1.2 KiB
1.2 KiB
| title | description | pubDate | image | authorImage | authorName |
|---|---|---|---|---|---|
| Dynamic Programming: Hidden Gems from Recent Contests | Elegant dynamic programming problems that showcase beautiful techniques and insights. | Jan 25 2024 | https://images.unsplash.com/photo-1509228468518-180dd4864904?w=400&auto=format&fit=crop&q=60 | /avatar/avatar1.png | Neeldhara |
Dynamic Programming: Hidden Gems from Recent Contests
These problems demonstrate the art of dynamic programming beyond standard patterns.
Problem 1: The Subsequence Symphony
Given a string, find the number of subsequences that form palindromes of prime length.
Solution Insight
The key is to maintain DP states for both position and palindrome center simultaneously. This reduces the state space from O(n³) to O(n²).
Problem 2: Graph Coloring with Constraints
Color a graph such that no two adjacent vertices share a color, and the total number of color changes along any path is minimized.
The DP Formulation
DP[node][color][changes] gives us the minimum cost. The trick is recognizing that we only need to track changes modulo 2.
Practice Makes Perfect
These problems teach us that DP is as much about problem modeling as it is about computation.