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What is memoization?

Cache sub-results to avoid recomputation.

What is memoization?

Memoization stores computed sub-results in a cache to prevent recomputation.

In recursive Fibonacci the same subproblem is solved many times; memoization prevents this.

Memoization turns exponential complexity into polynomial; fibonacci becomes Θ(n).

The cache

The cache is usually a dictionary or array. The key is the subproblem's parameter.

On first compute the result is written to the cache; later calls read from it.

So each subproblem is solved only once; total time drops.

Practice Fibonacci comparison

Write fib_naive(n). Recursive naive Fibonacci. Print 55 with print(fib_naive(10)).

Starter code

solution.py
def fib_naive(n):
    # Naive Fibonacci

Sample solution

solution.py
def fib_naive(n):
    # Naive Fibonacci
    if n <= 1:
        return n
    return fib_naive(n - 1) + fib_naive(n - 2)
print(fib_naive(10))

Expected output

55

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 What does memoization prevent?

  • Recomputation Correct answer
  • Memory usage
  • Recursion
  • Loops

Explanation: Recomputation.

2 Cache structure

Question 
memo = ____
Answer 
memo = {}

Explanation: {} is right.

3 What is memoization: match the terms

Term Meaning
memoization Cache
cache Dictionary
subproblem Subproblem
recursion Self-call

All lessons in Advanced

1 DP - Memoization

  1. What is memoization?
  2. Fibonacci memoization
  3. Dict-based cache
  4. Summary - Memoization

2 DP - Tabulation

  1. What is tabulation?
  2. Building the table
  3. Fibonacci tabulation
  4. Summary - Tabulation

3 LCS

  1. LCS definition
  2. DP table
  3. Backtracking the table
  4. Summary - LCS

4 Knapsack

  1. Knapsack problem
  2. 0/1 knapsack DP
  3. Decision table
  4. Summary - Knapsack

5 DP project

  1. Project: Overview
  2. Cost table
  3. DP solution
  4. Print the result

6 Matrix chain

  1. Multiplication order
  2. DP table
  3. Split point
  4. Summary - Matrix chain

7 Floyd-Warshall

  1. All pairs
  2. Triple loop
  3. Table update
  4. Summary - Floyd-Warshall

8 Dijkstra

  1. Single source
  2. Priority queue
  3. Relaxation
  4. Summary - Dijkstra

9 Bellman-Ford

  1. Negative weights
  2. Edge relaxation loop
  3. Negative cycle
  4. Summary - Bellman-Ford

10 Kruskal

  1. Minimum spanning tree
  2. Edge sorting
  3. Cycle check
  4. Summary - Kruskal

11 Prim

  1. Prim idea
  2. Priority queue
  3. Visited set
  4. Summary - Prim

12 Topological sort

  1. Dependency order
  2. DFS-based sort
  3. Kahn algorithm
  4. Summary - Topological sort

13 Union-find, trie, segment tree

  1. Union-find
  2. Trie
  3. Segment tree
  4. Summary - Advanced structures

14 Advanced final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4