Package g2101_2200.s2163_minimum_difference_in_sums_after_removal_of_elements

Class Solution

java.lang.Object
g2101_2200.s2163_minimum_difference_in_sums_after_removal_of_elements.Solution
public class Solution extends java.lang.Object
2163 - Minimum Difference in Sums After Removal of Elements.

Hard

You are given a 0-indexed integer array nums consisting of 3 * n elements.

You are allowed to remove any subsequence of elements of size exactly n from nums. The remaining 2 * n elements will be divided into two equal parts:

  • The first n elements belonging to the first part and their sum is sumfirst.
  • The next n elements belonging to the second part and their sum is sumsecond.

The difference in sums of the two parts is denoted as sumfirst - sumsecond.

  • For example, if sumfirst = 3 and sumsecond = 2, their difference is 1.
  • Similarly, if sumfirst = 2 and sumsecond = 3, their difference is -1.

Return the minimum difference possible between the sums of the two parts after the removal of n elements.

Example 1:

Input: nums = [3,1,2]

Output: -1

Explanation: Here, nums has 3 elements, so n = 1.

Thus we have to remove 1 element from nums and divide the array into two equal parts.

  • If we remove nums[0] = 3, the array will be [1,2]. The difference in sums of the two parts will be 1 - 2 = -1.

  • If we remove nums[1] = 1, the array will be [3,2]. The difference in sums of the two parts will be 3 - 2 = 1.

  • If we remove nums[2] = 2, the array will be [3,1]. The difference in sums of the two parts will be 3 - 1 = 2.

The minimum difference between sums of the two parts is min(-1,1,2) = -1.

Example 2:

Input: nums = [7,9,5,8,1,3]

Output: 1

Explanation: Here n = 2. So we must remove 2 elements and divide the remaining array into two parts containing two elements each.

If we remove nums[2] = 5 and nums[3] = 8, the resultant array will be [7,9,1,3]. The difference in sums will be (7+9) - (1+3) = 12.

To obtain the minimum difference, we should remove nums[1] = 9 and nums[4] = 1. The resultant array becomes [7,5,8,3]. The difference in sums of the two parts is (7+5) - (8+3) = 1.

It can be shown that it is not possible to obtain a difference smaller than 1.

Constraints:

  • nums.length == 3 * n
  • 1 <= n <= 105
  • 1 <= nums[i] <= 105

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    long
    minimumDifference(int[] nums)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • minimumDifference

      public long minimumDifference(int[] nums)