Restructure blogs as Astro monorepo

sites/reflections/src/content/puzzles/dynamic-programming-gems.md

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+---
+title: "Dynamic Programming: Hidden Gems from Recent Contests"
+description: "Elegant dynamic programming problems that showcase beautiful techniques and insights."
+pubDate: "Jan 25 2024"
+image: "https://images.unsplash.com/photo-1509228468518-180dd4864904?w=400&auto=format&fit=crop&q=60"
+authorImage: "/avatar/avatar1.png"
+authorName: "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.