Dynamic Programming (DP) = solve once, reuse many times.

## Fibonacci naive
```python
def fib(n):
    if n <= 1:
        return n
    return fib(n-1) + fib(n-2)
```

This repeats work.

## Memoized version
```python
def fib(n, memo={}):
    if n in memo:
        return memo[n]
    if n <= 1:
        return n
    memo[n] = fib(n-1) + fib(n-2)
    return memo[n]
```

## Graph
```mermaid
flowchart TD
  A[fib(5)] --> B[fib(4)]
  A --> C[fib(3)]
  B --> D[fib(3)]
  B --> E[fib(2)]
```

## Remember
- DP avoids recomputation
- memo = cache
- huge speedups


Understand dynamic programming as saving repeated work, with memoization and classic examples like Fibonacci.

Dynamic Programming Intro

Master fundamental data structures and their implementations.

Dynamic Programming Intro

Fibonacci naive ```python def fib(n): if n <= 1: return n return fib(n-1) + fib(n-2) ```

Memoized version ```python def fib(n, memo={}): if n in memo: return memo[n] if n <= 1: return n memo[n] = fib(n-1) + fib(n-2) return memo[n] ```

Graph ```mermaid flowchart TD A[fib(5)] --> B[fib(4)] A --> C[fib(3)] B --> D[fib(3)] B --> E[fib(2)] ```

Remember - DP avoids recomputation - memo = cache - huge speedups

More on Data Structures

Data Structures Intro

Big O Basics

List Fundamentals