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Problem · Greedy

Decreasing Subsequences

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Problem statement

Given an int array nums of length n. Split it into strictly decreasing subsequences. Output the min number of subsequences you can get by splitting.

Function

minSubsequences(nums: int[]) → int

Examples

Example 1

nums = [5, 2, 4, 3, 1, 6]return = 3

You can split this array into: [5, 2, 1], [4, 3], [6]. And there are 3 subsequences you get. Or you can split it into [5, 4, 3], [2, 1], [6]. Also 3 subsequences. But [5, 4, 3, 2, 1], [6] is not legal because [5, 4, 3, 2, 1] is not a subsequence of the original array.

Example 2

nums = [2, 9, 12, 13, 4, 7, 6, 5, 10]return = 4

You can split the array into: [2], [9, 4], [12, 10], [13, 7, 6, 5].

Example 3

nums = [1, 1, 1]return = 3

Because of the strictly descending order you have to split it into 3 subsequences: [1], [1], [1].

Constraints

1 ≤ nums.length ≤ 2 * 10^5
-10^9 ≤ nums[i] ≤ 10^9
Every input element must appear in exactly one output subsequence, and each subsequence preserves input order.