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3452. Find the Maximum Length of a Good Subsequence II

Hard
Array
Hash Table
Dynamic Programming
Solve on LeetCode View Solutions

Description

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 <= 5 * 103
  • 1 <= nums[i] <= 109
  • 0 <= k <= min(50, nums.length)

Hints

Hint 1
The absolute values in <code>nums</code> don’t really matter. So we can remap the set of values to the range <code>[0, n - 1]</code>.
Hint 2
Let <code>dp[i][j]</code> be the length of the longest subsequence till index <code>j</code> with at most <code>i</code> positions such that <code>seq[i] != seq[i + 1]</code>.
Hint 3
For each value <code>x</code> from left to right, update <code>dp[i][x] = max(dp[i][x] + 1, dp[i - 1][y] + 1)</code>, where <code>y != x</code>.

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