Dynamic Programming Made Easy: A Step-by-Step Beginner Guide

Master linear dynamic programming with a four-step approach—identify subproblems, define recurrence relations, solve bottom-up, and combine results—through concrete examples like Fibonacci, climbing stairs, house robber, and jump game.

Master dynamic programming approach to the climbing stairs problem. Use dp[i] = dp[i-1] + dp[i-2] with base cases dp[0] = dp[1] = 1 to count ways to reach step N.

Explore Kadane's algorithm, a one-pass method for maximum subarray problems. Track maximum sum so far, maintain current sum, and reset when negative; apply maximum circular subarray and maximum product variants.

Explores the maximum subarray problem using dynamic programming, introducing a DP table and the recurrence DP[i] = max(nums[i], DP[i-1] + nums[i]), to find the contiguous subarray with the largest sum.

Explore dynamic programming to solve the maximum circular subarray sum in a circular array. Handle normal and wrap-around cases using total sum and minimum subarray sum, including negative-number edge cases.

Learn how to find the maximum product subarray (contiguous) by tracking both maximum and minimum products at each step, using a dynamic programming approach with O(n) time and O(1) space.

Use dynamic programming to solve best time to buy and sell stock, buying low, selling high, and maximizing profit by tracking min price and max profit in a single pass.

Solve the subset sum problem with dynamic programming, guiding you through a dp table, base case sums, and include or exclude decisions to reach the target.

Learn how the unbounded knapsack uses unlimited item copies to maximize value with a dynamic programming table, and explore coin change and rod cutting variations.

Solve the coin change ii problem using dynamic programming to count the number of coin combinations that sum to a given amount, using an unbounded knapsack dp.

Solve the longest common subsequence problem using dynamic programming, showing a space-optimized approach with two arrays that reduces memory from O(mn) to O(n) while computing the LCS of two strings.

Solve the longest palindromic subsequence with dynamic programming, building a two-dimensional dp table and a space-optimized array. Apply matching and non-matching transitions and identify base cases to achieve O(n^2) time.