Dynamic Programming or DP

Dynamic Programming or DP

Last Updated : 18 Mar, 2025

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

Basic Problems

Easy Problems

Medium Problems

Hard Problems

DP Problems Sorted by Topic / Dimensions / Standard Problems

Advanced Concepts in Dynamic Programming (DP)

Quick Links:

Dynamic Programming or DP

H

harendrakumar123

Improve

Article Tags :

Practice Tags :

Similar Reads

DSA Tutorial - Learn Data Structures and Algorithms

DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively. Data structures manage how data is stored and accessed, while algorithms focus on

Array Data Structure Guide

In this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous

String in Data Structure

A string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut

Matrix Data Structure

Matrix Data Structure is a two-dimensional array arranged in rows and columns. It is commonly used to represent mathematical matrices and is fundamental in various fields like mathematics, computer graphics, and data processing. Matrices allow for efficient storage and manipulation of data in a stru

Searching Algorithms

Searching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input

Sorting Algorithms

A Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ

Hashing in Data Structure

Hashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The

Two Pointers Technique

Two pointers is really an easy and effective technique that is typically used for Two Sum in Sorted Arrays, Closest Two Sum, Three Sum, Four Sum, Trapping Rain Water and many other popular interview questions. Given a sorted array arr (sorted in ascending order) and a target, find if there exists an

Sliding Window Technique

Sliding Window Technique is a method used to solve problems that involve subarray or substring or window. The main idea is to use the results of previous window to do computations for the next window. This technique is commonly used in algorithms like finding subarrays with a specific sum, finding t

Prefix Sum Array - Implementation and Applications

Given an array arr[] of size n, the task is to find the prefix sum of the array. A prefix sum array is another array prefixSum[] of the same size, such that prefixSum[i] is arr[0] + arr[1] + arr[2] . . . arr[i].Examples: Input: arr[] = [10, 20, 10, 5, 15]Output: 10 30 40 45 60Explanation: For each i