tech-interview-handbook/contents/algorithms/dynamic-programming.md

---
id: dynamic-programming
title: Dynamic programming cheatsheet for coding interviews
description: Dynamic programming study guide for coding interviews, including practice questions, techniques, time complexity, and recommended resources
keywords:
  [
    dynamic programming coding interview study guide,
    dynamic programming tips for coding interviews,
    dynamic programming practice questions,
    dynamic programming useful techniques,
    dynamic programming time complexity,
    dynamic programming recommended study resources,
  ]
sidebar_label: Dynamic programming
toc_max_heading_level: 2
---

<head>
  <meta property="og:image" content="https://www.techinterviewhandbook.org/social/algorithms/algorithms/algorithms-dynamic-programming.png" />
</head>

## Introduction

Dynamic Programming (DP) is usually used to solve optimization problems. The only way to get better at DP is to practice. It takes some amount of practice to be able to recognize that a problem can be solved by DP.

## Learning resources

- [Demystifying Dynamic Programming](https://medium.freecodecamp.org/demystifying-dynamic-programming-3efafb8d4296)
- [Dynamic Programming – 7 Steps to Solve any DP Interview Problem](https://dev.to/nikolaotasevic/dynamic-programming--7-steps-to-solve-any-dp-interview-problem-3870)
- [Less Repetition, More Dynamic Programming](https://medium.com/basecs/less-repetition-more-dynamic-programming-43d29830a630), basecs
- [Dynamic Programming](http://www.cs.yale.edu/homes/aspnes/classes/223/notes.html#dynamicProgramming), James Aspnes, Yale University

## Techniques

Sometimes you do not need to store the whole DP table in memory, the last two values or the last two rows of the matrix will suffice.

## Essential questions

_These are essential questions to practice if you're studying for this topic._

- [Climbing Stairs](https://leetcode.com/problems/climbing-stairs/)
- [Coin Change](https://leetcode.com/problems/coin-change/)
- [House Robber](https://leetcode.com/problems/house-robber/)
- [Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence/)

## Recommended practice questions

_These are recommended questions to practice after you have studied for the topic and have practiced the essential questions._

- [0/1 Knapsack or Partition Equal Subset Sum](https://leetcode.com/problems/partition-equal-subset-sum/)
- [Longest Common Subsequence](https://leetcode.com/problems/longest-common-subsequence/)
- [Word Break Problem](https://leetcode.com/problems/word-break/)
- [Combination Sum](https://leetcode.com/problems/combination-sum-iv/)
- [House Robber II](https://leetcode.com/problems/house-robber-ii/)
- [Decode Ways](https://leetcode.com/problems/decode-ways/)
- [Unique Paths](https://leetcode.com/problems/unique-paths/)
- [Jump Game](https://leetcode.com/problems/jump-game/)

## Recommended courses

import AlgorithmCourses from '../\_courses/AlgorithmCourses.md'

### [Grokking Dynamic Programming Patterns for Coding Interviews](https://designgurus.org/link/kJSIoU?url=https%3A%2F%2Fdesigngurus.org%2Fcourse%3Fcourseid%3Dgrokking-dynamic-programming)

Brought to you by the same folks behind the famous ["Grokking the Coding Interview"](https://designgurus.org/link/kJSIoU?url=https%3A%2F%2Fdesigngurus.org%2Fcourse%3Fcourseid%3Dgrokking-the-coding-interview), this is one of the rare few courses focused on helping you get better at Dynamic Programming questions. If you are interviewing for companies who are famous for asking Dynamic Programming questions (-cough- Google -cough-), this course should be helpful.

<AlgorithmCourses />
-												website: add front matter

											
										
										
											5 years ago
+								---
 								id: dynamic-programming
-												website: add sidebar structure

											
										
										
											3 years ago
+								title: Dynamic programming cheatsheet for coding interviews
 								description: Dynamic programming study guide for coding interviews, including practice questions, techniques, time complexity, and recommended resources
 								keywords:
 								  [
 								    dynamic programming coding interview study guide,
 								    dynamic programming tips for coding interviews,
 								    dynamic programming practice questions,
 								    dynamic programming useful techniques,
 								    dynamic programming time complexity,
 								    dynamic programming recommended study resources,
 								  ]
 								sidebar_label: Dynamic programming
-												contents: revamp basic algo content

											
										
										
											3 years ago
+								toc_max_heading_level: 2
-												website: add front matter

											
										
										
											5 years ago
+								---
-												Squash commit

											
										
										
											7 years ago
-												seo: add social image

											
										
