Number of Longest Increasing Subsequence
A medium-tier problem at 50% community acceptance, tagged with Array, Dynamic Programming, Binary Indexed Tree. Reported in interviews at Commvault and 1 others.
You're at the tail end of a DP section, feeling solid on LIS, and suddenly the problem asks not just the length but how many different longest increasing subsequences exist. Commvault and Intuit have asked this. It's a medium with a 49% acceptance rate, which means half the candidates in the room walked away stuck. The trick isn't finding LIS anymore. It's counting every valid path without double-counting or missing edge cases. If you hit this live and blank on the state transition, StealthCoder surfaces a working solution in seconds while the proctor sees nothing.
Companies that ask "Number of Longest Increasing Subsequence"
Number of Longest Increasing Subsequence is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Made by a working FAANG engineer who treats the OA the way companies treat hiring: as a game with rules you should know.
Get StealthCoderThe catch is that you need two DP arrays running in parallel: one for the length of the longest increasing subsequence ending at each index, and one for the count of distinct subsequences that achieve that length. Naive approaches fail because they either only track length or they count duplicates. The real pressure point is handling the count carefully when you encounter an equal-length predecessor. If the new element can extend multiple different LIS chains of the same length, you can't just pick one. You need to sum the counts. Many candidates get the length right but crater on the counting logic. Binary Indexed Trees and Segment Trees are advanced optimizations for large arrays, but the core insight is the dual DP state. When you're stuck in the assessment, StealthCoder handles both the state design and the transition rules instantly.
Pattern tags
You know the problem.
Make sure you actually pass it.
Number of Longest Increasing Subsequence recycles across companies for a reason. It's medium-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Made by a working FAANG engineer who treats the OA the way companies treat hiring: as a game with rules you should know. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Number of Longest Increasing Subsequence interview FAQ
Is this actually harder than standard LIS problems?+
Yes. Standard LIS is one DP array and O(n^2) or O(n log n). This adds a counting layer that forces you to track multiple predecessors and sum their counts. The 49% acceptance rate reflects that jump in complexity. Most people nail the length part and fail the count.
Do Commvault and Intuit really ask this regularly?+
Both companies are in the input data for this problem. It's not a top-10 most-asked problem, but it shows up in their loops. If you're interviewing there, odds aren't high, but you can't afford to be blindsided by it.
What's the trick to not double-count subsequences?+
When you see a new element that matches the length of an existing LIS ending at a previous index, you add that previous count to your current count. Don't overwrite. The state is 'count of distinct LIS of length k ending here,' not 'count of ways to build LIS.' The distinction kills most wrong submissions.
When do I need Binary Indexed Tree or Segment Tree?+
Not for the basic solution. Those are optimizations to handle count queries and updates across a large value range faster than O(n^2). Start with the nested-loop DP. If TLE hits and the array is huge, then consider those advanced structures.
How does this problem relate to the other Array and DP topics listed?+
It combines Array iteration with DP state management. Binary Indexed Tree and Segment Tree are optional accelerators for range queries. The core is DP: understanding how to track two dimensions of state simultaneously without losing precision or counting duplicates.
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