Dynamic programming

2026-07-06 · Source: Data Science on Medium · Field: Technology & Digital — Software Development & Engineering, Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Intermediate, short

Summary

Dynamic Programming (DP) is a problem-solving technique that breaks down complex problems into smaller, overlapping subproblems, storing their solutions in a table to derive an optimal overall solution. Unlike a fixed algorithm, DP adapts to specific problems, consistently utilizing a data structure, typically a table, to store intermediate results. The article illustrates DP through two classic examples: the Knapsack Problem and the Longest Common Substring. For the Knapsack Problem, DP determines the highest-value item combination within a 4kg capacity, identifying "Guitar" and "Notebook" as optimal. In the Longest Common Substring problem, DP helps find common sequences between words like "hish" and "fish" for search suggestions, where the largest table value indicates the solution.

Key takeaway

For Software Engineers or Data Scientists tackling optimization challenges with constraints, Dynamic Programming offers a structured approach to ensure optimal solutions. You should consider modeling problems with overlapping subproblems using a table-based method, as demonstrated by the Knapsack and Longest Common Substring examples. This technique helps avoid redundant computations and systematically explores solution spaces, leading to efficient and accurate results for resource allocation or string matching tasks.

Key insights

Dynamic Programming optimizes complex problems by tabulating subproblem solutions to find global optima.

Principles

• Optimal solutions arise from subproblem solutions.
• A table stores intermediate results for reuse.
• Problem constraints guide table construction.

Method

To apply Dynamic Programming, divide the problem into subproblems, define cell values, and determine table axes. Calculate cell values using previously stored results.

In practice

• Solve knapsack-type resource allocation.
• Implement search suggestion features.
• Optimize sequence alignment tasks.

Topics

• Dynamic Programming
• Optimization Algorithms
• Knapsack Problem
• Longest Common Substring
• Algorithm Design
• Data Structures

Code references

• Gabriel-Pessoa/algorithms

Best for: Software Engineer, AI Student, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Data Science on Medium.