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 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 and Description
Solution()

Method Summary

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

Methods inherited from class java.lang.Object

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

Constructor Detail

Solution

public Solution()

Method Detail

minimumDifference

public long minimumDifference(int[] nums)