Memoization to Optimize Recursion in DSA Javascript - Build from Scratch

Memoization to Optimize Recursion

📖 Scenario: Imagine you want to calculate the number of ways to climb a staircase with a certain number of steps. You can climb either 1 or 2 steps at a time. This is a classic problem where recursion can be slow because it repeats the same calculations many times.Memoization is a technique that helps speed up recursion by remembering the results of previous calculations.

🎯 Goal: You will build a recursive function to calculate the number of ways to climb stairs, then optimize it using memoization to avoid repeated work.

📋 What You'll Learn

Create a recursive function called climbStairs that takes a number n and returns the number of ways to climb n steps.

Create an empty object called memo to store previously calculated results.

Modify the climbStairs function to use memo to return stored results if available.

Print the result of climbStairs(5).

💡 Why This Matters

🌍 Real World

Memoization is used in many real-world applications like calculating Fibonacci numbers, optimizing dynamic programming problems, and improving performance in algorithms that have overlapping subproblems.

💼 Career

Understanding memoization is important for software engineers to write efficient recursive algorithms and optimize code performance in interviews and real projects.

1

Create the recursive function climbStairs

Write a recursive function called climbStairs that takes a number n. If n is 0 or 1, return 1. Otherwise, return the sum of climbStairs(n - 1) and climbStairs(n - 2).

DSA Javascript

// Your code here

Hint

Use a function named climbStairs with a parameter n. Use an if statement to check if n is 0 or 1 and return 1 in that case. Otherwise, return the sum of recursive calls with n - 1 and n - 2.

2

Create an empty object memo to store results

Create an empty object called memo before the climbStairs function to store previously calculated results.

DSA Javascript

const memo = {};

function climbStairs(n) {
    if (n === 0 || n === 1) {
        return 1;
    }
    return climbStairs(n - 1) + climbStairs(n - 2);
}
// Your code here

Hint

Define const memo = {} before the function to hold cached results.

3

Modify climbStairs to use memo for caching

Inside the climbStairs function, first check if n exists as a key in memo. If yes, return memo[n]. Otherwise, calculate the result recursively, store it in memo[n], and then return it.

DSA Javascript

const memo = {};

function climbStairs(n) {
    // Check if result is in memo
    // Your code here

    if (n === 0 || n === 1) {
        return 1;
    }

    // Calculate and store in memo
    // Your code here
}

Hint

Use if (n in memo) to check cache. Store result with memo[n] = ....

4

Print the result of climbStairs(5)

Write a console.log statement to print the result of calling climbStairs(5).

DSA Javascript

const memo = {};

function climbStairs(n) {
    if (n in memo) {
        return memo[n];
    }
    if (n === 0 || n === 1) {
        return 1;
    }
    memo[n] = climbStairs(n - 1) + climbStairs(n - 2);
    return memo[n];
}

// Your code here

Hint

Use console.log(climbStairs(5)) to print the result.

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