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Grokking Dynamic Programming Interview in C++

Longest Alternating Subsequence

Explore how to find the longest alternating subsequence (LAS) in an integer array using dynamic programming techniques. Understand the problem definition, analyze naive recursive solutions, and then learn optimized top-down and bottom-up DP methods. This lesson helps you recognize overlapping subproblems and apply memoization and tabulation to improve time and space efficiency. By mastering these approaches, you’ll be able to solve LAS problems effectively in coding interviews.

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Statement

The Longest Alternating Subsequence (LAS) is the longest subsequence from a given array, in which the subsequence elements are in alternating order. Given an integer array, nums, find the length of the LAS in this array.

Let’s say we have an integer array, [4, 1, 5, 6, 3, 2, 1], and we want to get the longest alternating subsequence in this array. There are multiple alternating subsequences of different lengths, such as [4, 1], [1, 5], [5, 3], [4, 3], [4, 1, 5], [4, 1, 5, 3], [4, 1, 6], [4, 1, 6, 1], and so on. We observe that [4, 5, 6], [4, 3, 2, 1], and [4, 6, 3, 2, 1] are not alternating subsequences. The longest alternating subsequences, in this case, are [4, 1, 5, 3], [4, 1, 5, 2], [4, 1, 5, 1], [4, 1, 6, 3], [4, 1, 6, 2] and [4, 1, 6, 1], all of length 4.

Constraints:

  • 1≤1 \leq nums.length ≤103\leq 10^3
  • −104≤-10^4 \leq nums[i] ≤104\leq 10^4

Examples

No.

Input

Output

LAS

1

[3, 1, 5, 2]

4

[3, 1, 5, 2]

2

[10, 30, 50, 70]

2

[10, 30], [30, 50], [50, 70], [10, 50], [10, 70], [30, 70]

3

[5, 5, 5, 5, 5, 5, 5]

1

[5]

4

[4, 1, 5, 6, 3, 2, 1]

4

[4, 1, 5, 3], [4, 1, 5, 2], [4, 1, 5, 1], [4, 1, 6, 3], [4, 1, 6, 2], [4, 1, 6, 1]

Try it yourself

Implement your solution in the following playground.

C++
usercode > main.cpp
int LAS(vector<int> nums)

{

    // Write Your Code Here

    return -1;

}
Longest Alternating Subsequence

Note: If you clicked the “Submit” button and the code timed out, this means that your solution needs to be optimized in terms of running time.

Hint: Use dynamic programming and see the magic.

Solution

We will first explore the naive recursive solution to this problem and then see how it can be improved using the Longest Common Substring dynamic programming pattern.

Naive approach

Let’s consider how we might write a recursive solution to this problem. We need to move from the start of the list to the end, and we need to consider all the elements. Any given element ...