LeetCode-in-Java

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

Solution

import java.util.ArrayDeque;
import java.util.Arrays;

public class Solution {
    public long findMaximumElegance(int[][] items, int k) {
        Arrays.sort(items, (a, b) -> b[0] - a[0]);
        int n = items.length;
        boolean[] vis = new boolean[n];
        ArrayDeque<Long> arr = new ArrayDeque<>();
        long distinct = 0;
        long sum = 0;
        for (int i = 0; i < k; i++) {
            sum += items[i][0];
            if (vis[items[i][1] - 1]) {
                arr.push((long) items[i][0]);
            } else {
                ++distinct;
                vis[items[i][1] - 1] = true;
            }
        }
        long ans = sum + distinct * distinct;
        for (int i = k; i < n && distinct < k; i++) {
            if (!vis[items[i][1] - 1]) {
                sum -= arr.pop();
                sum += items[i][0];
                ++distinct;
                vis[items[i][1] - 1] = true;
                ans = Math.max(ans, sum + distinct * distinct);
            }
        }
        return ans;
    }
}

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