Problem Statement: Find the Maximum Length of a Good Subsequence

You are given an integer array nums and a non-negative integer k. A sequence of integers seq is called good if there are at most k indices i in the range [0, seq.length - 2] such that seq[i] != seq[i + 1].

Return the maximum possible length of a good subsequence of nums.

Example 1:

Input:

nums = [1, 2, 1, 1, 3], k = 2

Output:

4

Explanation:
The maximum length subsequence is [1, 2, 1, 1, 3].

Example 2:

Input:

nums = [1, 2, 3, 4, 5, 1], k = 0

Output:

2

Explanation:
The maximum length subsequence is [1, 2, 3, 4, 5, 1].

Constraints:

1. 1 ≤ nums.length ≤ 500
2. 1 ≤ nums[i] ≤ 10^9
3. 0 ≤ k ≤ min(nums.length, 25)

Problem Statement: Remove Stones to Minimize the Total

You are given a 0-indexed integer array piles, where piles[i] represents the number of stones in the i-th pile, and an integer k. You should apply the following operation exactly k times:

• Choose any piles[i] and remove floor(piles[i] / 2) stones from it.

Notice:

• You can apply the operation on the same pile more than once.

Goal:
Return the minimum possible total number of stones remaining after applying the k operations.

floor(x) is the greatest integer that is smaller than or equal to x (i.e., rounds x down).

Examples

Example 1:

Input:

piles = [5,4,9], k = 2

Output:

12

Explanation:
Steps of a possible scenario are:

1. Apply the operation on pile 2. The resulting piles are [5, 4, 5].
2. Apply the operation on pile 0. The resulting piles are [3, 4, 5].

The total number of stones in [3, 4, 5] is 12.

Example 2:

Input:

piles = [4,3,6,7], k = 3

Output:

12

Explanation:
Steps of a possible scenario are:

1. Apply the operation on pile 2. The resulting piles are [4, 3, 3, 7].
2. Apply the operation on pile 3. The resulting piles are [4, 3, 3, 4].
3. Apply the operation on pile 0. The resulting piles are [2, 3, 3, 4].

The total number of stones in [2, 3, 3, 4] is 12.

Constraints:

1. 1 ≤ piles.length ≤ 10^5
2. 1 ≤ piles[i] ≤ 10^4
3. 1 ≤ k ≤ 10^5

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