Package g2801_2900.s2813_maximum_elegance_of_a_k_length_subsequence

Class Solution

java.lang.Object
g2801_2900.s2813_maximum_elegance_of_a_k_length_subsequence.Solution
public class Solution extends java.lang.Object
2813 - Maximum Elegance of a K-Length Subsequence.

Hard

You are given a 0-indexed 2D integer array items of length n and an integer k.

items[i] = [profiti, categoryi], where profiti and categoryi denote the profit and category of the ith item respectively.

Let’s define the elegance of a subsequence of items as total_profit + distinct_categories2, where total_profit is the sum of all profits in the subsequence, and distinct_categories is the number of distinct categories from all the categories in the selected subsequence.

Your task is to find the maximum elegance from all subsequences of size k in items.

Return an integer denoting the maximum elegance of a subsequence of items with size exactly k.

Note: A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the remaining elements’ relative order.

Example 1:

Input: items = [[3,2],[5,1],[10,1]], k = 2

Output: 17

Explanation:

In this example, we have to select a subsequence of size 2.

We can select items[0] = [3,2] and items[2] = [10,1].

The total profit in this subsequence is 3 + 10 = 13, and the subsequence contains 2 distinct categories [2,1].

Hence, the elegance is 13 + 22 = 17, and we can show that it is the maximum achievable elegance.

Example 2:

Input: items = [[3,1],[3,1],[2,2],[5,3]], k = 3

Output: 19

Explanation:

In this example, we have to select a subsequence of size 3.

We can select items[0] = [3,1], items[2] = [2,2], and items[3] = [5,3].

The total profit in this subsequence is 3 + 2 + 5 = 10, and the subsequence contains 3 distinct categories [1,2,3].

Hence, the elegance is 10 + 32 = 19, and we can show that it is the maximum achievable elegance.

Example 3:

Input: items = [[1,1],[2,1],[3,1]], k = 3

Output: 7

Explanation:

In this example, we have to select a subsequence of size 3.

We should select all the items.

The total profit will be 1 + 2 + 3 = 6, and the subsequence contains 1 distinct category [1].

Hence, the maximum elegance is 6 + 12 = 7.

Constraints:

  • 1 <= items.length == n <= 105
  • items[i].length == 2
  • items[i][0] == profiti
  • items[i][1] == categoryi
  • 1 <= profiti <= 109
  • 1 <= categoryi <= n
  • 1 <= k <= n

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    long
    findMaximumElegance(int[][] items, int k)
     

    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

    • findMaximumElegance

      public long findMaximumElegance(int[][] items, int k)