										
											3 years ago
+								<head>
 								  <meta property="og:image" content="https://www.techinterviewhandbook.org/social/algorithms/algorithms/algorithms-dynamic-programming.png" />
 								</head>
-												contents: revamp basic algo content

											
										
										
											3 years ago
+								## Introduction
 								Dynamic Programming (DP) is usually used to solve optimization problems. The only way to get better at DP is to practice. It takes some amount of practice to be able to recognize that a problem can be solved by DP.
 								## Learning resources
-												website: launch website

											
										
										
											5 years ago
 								- [Demystifying Dynamic Programming](https://medium.freecodecamp.org/demystifying-dynamic-programming-3efafb8d4296)
 								- [Dynamic Programming – 7 Steps to Solve any DP Interview Problem](https://dev.to/nikolaotasevic/dynamic-programming--7-steps-to-solve-any-dp-interview-problem-3870)
-												contents: revamp basic algo content

											
										
										
											3 years ago
+								- [Less Repetition, More Dynamic Programming](https://medium.com/basecs/less-repetition-more-dynamic-programming-43d29830a630), basecs
 								- [Dynamic Programming](http://www.cs.yale.edu/homes/aspnes/classes/223/notes.html#dynamicProgramming), James Aspnes, Yale University
-												website: launch website

											
										
										
											5 years ago
-												contents: revamp basic algo content

											
										
										
											3 years ago
+								## Techniques
-												website: launch website

											
										
										
											5 years ago
 								Sometimes you do not need to store the whole DP table in memory, the last two values or the last two rows of the matrix will suffice.
-												contents(algo): split recommended qns into essential vs practice

											
										
										
											3 years ago
+								## Essential questions
 								_These are essential questions to practice if you're studying for this topic._
-												website: launch website

											
										
										
											5 years ago
 								- [Climbing Stairs](https://leetcode.com/problems/climbing-stairs/)
 								- [Coin Change](https://leetcode.com/problems/coin-change/)
-												contents(algo): split recommended qns into essential vs practice

											
										
										
											3 years ago
+								- [House Robber](https://leetcode.com/problems/house-robber/)
-												website: launch website

											
										
										
											5 years ago
+								- [Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence/)
-												contents(algo): split recommended qns into essential vs practice

											
										
										
											3 years ago
 								## Recommended practice questions
 								_These are recommended questions to practice after you have studied for the topic and have practiced the essential questions._
 								- [0/1 Knapsack or Partition Equal Subset Sum](https://leetcode.com/problems/partition-equal-subset-sum/)
-												contents: link to LeetCode's Longest Common Subsequence question (#150)


											
										
										
											5 years ago
+								- [Longest Common Subsequence](https://leetcode.com/problems/longest-common-subsequence/)
-												website: launch website

											
										
										
											5 years ago
+								- [Word Break Problem](https://leetcode.com/problems/word-break/)
 								- [Combination Sum](https://leetcode.com/problems/combination-sum-iv/)
-												contents(algo): split recommended qns into essential vs practice

											
										
										
											3 years ago
+								- [House Robber II](https://leetcode.com/problems/house-robber-ii/)
-												website: launch website

											
										
										
											5 years ago
+								- [Decode Ways](https://leetcode.com/problems/decode-ways/)
 								- [Unique Paths](https://leetcode.com/problems/unique-paths/)
 								- [Jump Game](https://leetcode.com/problems/jump-game/)
-												contents: add Educative

											
										
										
											3 years ago
-												contents: reorganize algorithms section

											
										
										
											3 years ago
+								## Recommended courses
-												contents: add Educative

											
										
										
											3 years ago
-												contents: reorganize algorithms section

											
										
										
											3 years ago
+								import AlgorithmCourses from '../\_courses/AlgorithmCourses.md'
-												misc: s/Educative/Design Gurus

											
										
										
											2 years ago
+								### [Grokking Dynamic Programming Patterns for Coding Interviews](https://designgurus.org/link/kJSIoU?url=https%3A%2F%2Fdesigngurus.org%2Fcourse%3Fcourseid%3Dgrokking-dynamic-programming)
 								Brought to you by the same folks behind the famous ["Grokking the Coding Interview"](https://designgurus.org/link/kJSIoU?url=https%3A%2F%2Fdesigngurus.org%2Fcourse%3Fcourseid%3Dgrokking-the-coding-interview), this is one of the rare few courses focused on helping you get better at Dynamic Programming questions. If you are interviewing for companies who are famous for asking Dynamic Programming questions (-cough- Google -cough-), this course should be helpful.
-												contents: reorganize algorithms section

											
										
										
											3 years ago
+								<AlgorithmCourses />