Package g2801_2900.s2813_maximum_elegance_of_a_k_length_subsequence

Class Solution

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public final class Solution

    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.

    <code>itemsi = profit<sub>i</sub>, category<sub>i</sub></code>, where <code>profit<sub>i</sub></code> and <code>category<sub>i</sub></code> denote the profit and category of the <code>i<sup>th</sup></code> item respectively.

    Let's define the elegance of a subsequence of items as <code>total_profit + distinct_categories<sup>2</sup></code>, 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 items0 = 3,2 and items2 = 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 + 2<sup>2</sup> = 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 items0 = 3,1, items2 = 2,2, and items3 = 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 + 3<sup>2</sup> = 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 + 1<sup>2</sup> = 7.

    Constraints:

    • <code>1 <= items.length == n <= 10<sup>5</sup></code>

    • items[i].length == 2

    • <code>items0 == profit<sub>i</sub></code>

    • <code>items1 == category<sub>i</sub></code>

    • <code>1 <= profit<sub>i</sub><= 10<sup>9</sup></code>

    • <code>1 <= category<sub>i</sub><= n</code>

    • 1 &lt;= k &lt;= n

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Long findMaximumElegance(Array<IntArray> items, Integer k)

      • Methods inherited from class java.lang.Object

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