Package g2101_2200.s2163_minimum_difference_in_sums_after_removal_of_elements

Class 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 Detail

      • Solution

        public Solution()

    • Method Detail

      • minimumDifference

        public long minimumDifference​(int[] nums)