Partition a set into two subsets such that difference between max of one and min of other is minimized
Last Updated :
31 Jan, 2023
Given an array arr[] of N integers, the task is to split the array into two subsets such that the absolute difference between the maximum of first subset and minimum of second subset is minimum.
Examples:
Input: arr[] = {3, 1, 2, 6, 4}
Output: 1
Explanation:
Splitting the given array in two subsets, A = [1, 2, 4], B = [3, 6]. Difference of maximum of first set is 4 and minimum of second set is 3 and their difference is 1.
Input: arr[] = {2, 1, 3, 2, 4, 3}
Output: 0
Explanation:
Splitting the given array in two subsets, A = [1, 2, 2, 3], B = [3, 4]. Difference of maximum of first set is 3 and minimum of second set is 3 and their difference is 0.
Approach: To solve the above problem we have to find the two integers such that m and n such that max of first set is m and the min of second set is n. The idea is to sort the given array ascending order and after sorting the array, the minimum difference between the consecutive element is the required minimum difference after partitioning the array elements into subsets.
Below is the implementation of above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int splitArray( int arr[], int N)
{
sort(arr, arr + N);
int result = INT_MAX;
for ( int i = 1; i < N; i++) {
result = min(result,
arr[i] - arr[i - 1]);
}
return result;
}
int main()
{
int arr[] = { 3, 1, 2, 6, 4 };
int N = sizeof (arr) / sizeof (arr[0]);
cout << splitArray(arr, N);
return 0;
}
|
Java
import java.util.*;
class GFG{
static int splitArray( int arr[], int N)
{
Arrays.sort(arr);
int result = Integer.MAX_VALUE;
for ( int i = 1 ; i < N; i++)
{
result = Math.min(result,
arr[i] - arr[i - 1 ]);
}
return result;
}
public static void main(String[] args)
{
int arr[] = { 3 , 1 , 2 , 6 , 4 };
int N = arr.length;
System.out.print(splitArray(arr, N));
}
}
|
Python3
def splitArray(arr, N):
arr = sorted (arr)
result = 10 * * 9
for i in range ( 1 , N):
result = min (result, arr[i] - arr[i - 1 ])
return result
if __name__ = = '__main__' :
arr = [ 3 , 1 , 2 , 6 , 4 ]
N = len (arr)
print (splitArray(arr, N))
|
C#
using System;
class GFG{
static int splitArray( int []arr, int N)
{
Array.Sort(arr);
int result = Int32.MaxValue;
for ( int i = 1; i < N; i++)
{
result = Math.Min(result,
arr[i] - arr[i - 1]);
}
return result;
}
public static void Main()
{
int []arr = { 3, 1, 2, 6, 4 };
int N = arr.Length;
Console.Write(splitArray(arr, N));
}
}
|
Javascript
<script>
function splitArray(arr, N)
{
arr.sort();
let result = Number.MAX_VALUE;
for (let i = 1; i < N; i++) {
result = Math.min(result,
arr[i] - arr[i - 1]);
}
return result;
}
let arr = [ 3, 1, 2, 6, 4 ];
let N = arr.length;
document.write(splitArray(arr, N));
</script>
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Time Complexity: O(N*log N)
Space Complexity : O(1)
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