Post by Manik Sharma

🚀#Day9 of my DP Series : Coin Change II 💰 Aagye meri maut ka tamasha dekhne Sab Dekho .......Dekho Aacha h Aacha h....... 😁 Today I worked on Coin Change II (LeetCode) 💰 — another interesting problem from the Unbounded Knapsack pattern. 📝 Problem statement: Given coins of different denominations and a total amount, find the number of combinations that make up that amount. (Order of coins doesn’t matter, only combinations count.) 🔑 My approach (2D DP): 1️⃣ Create a DP table t[n+1][amount+1] where t[i][j] represents the number of ways to make sum j using the first i coins. 2️⃣ Base case: There is always 1 way to make amount 0 (by choosing nothing). 3️⃣ Transition: If the coin value ≤ current amount → include it (t[i][j - coin]) + exclude it (t[i-1][j]). Else → carry over the value from above (t[i-1][j]). 4️⃣ Final answer is stored in t[n][amount]. 💡 Key Learnings: When order doesn’t matter, treat it as combinations, not permutations. The “include / exclude” approach still holds strong in the unbounded knapsack world. Small changes in problem statements (min coins ➝ total ways) can completely shift the DP perspective. 🌱 Each new problem strengthens my grasp on patterns and makes the bigger DP picture clearer. Truly, consistency compounds over time! #DynamicProgramming #DPSeries #ProblemSolving #DSA #CodingJourney #Learning