What is Dynamic Programming?

Introduction

0/1 Knapsack

Solution: 0/1 Knapsack

Equal Subset Sum Partition

Solution: Equal Subset Sum Partition

Subset Sum

Solution: Subset Sum

Minimum Subset Sum Difference

Solution: Minimum Subset Sum Difference

Count of Subset Sum

Solution: Count of Subset Sum

Target Sum

Solution: Target Sum

Pattern 1: 0/1 Knapsack

Unbounded Knapsack

Solution: Unbounded Knapsack

Rod Cutting

Solution: Rod Cutting

Coin Change

Solution: Coin Change

Minimum Coin Change

Solution: Minimum Coin Change 

Maximum Ribbon Cut

Solution: Maximum Ribbon Cut

Pattern 2: Unbounded Knapsack

Fibonacci numbers

Solution: Fibonacci numbers

Staircase

Solution: Staircase

Number factors

Solution: Number factors

Minimum jumps to reach the end

Solution: Minimum jumps to reach the end

Minimum jumps with fee

Solution: Minimum jumps with fee

House thief

Solution: House thief

Pattern 3: Fibonacci Numbers

Longest Palindromic Subsequence

Solution: Longest Palindromic Subsequence

Longest Palindromic Substring

Solution: Longest Palindromic Substring

Count of Palindromic Substrings

Solution: Count of Palindromic Substrings

Minimum Deletions in a String to make it a Palindrome

Solution: Minimum Deletions in a String to make it a Palindrome

Palindromic Partitioning

Solution: Palindromic Partitioning

Pattern 4: Palindromic Subsequence

Longest Common Substring

Solution: Longest Common Substring

Longest Common Subsequence

Solution: Longest Common Subsequence

Minimum Deletions & Insertions to Transform a String into another

Solution: Minimum Deletions & Insertions to Transform a String into another

Longest Increasing Subsequence

Solution: Longest Increasing Subsequence

Maximum Sum Increasing Subsequence

Solution: Maximum Sum Increasing Subsequence

Shortest Common Super-sequence

Solution: Shortest Common Super-sequence

Minimum Deletions to Make a Sequence Sorted

Solution: Minimum Deletions to Make a Sequence Sorted

Longest Repeating Subsequence

Solution: Longest Repeating Subsequence

Subsequence Pattern Matching

Solution: Subsequence Pattern Matching

Longest Bitonic Subsequence

Solution: Longest Bitonic Subsequence

Longest Alternating Subsequence

Solution: Longest Alternating Subsequence

Edit Distance

Solution: Edit Distance

Strings Interleaving

Solution: Strings Interleaving

Pattern 5: Longest Common Substring

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Appendix

Grokking Dynamic Programming Patterns for Coding Interviews

## Problem Statement
Given a sequence, find the length of its Longest Palindromic Subsequence (LPS). In a palindromic subsequence, elements read the same backward and forward.

A [subsequence](https://en.wikipedia.org/wiki/Subsequence) is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements. 

**Example 1:**
```
Input: "abdbca"
Output: 5
Explanation: LPS is "abdba".
```

**Example 2:**
```
Input: = "cddpd"
Output: 3
Explanation: LPS is "ddd".
```

**Example 3:**
```
Input: = "pqr"
Output: 1
Explanation: LPS could be "p", "q" or "r".
```

**Constraints:**

- `1 <= st.length <= 1000`
- `sy` consists only of lowercase English letters.

## Try it yourself
Try solving this question here: