Longest Decreasing Subsequence Problem Statement

Given an array/list of integers ARR consisting of N integers, your task is to determine the length of the longest decreasing subsequence.

Explanation:

A subsequence is a sequence derived by deleting zero or more elements from the array/list without changing the order of the remaining elements. A decreasing subsequence is one where each subsequent element is strictly less than the previous element.

Input:

T: Integer, number of test cases N: Integer, size of array/list for each test case ARR: List of integers, each representing elements of the array/list

Output:

For each test case, output the length of the longest decreasing subsequence. Separate each test case result with a new line.

Example:

Input: 1 5 [5, 0, 3, 2, 9] Output: 3 Explanation: For the given array [5, 0, 3, 2, 9], the longest decreasing subsequence is of length 3, e.g., [5, 3, 2].

Constraints:

1 ≤ T ≤ 50

1 ≤ N ≤ 5000

1 ≤ ARR[i] ≤ 10^9

Time Limit: 1 sec

Note:

There can be more than one subsequence with the longest length. Attempt to solve the problem in O(N log N) time complexity.

Question

Longest Decreasing Subsequence Problem Statement

Given an array/list of integers ARR consisting of N integers, your task is to determine the length of the longest decreasing subsequence.

Explanation:

A subsequence is a sequence derived by deleting zero or more elements from the array/list without changing the order of the remaining elements. A decreasing subsequence is one where each subsequent element is strictly less than the previous element.

Input:

T: Integer, number of test cases
N: Integer, size of array/list for each test case
ARR: List of integers, each representing elements of the array/list

Output:

For each test case, output the length of the longest decreasing subsequence.
Separate each test case result with a new line.

Example:

Input:
1
5
[5, 0, 3, 2, 9]
Output:
3

Explanation:
For the given array [5, 0, 3, 2, 9], the longest decreasing subsequence is of length 3, e.g., [5, 3, 2].

Constraints:

1 ≤ T ≤ 50
1 ≤ N ≤ 5000
1 ≤ ARR[i] ≤ 10^9
Time Limit: 1 sec

Note:

There can be more than one subsequence with the longest length.
Attempt to solve the problem in O(N log N) time complexity.

Accepted Answer

Find the length of the longest decreasing subsequence in an array of integers.

Use dynamic programming to keep track of the length of the longest decreasing subsequence ending at each index.
Initialize an array to store the length of the longest decreasing subsequence for each element.
Iterate through the array and update the length of the longest decreasing subsequence for each element based on previous elements.
Return the maximum length of the longest decreasing subsequence found.
Example: For [5, 0, 3, 2, 9], the longest decreasing subsequence is [5, 3, 2] with a length of 3.