3490. Find the Maximum Length of Valid Subsequence I

Medium
Array
Dynamic Programming

Description

You are given an integer array nums.

A subsequence sub of nums with length x is called valid if it satisfies:

  • (sub[0] + sub[1]) % 2 == (sub[1] + sub[2]) % 2 == ... == (sub[x - 2] + sub[x - 1]) % 2.

Return the length of the longest valid subsequence of nums.

A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

 

Example 1:

Input: nums = [1,2,3,4]

Output: 4

Explanation:

The longest valid subsequence is [1, 2, 3, 4].

Example 2:

Input: nums = [1,2,1,1,2,1,2]

Output: 6

Explanation:

The longest valid subsequence is [1, 2, 1, 2, 1, 2].

Example 3:

Input: nums = [1,3]

Output: 2

Explanation:

The longest valid subsequence is [1, 3].

 

Constraints:

  • 2 <= nums.length <= 2 * 105
  • 1 <= nums[i] <= 107

Hints

Hint 1
The possible sequence either contains all even elements, all odd elements, alternate even odd, or alternate odd even elements.
Hint 2
Considering only the parity of elements, there are only 4 possibilities and we can try all of them.
Hint 3
When selecting an element with any parity, try to select the earliest one.

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