[Very Important Coding Interviews Series : Dynamic Programming #01] How To Solve ANY Dynamic Programming Question ( Pattern Approach with Shortcuts) : How it Works ( With Implementation Code)

Everything you MUST know to solve any DP question...

This is the best hands-on guide you will ever find on Dynamic Programming which follows Pattern based Approach to Solve any DP question and Shortcuts You MUST READ and Implement.

Objective : Conquer the 8 essential Dynamic Programming patterns that appear in 100% of coding interview problems.

---

Table of Contents

1. What is Dynamic Programming?

2. Pattern 1: Fibonacci Pattern

3. Pattern 2: 0/1 Knapsack Pattern

4. Pattern 3: Unbounded Knapsack Pattern

5. Pattern 4: Palindromic Pattern

6. Pattern 5: LCS/String DP Pattern

7. Pattern 6: Grid/Matrix DP Pattern

8. Pattern 7: Longest Increasing Subsequence (LIS) Pattern

9. Pattern 8: Intervals/Partition DP Pattern

10. Quick Reference Guide and Shortcuts

Note : Each pattern comes with its Python Implementation ( can be found as you scroll) and at the end of thus post along with Dynamic Programming Shortcuts and problem examples.

Learn how to solve ANY Backtracking Programming Problem ( Pattern Based Approach) - How To Solve ANY Backtracking Programming Question ( Pattern Approach with Shortcuts) : How it Works ( With Implementation Code)

Read ( major compilations of LLM System Design, ML System Design and 300+ Implemented Projects) —

[Important Bookmark Compilation] Complete Hands On LLM System Design Roadmap with Projects You MUST Follow (200000 Reads and Counting)

[Important] Compilation of Most Asked System Design, ML System Design Case Studies and LLM System Design

[Important Bookmark] Compilation of All Implemented Projects ( with Code Implementation Files)

Next Post — How to Solve ANY Backtracking question.

---

What is Dynamic Programming?

The Core Insight

Imagine you’re trying to find the fastest route from New York to Los Angeles. You could:

• Option A (Brute Force): Try EVERY possible path, even ones that backtrack to places you’ve already visited

• Option B (Dynamic Programming): Remember the best way to get to Chicago, and when you need to go through Chicago again, just look up your notes instead of recalculating

Dynamic Programming is just recursion with a memory.

All DP Patterns with videos covered here (subscribe) : Ignito Youtube

The Three Pillars of DP

┌─────────────────────────────────────────────────────────────┐
│                   DYNAMIC PROGRAMMING                        │
├─────────────────────────────────────────────────────────────┤
│  1. OPTIMAL SUBSTRUCTURE                                    │
│     └─> Solution to big problem uses solutions to smaller   │
│         versions of the same problem                         │
│                                                              │
│  2. OVERLAPPING SUBPROBLEMS                                 │
│     └─> Same smaller problems are solved multiple times     │
│                                                              │
│  3. MEMOIZATION or TABULATION                               │
│     └─> Store results to avoid recalculation                │
└─────────────────────────────────────────────────────────────┘

When to Think DP? Detect the below Patterns to solve any Dynamic Programming Problem —