How do you approach Wiggle Subsequence?

Track the longest wiggle ending on an up-step and on a down-step.

What are common mistakes on Wiggle Subsequence?

Iterating the dimensions in an order that reads a cell before it has been written. Getting the base case wrong. It carries the whole recurrence, and the error stays invisible until a large input. Rolling down to one dimension without reversing the inner loop, which lets a 0/1 item be taken twice.

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Wiggle Subsequence

MediumAlgorithms

Description

A **wiggle sequence** is one where the differences between successive numbers strictly alternate between positive and negative. Given an integer array `nums`, return the length of the longest wiggle **subsequence** obtainable by deleting some elements (keeping order).

Example 1

Input: nums = [1,7,4,9,2,5]

Output: 6

Explanation: The whole array already wiggles.

Example 2

Input: nums = [1,2,3,4,5,6,7,8,9]

Output: 2

Explanation: Only one rise can be kept.

Constraints

- 1 <= nums.length <= 1000 - 0 <= nums[i] <= 1000

Wiggle Subsequence: approach, complexity and pitfalls

A medium dynamic programming problem, graded against 4 test cases (2 of them hidden).

The pattern: Dynamic Programming

Overlapping subproblems solved once and reused - the pattern candidates fear most.

Reach for it when you see: "Number of ways", "minimum/maximum cost", or a recursion that recomputes the same state.

More Dynamic Programmingproblems →

If you are stuck

Show the 2-step hint ladder

Track the longest wiggle ending on an up-step and on a down-step.
An up-step extends the best down-ending sequence, and vice versa.

The optimal approach

Show the approach: The approach

Greedy up/down tracking. Maintain `up` and `down`, the lengths of the longest wiggle subsequences ending with a rise or a fall. On each rise set `up = down + 1`; on each fall set `down = up + 1`. The answer is `max(up, down)`.

Time: O(n). Space: O(1).

The full reference solution in every supported language stays in the editor above - reveal it there once you have had a real attempt.

What the tests check

Read off this problem's own test suite, so these are the cases a submission actually has to survive.

Single element. A one-element case is included. Two-pointer and window solutions frequently return the wrong thing when the two indices start out equal.
Duplicate values. Repeated values appear in the input, so any logic that assumes distinct elements - or that skips over equal neighbours - is exercised.

Common Dynamic Programming mistakes

These apply to the pattern as a whole, not just this problem.

Iterating the dimensions in an order that reads a cell before it has been written.
Getting the base case wrong. It carries the whole recurrence, and the error stays invisible until a large input.
Rolling down to one dimension without reversing the inner loop, which lets a 0/1 item be taken twice.