3685 - Subsequence Sum After Capping Elements.

Medium

You are given an integer array nums of size n and a positive integer k.

An array capped by value x is obtained by replacing every element nums[i] with min(nums[i], x).

For each integer x from 1 to n, determine whether it is possible to choose a subsequence from the array capped by x such that the sum of the chosen elements is exactly k.

Return a 0-indexed boolean array answer of size n, where answer[i] is true if it is possible when using x = i + 1, and false otherwise.

Example 1:

Input: nums = 4,3,2,4, k = 5

Output: false,false,true,true

Explanation:

• For x = 1, the capped array is [1, 1, 1, 1]. Possible sums are 1, 2, 3, 4, so it is impossible to form a sum of 5.

• For x = 2, the capped array is [2, 2, 2, 2]. Possible sums are 2, 4, 6, 8, so it is impossible to form a sum of 5.

• For x = 3, the capped array is [3, 3, 2, 3]. A subsequence [2, 3] sums to 5, so it is possible.

• For x = 4, the capped array is [4, 3, 2, 4]. A subsequence [3, 2] sums to 5, so it is possible.

Example 2:

Input: nums = 1,2,3,4,5, k = 3

Output: true,true,true,true,true

Explanation:

For every value of x, it is always possible to select a subsequence from the capped array that sums exactly to 3.

Constraints:

• 1 <= n == nums.length <= 4000

• 1 <= nums[i] <= n

• 1 <= k <= 4000