Memoization Top Down DP in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to check if the result is already computed in the memo object.

DSA Javascript

if (memo.hasOwnProperty([1])) {
  return memo[n];
}

Drag options to blanks, or click blank then click option'

An

Bmemo

Cresult

Dcache

Attempts:

3 left

💡 Hint

Common Mistakes

Checking for a wrong variable name in memo.

Using memo instead of the key variable.

We check if the memo object has the key 'n' to avoid recomputing the value.

2fill in blank

medium

Complete the code to store the computed result in the memo object.

DSA Javascript

memo[n] = [1];

Drag options to blanks, or click blank then click option'

Afib(n - 1) + fib(n - 2)

Bmemo[n]

Cn

Dresult

Attempts:

3 left

💡 Hint

Common Mistakes

Storing the input 'n' instead of the computed result.

Trying to store the recursive call directly.

We store the computed result in memo[n] to reuse it later.

3fill in blank

hard

Fix the error in the base case condition to stop recursion correctly.

DSA Javascript

if (n [1] 1) {
  return n;
}

Drag options to blanks, or click blank then click option'

A==

B>=

C<=

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using '==' which only covers n=1.

Using '!=' which causes infinite recursion.

The base case for Fibonacci is when n is less than or equal to 1, return n.

4fill in blank

hard

Fill both blanks to complete the recursive calls with memoization.

DSA Javascript

const result = fib([1]) + fib([2]);

Drag options to blanks, or click blank then click option'

An - 1

Bn + 1

Cn - 2

Dn * 2

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or multiplication instead of subtraction.

Using wrong indices causing wrong results.

Fibonacci is sum of fib(n-1) and fib(n-2).

5fill in blank

hard

Fill all three blanks to complete the memoized Fibonacci function.

DSA Javascript

function fib(n, memo = {}) {
  if (n [1] 1) {
    return n;
  }
  if (memo.hasOwnProperty([2])) {
    return memo[n];
  }
  const result = fib(n [3] 1, memo) + fib(n - 2, memo);
  memo[n] = result;
  return result;
}

Drag options to blanks, or click blank then click option'

A<=

Bn

C-

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using '+' instead of '-' in recursive call.

Checking wrong base case condition.

Using wrong memo key.

Base case uses '<=', memo key is 'n', recursive call subtracts 1 from n.

Practice

1. What is the main purpose of memoization in top-down dynamic programming?

easy

A. To store results of subproblems to avoid repeated calculations

B. To sort the input data before processing

C. To convert recursive code into iterative code

D. To reduce the memory usage by deleting variables

Solution

1. Step 1: Understand memoization concept

   Memoization saves the results of expensive function calls and returns the cached result when the same inputs occur again.

2. Step 2: Identify its role in top-down DP

   In top-down dynamic programming, memoization prevents repeated calculations of the same subproblems by storing their results.

3. Final Answer:

   To store results of subproblems to avoid repeated calculations -> Option A

4. Quick Check:

   Memoization = Store subproblem results [OK]

Hint: Memoization caches answers to reuse later [OK]

Common Mistakes:

• Confusing memoization with sorting
• Thinking memoization reduces memory usage
• Believing memoization converts recursion to iteration

2. Which of the following is the correct way to declare a memo object in JavaScript for top-down DP?

easy

A. const memo = 0;

B. let memo = [];

C. const memo = new Map();

D. var memo = function() {};

Solution

1. Step 1: Identify memo storage type

   Memoization requires a data structure to store key-value pairs of subproblem results. Map is ideal for this in JavaScript.

2. Step 2: Check options for correct syntax

   const memo = new Map(); uses new Map() which is correct. let memo = []; is an array, which can work but less flexible. var memo = function() {}; is a function, incorrect. const memo = 0; is a number, incorrect.

3. Final Answer:

   const memo = new Map(); -> Option C

4. Quick Check:

   Memo object = Map() [OK]

Hint: Use Map() for flexible memo keys [OK]

Common Mistakes:

• Using a function instead of an object
• Initializing memo as a number
• Confusing array with Map for memo

3. What will be the output of the following JavaScript code using memoization for Fibonacci?

const memo = new Map();
function fib(n) {
  if (n <= 1) return n;
  if (memo.has(n)) return memo.get(n);
  const result = fib(n - 1) + fib(n - 2);
  memo.set(n, result);
  return result;
}
console.log(fib(5));

medium

A. 5

B. 8

C. 3

D. 13

Solution

1. Step 1: Understand Fibonacci sequence

   Fibonacci sequence starts as 0,1,1,2,3,5,8,... So fib(5) = 5.

2. Step 2: Trace the code execution

   The function uses memoization to avoid repeated calls. fib(5) calculates fib(4)+fib(3), and so on, finally returning 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   fib(5) = 5 [OK]

Hint: Recall Fibonacci sequence values [OK]

Common Mistakes:

• Confusing fib(5) with fib(6)
• Ignoring base cases
• Not understanding memo usage

4. Identify the bug in this memoized factorial function and select the fix:

const memo = {};
function factorial(n) {
  if (n === 0) return 1;
  if (memo[n]) return memo[n];
  memo[n] = n * factorial(n - 1);
  return memo[n];
}
console.log(factorial(5));

medium

A. Change base case to 'if (n === 1) return 1;'

B. Change 'if (memo[n])' to 'if (memo.hasOwnProperty(n))'

C. Initialize memo as 'const memo = new Map();'

D. Remove memo and use plain recursion

Solution

1. Step 1: Understand the bug in memo check

   Using 'if (memo[n])' fails when memo[n] is 0 or falsy. It should check if the key exists.

2. Step 2: Fix by checking key existence

   Using 'memo.hasOwnProperty(n)' correctly checks if the result is stored, avoiding false negatives.

3. Final Answer:

   Change 'if (memo[n])' to 'if (memo.hasOwnProperty(n))' -> Option B

4. Quick Check:

   Check key existence, not truthiness [OK]

Hint: Check key presence, not value truthiness [OK]

Common Mistakes:

• Checking memo[n] directly causes bugs for 0 or falsy values
• Changing base case unnecessarily
• Removing memo defeats purpose

5. Given the following top-down memoized function to count ways to climb stairs, what is the output of countWays(4)?

const memo = {};
function countWays(n) {
  if (n === 0) return 1;
  if (n < 0) return 0;
  if (memo.hasOwnProperty(n)) return memo[n];
  memo[n] = countWays(n - 1) + countWays(n - 2);
  return memo[n];
}
console.log(countWays(4));

hard

A. 7

B. 6

C. 8

D. 5

Solution

1. Step 1: Understand the problem

   This function counts ways to climb stairs taking 1 or 2 steps. Base cases: countWays(0)=1, countWays(negative)=0.

2. Step 2: Calculate countWays(4) step-by-step

   countWays(4) = countWays(3) + countWays(2) countWays(3) = countWays(2) + countWays(1) countWays(2) = countWays(1) + countWays(0) countWays(1) = countWays(0) + countWays(-1) countWays(0) = 1, countWays(-1) = 0 So countWays(1) = 1 + 0 = 1 countWays(2) = 1 + 1 = 2 countWays(3) = 2 + 1 = 3 countWays(4) = 3 + 2 = 5

3. Final Answer:

   5 -> Option D

4. Quick Check:

   Ways to climb 4 stairs = 5 [OK]

Hint: Count ways as sum of previous two counts [OK]

Common Mistakes:

• Miscounting base cases
• Forgetting negative input returns 0
• Mixing up addition order