Memoization to Optimize Recursion in DSA Javascript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is memoization in the context of recursion?

Memoization is a technique where we save the results of expensive function calls and return the cached result when the same inputs occur again, avoiding repeated calculations.

beginner

How does memoization improve recursive function performance?

Memoization reduces the number of recursive calls by storing results of subproblems, so the function does not recompute the same values multiple times, making it faster.

beginner

In JavaScript, what data structure is commonly used to implement memoization?

A JavaScript object or Map is commonly used to store previously computed results with input values as keys for quick lookup.

intermediate

What problem does memoization solve in recursive Fibonacci calculation?

It prevents the exponential growth of calls by caching Fibonacci numbers already calculated, turning an exponential time problem into a linear time problem.

beginner

True or False: Memoization changes the logic of the recursive function.

False. Memoization does not change the logic; it only stores results to avoid repeated work, keeping the original recursive logic intact.

What is the main benefit of using memoization in recursion?

A Use more memory without speed gain

B Make the code shorter

C Avoid repeated calculations by caching results

D Eliminate the need for base cases

Memoization caches results to avoid repeated calculations, improving speed.

Which data structure is best suited for memoization in JavaScript?

A Array

B String

C Set

D Object or Map

Objects or Maps store key-value pairs for quick lookup of cached results.

Memoization is especially useful for which type of recursive problems?

A Problems with overlapping subproblems

B Problems with no recursion

C Problems with only one recursive call

D Problems that do not return values

Memoization helps when recursive calls repeat the same subproblems multiple times.

What happens if you do not use memoization in Fibonacci recursion?

A The function runs in exponential time

B The function does not return correct results

C The function runs in linear time

D The function uses no memory

Without memoization, Fibonacci recursion repeats many calls, causing exponential time complexity.

Which of these is NOT a characteristic of memoization?

A Caching results

B Changing the recursive logic

C Improving performance

D Using extra memory

Memoization does not change the recursive logic; it only caches results.

Explain how memoization optimizes a recursive function like Fibonacci.

Think about how saving answers helps avoid doing the same work again.

Describe the steps to add memoization to a simple recursive function in JavaScript.

Focus on how to remember and reuse previous answers.

Practice

1. What is the main purpose of using memoization in recursive functions?

easy

A. To make the function run slower by adding extra steps

B. To store results of expensive function calls and reuse them later

C. To avoid using recursion altogether

D. To increase the number of recursive calls

Solution

1. Step 1: Understand what memoization does

   Memoization saves the results of function calls so that if the same inputs occur again, the saved result is used instead of recalculating.

2. Step 2: Identify the effect on recursion

   This reduces repeated work and speeds up recursive functions by avoiding duplicate calculations.

3. Final Answer:

   To store results of expensive function calls and reuse them later -> Option B

4. Quick Check:

   Memoization = Store and reuse results [OK]

Hint: Memoization saves repeated work to speed recursion [OK]

Common Mistakes:

• Thinking memoization makes recursion slower
• Confusing memoization with iteration
• Believing memoization removes recursion

2. Which of the following is the correct way to declare a memo object inside a recursive function in JavaScript?

easy

A. const memo = {}; inside the function, then pass it as a parameter

B. var memo = []; inside the function without passing it

C. let memo = 0; inside the function

D. memo = new Map(); outside the function and never pass it

Solution

1. Step 1: Understand memo object usage

   The memo object should be an object or map to store key-value pairs of inputs and results.

2. Step 2: Correct placement and passing

   Declaring const memo = {} inside the function and passing it as a parameter ensures the same memo is used across recursive calls.

3. Final Answer:

   const memo = {}; inside the function, then pass it as a parameter -> Option A

4. Quick Check:

   Memo object declared and passed = const memo = {}; inside the function, then pass it as a parameter [OK]

Hint: Declare memo as object and pass it to recursive calls [OK]

Common Mistakes:

• Using array instead of object for memo
• Not passing memo to recursive calls
• Declaring memo as a number

3. What will be the output of the following code?

function fib(n, memo = {}) {
  if (n <= 1) return n;
  if (memo[n]) return memo[n];
  memo[n] = fib(n - 1, memo) + fib(n - 2, memo);
  return memo[n];
}
console.log(fib(5));

medium

A. 5

B. 8

C. 3

D. Undefined

Solution

1. Step 1: Understand Fibonacci calculation with memoization

   fib(5) calculates Fibonacci number at position 5 using memo to avoid repeated calls.

2. Step 2: Calculate fib(5) step-by-step

   fib(0)=0, fib(1)=1, fib(2)=1, fib(3)=2, fib(4)=3, fib(5)=5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   fib(5) = 5 [OK]

Hint: Remember Fibonacci sequence: 0,1,1,2,3,5... [OK]

Common Mistakes:

• Confusing fib(5) with fib(6)
• Ignoring memo and recalculating
• Assuming output is 8

4. Identify the error in this memoized factorial function and choose the fix:

function factorial(n, memo = {}) {
  if (n === 0) return 1;
  if (memo[n]) return memo[n];
  memo[n] = n * factorial(n - 1);
  return memo[n];
}

medium

A. Remove memo object completely

B. Change base case to n === 1

C. Pass memo in recursive call: factorial(n - 1, memo)

D. Initialize memo as an array instead of object

Solution

1. Step 1: Check recursive call parameters

   The recursive call to factorial misses passing the memo object, so memo is reset each time.

2. Step 2: Fix by passing memo in recursion

   Change call to factorial(n - 1, memo) to keep memo consistent across calls.

3. Final Answer:

   Pass memo in recursive call: factorial(n - 1, memo) -> Option C

4. Quick Check:

   Pass memo to recursive calls to fix [OK]

Hint: Always pass memo object in recursive calls [OK]

Common Mistakes:

• Forgetting to pass memo in recursion
• Changing base case unnecessarily
• Removing memo defeats optimization

5. You want to optimize a recursive function that calculates the number of ways to climb n stairs taking 1 or 2 steps at a time. Which memoization approach below correctly improves performance?

hard

A. Store results only for even stair numbers in memo

B. Use a global variable to count calls without storing results

C. Rewrite the function to use a loop without memoization

D. Use a memo object passed through recursive calls to store results for each stair number

Solution

1. Step 1: Understand the problem and recursion

   The function counts ways to climb stairs by summing ways(n-1) and ways(n-2).

2. Step 2: Apply memoization correctly

   Passing a memo object through recursive calls stores results for each stair number, avoiding repeated calculations.

3. Step 3: Evaluate other options

   Global counters don't store results, loops change approach, and storing only even results misses odd cases.

4. Final Answer:

   Use a memo object passed through recursive calls to store results for each stair number -> Option D

5. Quick Check:

   Memo object for all inputs optimizes recursion [OK]

Hint: Memoize all inputs to avoid repeated stair count calculations [OK]

Common Mistakes:

• Not passing memo object through recursion
• Partial memoization missing some inputs
• Confusing memoization with iteration