Sep 19, 2026 · Fundamentals

Dynamic Programming Mastery: 11 Classic Problems Solved with Recurrences & C Code

This article analyzes 11 classic dynamic programming problems including coin change, edit distance, LCS, LIS, maximum subarray, matrix chain multiplication, 0-1 knapsack, constrained shortest path, tiling with state compression, work allocation, and three-pass apple picking, providing recurrence relations, C implementations, and optimization techniques.

0-1 knapsackcoin changedynamic programming

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Dynamic Programming Mastery: 11 Classic Problems Solved with Recurrences & C Code

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Nov 24, 2023 · Fundamentals

How to Solve the Coin Change Problem Using Dynamic Programming

This article explains the classic coin change problem, models it as a minimum‑coin DP task, derives the recurrence relation, shows how to initialize the DP array with a large sentinel value, and provides a complete Go implementation that returns the optimal count or -1 when impossible.

DP recurrenceGoalgorithm

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How to Solve the Coin Change Problem Using Dynamic Programming