Is Number of Longest Increasing Subsequence easy or hard?

The problem is rated Medium because it extends the classic Longest Increasing Subsequence problem. Finding the LIS length is already a common dynamic programming problem, but counting the number of optimal subsequences adds an extra layer of reasoning.

Number of Longest Increasing Subsequence Python/Java solution

Most implementations maintain two arrays: length[i] for LIS length ending at index i and count[i] for the number of such subsequences. This logic is straightforward to implement in Python, Java, C++, JavaScript, or C# with nested loops and simple array updates.

How to solve Number of Longest Increasing Subsequence in O(n log n)?

Use coordinate compression and maintain a Binary Indexed Tree or Segment Tree that stores the best LIS length and number of ways for each value range. For each number, query the structure for the best result among smaller values, then update the tree with the new length and count.

What is the best approach for Number of Longest Increasing Subsequence?

The most common approach uses dynamic programming with two arrays: one tracking the LIS length ending at each index and another tracking how many subsequences achieve that length. This solution runs in O(n^2) time and O(n) space and is the approach most interviewers expect.

Is Number of Longest Increasing Subsequence asked at Google/Amazon/Meta?

Variants of LIS and counting subsequences appear frequently in interviews at companies like Amazon, Google, and Meta. Interviewers often expect candidates to first recognize the LIS pattern and then extend it to count how many optimal subsequences exist.

What data structure is used in Number of Longest Increasing Subsequence?

The core solution uses arrays for dynamic programming. Optimized solutions may use advanced data structures such as Binary Indexed Trees (Fenwick Trees) or Segment Trees to efficiently query and update LIS states in O(log n) time.

What is the time complexity of Number of Longest Increasing Subsequence?

The standard dynamic programming solution runs in O(n^2) time because each element compares with all previous elements. Space complexity is O(n) for the length and count arrays. Optimized approaches using Fenwick Tree or Segment Tree reduce the time to O(n log n).

Description Solution Video 20:46

673. Number of Longest Increasing Subsequence

Medium52.8% acceptance6 companies

Given an integer array nums, return the number of longest increasing subsequences.

Notice that the sequence has to be strictly increasing.

Example 1:

Input: nums = [1,3,5,4,7]
Output: 2
Explanation: The two longest increasing subsequences are [1, 3, 4, 7] and [1, 3, 5, 7].

Example 2:

Input: nums = [2,2,2,2,2]
Output: 5
Explanation: The length of the longest increasing subsequence is 1, and there are 5 increasing subsequences of length 1, so output 5.

Constraints: