Maximum Elegance of a K-Length Subsequence - Practice Coding | SlaveCode
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2813. Maximum Elegance of a K-Length Subsequence
Hard
50 Points
Array
Hash Table
Stack
Greedy
Sorting
Heap (Priority Queue)
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.
Examples
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
2813. Maximum Elegance of a K-Length Subsequence
Hard
50 Points
Array
Hash Table
Stack
Greedy
Sorting
Heap (Priority Queue)
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.
Examples
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.