math plus combinatorics Pattern
4 problems
Pattern pages help build reusable solving frames. Identify signals first, then explain state, transition, and edge handling.
Recognition Signals
- Candidate suggests an efficient combinatorial approach.
- Candidate considers dynamic programming for optimization.
- Strong understanding of combinatorics and enumeration techniques.
Solve Flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common Misses
- Forgetting to check that the sum of candies matches n.
- Forgetting to account for the limit on the number of candies each child can receive.
- Not correctly handling the modulo operation, leading to overflow errors.
Recommended Ladder
Distribute Candies Among Children I
Given two integers n and limit, find the number of ways to distribute n candies among 3 children, with no child receivin…
Distribute Candies Among Children II
Determine how to distribute n candies among 3 children without exceeding a limit on individual candies.
Count the Number of Arrays with K Matching Adjacent Elements
Count the number of valid arrays with exactly k adjacent elements that are equal, using math and combinatorics technique…
Manhattan Distances of All Arrangements of Pieces
This problem challenges you to calculate Manhattan distances in all valid arrangements of identical pieces on a grid.