Is Maximum Value of an Alternating Sequence easy or hard?

Maximum Value of an Alternating Sequence is generally considered a medium-level dynamic programming problem. The recurrence is straightforward once you identify the alternating states, but recognizing the optimal transition can take practice.

Maximum Value of an Alternating Sequence Python/Java solution

Python solutions typically use iterative DP with two variables for concise implementation. Java solutions follow the same transition logic with integer or long variables depending on constraints. Both versions achieve O(n) time complexity.

How to solve Maximum Value of an Alternating Sequence in O(n)?

Iterate through the array while maintaining two DP states representing alternating positions. For each value, update the best possible positive-state score and negative-state score using previous results. This converts the recursive transition into a linear scan.

What is the best approach for Maximum Value of an Alternating Sequence?

The best approach uses dynamic programming with two compressed states. One state tracks the best value when the current number contributes positively, and the other tracks the best value when it contributes negatively. This solution runs in O(n) time and O(1) space.

Is Maximum Value of an Alternating Sequence asked at Google/Amazon/Meta?

Alternating subsequence and DP state-transition problems are common in interviews at Google, Amazon, Meta, and similar companies. Interviewers often use them to test optimization skills, recurrence design, and space reduction techniques.

What data structure is used in Maximum Value of an Alternating Sequence?

The core solution primarily uses dynamic programming states stored in variables or arrays. No advanced data structure is required. Most implementations use simple integer variables for constant-space optimization.

What is the time complexity of Maximum Value of an Alternating Sequence?

The optimal dynamic programming solution runs in O(n) time because each element is processed exactly once. Space complexity can be reduced to O(1) by storing only the previous alternating states instead of a full DP table.

Description Hints 5 Solution Video 8:29

3993. Maximum Value of an Alternating Sequence

Medium31.5% acceptance

You are given three integers n, s, and m.

A sequence seq of integers of length n is considered valid if:

seq[0] = s.
The sequence is alternating, meaning that either:
- seq[0] > seq[1] < seq[2] > ..., or
- seq[0] < seq[1] > seq[2] < ....
For every adjacent pair, |seq[i] - seq[i - 1]| <= m.

A sequence of length 1 is considered alternating.

Return the maximum possible element that can appear in any valid sequence.

Example 1:

Input: n = 4, s = 3, m = 5

Output: 12

Explanation:

One valid sequence is [3, 8, 7, 12].
The maximum element in the sequence is 12.

Example 2:

Input: n = 2, s = 4, m = 3

Output: 7

Explanation:

One valid sequence is [4, 7].
The maximum element in the sequence is 7.

Constraints:

1 <= n, s <= 10⁹
1 <= m <= 10⁵

Topics

Greedy Math

Hints open one at a time

Hint 1

To make values grow as much as possible, use the maximum allowed increase m when moving to a high point.

Hint 2

Between two high points, there must be a lower element. To lose as little value as possible, make that lower element smaller by only 1.

Hint 3

Therefore, after the first high point, every two additional positions can increase the maximum reachable high value by m - 1.

Hint 4

Consider both possible alternating patterns: starting with a decrease and starting with an increase.

Hint 5

Handle n == 1 separately.

8:29

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1class Solution:
2    def maximumValue(self, n: int, s: int, m: int) -> int:
3        

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Input

4
3
5

Input

2
4
3

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