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 ≤ nums.length ≤ 5001 ≤ nums[i] ≤ 10^90 ≤ 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:
- Apply the operation on pile 2. The resulting piles are
[5, 4, 5]. - 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:
- Apply the operation on pile 2. The resulting piles are
[4, 3, 3, 7]. - Apply the operation on pile 3. The resulting piles are
[4, 3, 3, 4]. - 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 ≤ piles.length ≤ 10^51 ≤ piles[i] ≤ 10^41 ≤ k ≤ 10^5
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