i < left.Length) {
            arr[k] = left[i];
            i += 1;
            k += 1;
        }
        while (j < right.Length) {
            arr[k] = right[j];
            j += 1;
            k += 1;
        }
        return minDiff;
    }
}

Javascript

// JavaScript code
class Solution {
    // Function to find minimum difference between any pair
    // of elements in an array.
    MinimumDifference(arr, n) {
        if (n < 2)
              return Number.MAX_SAFE_INTEGER;
        var mid = Math.floor(n / 2);
        var left = arr.slice(0, mid);
        var right = arr.slice(mid);

        var ls = this.MinimumDifference(left, mid);
        var rs = this.MinimumDifference(right, n - mid);
        var mg = this.mergeHelper(left, right, arr, mid, n - mid);

        return Math.min(mg, Math.min(ls, rs));
      }

    // Helper function for merge sort
    mergeHelper(left, right, arr, n1, n2) {
          var i = 0;
          var j = 0;
          var k = 0;
          var minDiff = Number.MAX_SAFE_INTEGER;

        while (i < n1 && j < n2) {
              if (left[i] <= right[j]) {
                minDiff = Math.min(minDiff, right[j] - left[i]);
                arr[k] = left[i];
                i++;
              }
            else {
                minDiff = Math.min(minDiff, left[i] - right[j]);
                arr[k] = right[j];
                j++;
              }
              k++;
        }

        while (i < n1) {
              arr[k] = left[i];
              i++;
              k++;
        }
        while (j < n2) {
              arr[k] = right[j];
              j++;
              k++;
        }

        return minDiff;
      }
}

// Code
var arr = [1, 5, 3, 19, 18, 25];
var n = arr.length;

// Function call
var sln = new Solution();
var minDiff = sln.MinimumDifference(arr, n);
console.log("Minimum difference is " + minDiff);

// This code is contributed by Prasad Kandekar(prasad264)

Output

Minimum difference is 1

Time Complexity: O(N * log N)  Merge sort algorithm uses (n * log n) complexity.
Auxiliary Space: O(N) In merge sort algorithm all elements are copied into an auxiliary array.

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.