array plus binary indexed tree Pattern
5 problems
Pattern pages help build reusable solving frames. Identify signals first, then explain state, transition, and edge handling.
Recognition Signals
- Look for understanding of sorting and binary indexed trees.
- Check if the candidate can explain the interaction between sorting and efficient placement using BIT.
- Check if the candidate understands how to apply a Binary Indexed Tree for array manipulation and position tracking.
Solve Flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common Misses
- Not understanding the need for sorting the array by height before inserting people into the queue.
- Not using a Binary Indexed Tree or another efficient data structure could lead to a time complexity of O(n*m), which is inefficient for larger inputs.
- Failing to efficiently track counts of greater elements using an appropriate data structure.
Recommended Ladder
Queue Reconstruction by Height
Reconstruct a queue based on the given heights and the number of taller people in front, using sorting and binary indexe…
Queries on a Permutation With Key
This problem involves processing queries on a permutation using an array and binary indexed tree for efficient results.
Distribute Elements Into Two Arrays II
Distribute elements into two arrays based on conditions, utilizing a Binary Indexed Tree for efficient counting and simu…
Peaks in Array
Determine peaks in a dynamic integer array using efficient Binary Indexed Tree updates and range queries for fast result…
Alternating Groups III
Solve Alternating Groups III using array manipulation and a binary indexed tree to track maximal alternating sequences e…