This series of videos are focused on explaining dynamic programming by illustrating the application of DP through the use of selected problems from platforms like Codeforces, Codechef, SPOJ, CSES and Atcoder.

After going through this series, you should find yourself confident in approaching dynamic programming problems and also implementing them in a reasonable amount of time.

I will also live code and submit the solutions to the problem on the coding platform from where the problem comes.

# Some Basic elements of Dynamic Programming

Some general ideas and my thoughts about DP to help you get started:

Part 1: https://youtu.be/24hk2qW_BCU

1. What is Divide and Conquer?

2. What is Dynamic Programming?

3. Types of DP problems.

Part 2: https://youtu.be/yfgKw6BUZUk

1. What is a DP-state?

2. Characterizing a DP-state.

3. What is a recurrence?

4. Top Down v/s Bottom Up.

Part 3: https://youtu.be/X-3HklSPx6k

1. Directed Acyclic Graph(DAG) Representation of DP solution

2. Visualizing Top-Down and Bottom-Up.

3. Evaluation order for bottom-up codes.

4. Analyzing the space and time complexity for a DP solution(derivation).

## Problem 1: Dice Combinations

Source: CSES

Problem link: https://cses.fi/problemset/task/1633

Explanation: https://youtu.be/5gd5jptXWAM

## Problem 2: Coin Combinations I

Source: CSES

Problem link: https://cses.fi/problemset/task/1635

Explanation: https://youtu.be/5BdAl6gfusg

## Problem 3: Coin Combinations II

Source: CSES

Problem link: https://cses.fi/problemset/task/1636

Explanation: https://youtu.be/-pXjopzMVrE

## Problem 4: Removing Digits

Source: CSES

Problem link: https://cses.fi/problemset/task/1637

Explanation: https://youtu.be/32qvB7OP4V8

## Problem 5: Grid Paths

Source: CSES

Problem link: https://cses.fi/problemset/task/1638

Explanation: https://youtu.be/V64F4wlodUM

## Problem 6: Book Shop

Source: CSES

Problem link: https://cses.fi/problemset/task/1633

Explanation: https://youtu.be/qpNy2nuSuaI

## Problem 7: Array Description

Source: CSES

Problem link: https://cses.fi/problemset/task/1158

Explanation: https://youtu.be/d1H5JylYG4I

## Problem 8: Edit Distance

Source: CSES

Problem link: https://cses.fi/problemset/task/1639

Explanation: https://youtu.be/Ev80c1oIRFg

## Problem 9: Rectangle Cutting

Source: CSES

Problem link: https://cses.fi/problemset/task/1744

Explanation: https://youtu.be/LdynQjWsO5Q

## Problem 10: Two Sets II

Source: CSES

Problem link: https://cses.fi/problemset/task/1093

Explanation: https://youtu.be/TOsD3BkIKoQ

## Problem 11: Beautiful Array

Source: Codeforces

Problem link: https://codeforces.com/problemset/problem/1155/D

Explanation: https://youtu.be/IgBLv32QFoQ

## Problem 12: Number of Valid Arrays

Source: Coding Interview

Problem link: Problem Statement

Explanation: https://youtu.be/QGJXQAaDs3I

## Problem 13: Longest Increasing Subsequence O(NlogN)

Source: CSES

Problem link: https://codeforces.com/problemset/problem/1155/D

Proof and optimization to NlogN: https://youtu.be/66w10xKzbRM

Implementation of the algorithm: https://youtu.be/wqLwv7E1GF0

## Problem 14: Projects

Source: CSES

Problem link: https://cses.fi/problemset/task/1140

Solution Approach: https://youtu.be/MJn3ogwsUbo

Implementation of the algorithm: https://youtu.be/ISuIwMnSyXc

## Problem 15: Beauty of Tree

Source: Kick Start

Problem link: Long link

Explanation: https://youtu.be/ueLRceYVcdE

## Problem 16: Catch Some

Source: Kick Start

Problem link: Long link

Explanation: https://youtu.be/ljLIrNKLANE

## Problem 17: Vasya and Binary Strings

Source: Codeforces (rated:2400)

Problem link: https://codeforces.com/problemset/problem/1107/E

Explanation: https://youtu.be/NINZAQFW_AE

## Problem 18: Counting Towers

Source: CSES 2021 problem

Problem link: https://cses.fi/problemset/task/2413

Explanation: https://youtu.be/pMEYMYTX-r0

I am quite confident that many beginners/intermediates will definitely enjoy watching this series on dynamic programming and it will definitely help in getting better at dynamic programming and problem solving in general. I have tried to teach in a way such that not many prior prerequisites are required to understand the explanations even to the harder problems.

If people find this helpful then I will make sure that this list of problems will keep growing, cheers!

Link for introduction to DP on Trees: https://codeforces.com/blog/entry/79857

**UPD**: Added 2 more problems from CSES: Projects and Removing digits.

**UPD**: Added 3 parts on basic elements of DP to get you started.

**UPD**: I have also started a series on DP with bitmasking(starting from the very basics) and in the future will make a separate blog for both Digit DP series and DP with bitmasking series, till then interested people can check: Dynamic Programming with bitmasking

**UPD**: added solution to problem Vasya and Binary Strings

**UPD**: added solution to problem Counting towers from CSES