dsa4 min read
1D Dynamic Programming — Complete Guide
Master 1D DP: Fibonacci/Climbing Stairs, House Robber, LIS, Coin Change, Jump Game, and Kadane patterns with 5-language templates.
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Knapsack
9 articles
dsa2 min read
Coin Change — Unbounded Knapsack DP
Find minimum coins to make amount. Unbounded knapsack DP: dp[amount] = min(dp[amount-coin]+1) over all coins. Bottom-up from 0 to amount.
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Coin Change II — Count Ways Unbounded Knapsack
Count number of combinations making up amount. Process each coin denomination completely (outer loop = coin) to avoid counting permutations.
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Perfect Squares — Coin Change with Squares
Minimum perfect squares summing to n. Isomorphic to Coin Change where coins = all perfect squares ≤ n.
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Partition Equal Subset Sum — 0/1 Knapsack
Can array be partitioned into two equal-sum subsets? 0/1 knapsack: can we pick some numbers summing to total/2? Bitset or DP boolean array.
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dsa1 min read
Target Sum — DP Count Ways
Assign + or - to each number to reach target sum. DP counts ways to reach each sum. Reduces to 0/1 knapsack subset sum count.
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2D Dynamic Programming — Complete Guide
Master 2D DP: LCS, Edit Distance, grid path counting, matrix chain, interval DP, and stock patterns with 5-language templates.
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Ones and Zeroes — 2D 0/1 Knapsack
Find maximum strings using at most m zeros and n ones. 2D 0/1 knapsack: dp[i][j] = max strings using i zeros and j ones.
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dsa2 min read
Partition Problems: Equal Subset Sum and K Equal Parts
Solve partition backtracking problems: equal sum subset (NP-hard, backtrack with pruning) and k equal sum subsets.
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