blogs/src/content/problems/dynamic-programming-gems.md
Neeldhara Misra b47b761f1c feat: Complete multi-blog setup with 12 collections and subdomain routing
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- Fixed TypeScript collection recognition by removing duplicate config
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Ready for GitHub/Netlify deployment with subdomain support.
2025-08-10 01:22:06 +05:30

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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.