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Subset Sum
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Divide and Conquer Algorithm

Dynamic Programming or DP

Last Updated : 18 Mar, 2025

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Dynamic Programming is an algorithmic technique with the following properties.

It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming.
The idea is to simply store the results of subproblems so that we do not have to re-compute them when needed later. This simple optimization typically reduces time complexities from exponential to polynomial.
Some popular problems solved using Dynamic Programming are Fibonacci Numbers, Diff Utility (Longest Common Subsequence), Bellman–Ford Shortest Path, Floyd Warshall, Edit Distance and Matrix Chain Multiplication.

Basic of DP

Introduction to DP
Tabulation vs Memoization
Steps to solve a DP Problem

Basic Problems

Fibonacci numbers
Tribonacci Numbers
Lucas Numbers
Climbing Stairs
Climbing Stairs with 3 Moves
Weighted Climbing Stairs
Maximum Segments
nth Catalan Number
Count Unique BSTs
Count Valid Parenthesis
Ways to Triangulate a Polygon
Min Sum in a Triangle
Minimum Perfect Squares
Ways to Partition a Set
Binomial Coefficient
Pascal's Triangle
Nth Row of Pascal Triangle
Min Sum in a Triangle

Easy Problems

House Robber
Min Cost Path
Decode Ways
Subset Sum Problem
Coin change problem - Count Ways
Coin Change – Minimum Coins to Make Sum
Painting Fence Algorithm
Cutting a Rod
Jump Game
Longest Common Substring
Count all paths in a Grid
Paths in a Grid with Obstacles
Permutations with K Inversions
Max A's using Special Keyboard

Medium Problems

Water Overflow
Longest Common Subsequence
Longest Increasing Subsequence
Edit Distance
Largest Divisible Subset
Weighted Job Schedulling
0-1 Knapsack Problem
Printing Items in 0/1 Knapsack
Unbounded Knapsack
Word Break Problem
Tile Stacking Problem
Box-Stacking Problem
Partition Problem
Longest Palindromic Subsequence
Longest Common Increasing Subsequence (LCS + LIS)
All distinct subset (or subsequence) sums
Count Derangements
Minimum insertions for palindrome
Wildcard Pattern Matching
Regular Expression Matching
Arrange Balls with adjacent of different types
Longest Subsequence with 1 adjacent difference
Maximum size square sub-matrix with all 1s
Bellman–Ford Algorithm
Floyd Warshall Algorithm
Maximum Tip Calculator

Hard Problems

Largest X Bordered Square
Egg Dropping Problem
Palindrome Partitioning
Palindromic Substring Count
Word Wrap Problem
Optimal Strategy for a Game
The painter’s partition problem
Program for Bridge and Torch problem
Matrix Chain Multiplication
Printing Matrix Chain Multiplication
Maximum sum rectangle
Stock Buy and Sell - At-Most k Times
Stock Buy and Sell - At Most 2 Times
Min cost to sort strings using Reversals
Count of AP Subsequences
DP on Trees
Max Height of Tree when any Node can be Root
Longest repeating and non-overlapping substring
Palindrome Substrings Count

DP Problems Sorted by Topic / Dimensions / Standard Problems

DP Standard Problems and Variations.
DP Problems Dimension Wise (1D, 2D and 3D)
DP Problems Topic Wise

Advanced Concepts in Dynamic Programming (DP)

Bitmasking and Dynamic Programming | Set 1
Bitmasking and Dynamic Programming | Set-2 (TSP)
Digit DP | Introduction
Sum over Subsets | Dynamic Programming

Quick Links:

Learn Data Structure and Algorithms | DSA Tutorial
Top 20 Dynamic Programming Interview Questions
‘Practice Problems’ on Dynamic Programming
‘Quiz’ on Dynamic Programming

Divide and Conquer Algorithm

H

harendrakumar123

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Article Tags :

Algorithms
Dynamic Programming
DSA

Practice Tags :

Algorithms
Dynamic Programming

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