Why Dynamic Programming and When Recursion Alone Fails in DSA Typescript - Test Your Knowledge

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate Fibonacci numbers using simple recursion.

DSA Typescript

function fib(n: number): number {
  if (n <= 1) return n;
  return fib(n - 1) [1] fib(n - 2);
}

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

A*

B-

C+

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using subtraction or multiplication instead of addition.

Forgetting to handle base cases.

The Fibonacci sequence is calculated by adding the two previous numbers. So we use the '+' operator.

2fill in blank

medium

Complete the code to add memoization to the recursive Fibonacci function.

DSA Typescript

function fibMemo(n: number, memo: number[] = []): number {
  if (n <= 1) return n;
  if (memo[n] !== undefined) return memo[n];
  memo[n] = fibMemo(n - 1, memo) [1] fibMemo(n - 2, memo);
  return memo[n];
}

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Not using memo array to store results.

Using wrong operator instead of addition.

Memoization stores results to avoid repeated calculations. The addition operator '+' combines the two previous Fibonacci numbers.

3fill in blank

hard

Fix the error in the recursive factorial function to correctly calculate factorial.

DSA Typescript

function factorial(n: number): number {
  if (n === 0) return 1;
  return n [1] factorial(n - 1);
}

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

A+

B-

C/

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or subtraction instead of multiplication.

Missing base case for n=0.

Factorial is the product of all positive integers up to n, so we multiply n by factorial(n-1).

4fill in blank

hard

Fill both blanks to create a dynamic programming solution for Fibonacci using bottom-up approach.

DSA Typescript

function fibDP(n: number): number {
  const dp: number[] = [0, 1];
  for (let i = 2; i [1] n; i++) {
    dp[i] = dp[i - 1] [2] dp[i - 2];
  }
  return dp[n];
}

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

A<=

B<

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using <= in loop condition causing extra iteration.

Using subtraction instead of addition for dp calculation.

The loop runs while i is less than or equal to n, and each dp[i] is the sum of the two previous dp values.

5fill in blank

hard

Fill all three blanks to implement memoized recursion for the coin change problem.

DSA Typescript

function coinChange(coins: number[], amount: number, memo: Map<number, number> = new Map()): number {
  if (amount === 0) return 0;
  if (amount < 0) return -1;
  if (memo.has(amount)) return memo.get(amount) as number;
  let minCoins = Infinity;
  for (const coin of coins) {
    const res = coinChange(coins, amount [1] coin, memo);
    if (res >= 0 && res [2] minCoins) {
      minCoins = res [3] 1;
    }
  }
  memo.set(amount, minCoins === Infinity ? -1 : minCoins);
  return memo.get(amount) as number;
}

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

A-

B<

C+

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of subtraction for amount update.

Using > instead of < for comparison.

Forgetting to add 1 when updating minCoins.

We subtract the coin value from amount, check if result is less than minCoins, and update minCoins by adding 1 to res.

Practice

1. Why do we use dynamic programming instead of just recursion for some problems?

easy

A. Because recursion alone can repeat the same calculations many times, making it slow.

B. Because recursion cannot solve problems with multiple steps.

C. Because dynamic programming uses loops instead of functions.

D. Because recursion always causes errors in large problems.

Solution

1. Step 1: Understand recursion's limitation

   Recursion solves problems by calling itself but often recalculates the same results multiple times.

2. Step 2: Recognize dynamic programming's advantage

   Dynamic programming stores results of subproblems to avoid repeated work, making it faster.

3. Final Answer:

   Because recursion alone can repeat the same calculations many times, making it slow. -> Option A

4. Quick Check:

   Recursion repeats work, DP saves results [OK]

Hint: DP saves repeated results to speed up recursion [OK]

Common Mistakes:

• Thinking recursion cannot handle multiple steps
• Believing DP only uses loops
• Assuming recursion always causes errors

2. Which of the following TypeScript function signatures correctly shows a recursive function with memoization parameter for dynamic programming?

easy

A. function fib(n: number): number[]

B. function fib(n: string, memo: number): number

C. function fib(memo: number[], n: number): void

D. function fib(n: number, memo: number[] = []): number

Solution

1. Step 1: Check parameter types and order

   function fib(n: number, memo: number[] = []): number has number n and optional memo array with default empty array, suitable for memoization.

2. Step 2: Verify return type and parameters

   function fib(n: number, memo: number[] = []): number returns number (the Fibonacci number), others have wrong types or order.

3. Final Answer:

   function fib(n: number, memo: number[] = []): number -> Option D

4. Quick Check:

   Correct memo param with default empty array [OK]

Hint: Memo param usually an array with default empty value [OK]

Common Mistakes:

• Swapping parameter order
• Using wrong return type
• Not providing default value for memo

3. What is the output of this TypeScript code snippet?

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

medium

A. 3

B. 8

C. 5

D. Undefined

Solution

1. Step 1: Trace fib(5) calls with memo

   fib(5) = fib(4) + fib(3), memo stores results to avoid repeats.

2. Step 2: Calculate fib values

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

3. Final Answer:

   5 -> Option C

4. Quick Check:

   Fibonacci of 5 = 5 [OK]

Hint: Memo avoids repeats; fib(5) = 5 [OK]

Common Mistakes:

• Confusing fib(5) with fib(6)
• Ignoring memoization effect
• Assuming output is sum of all calls

4. Identify the bug in this recursive Fibonacci function without memoization:

function fib(n: number): number {
  if (n === 0) return 0;
  if (n === 1) return 1;
  return fib(n - 1) + fib(n - 2);
}
console.log(fib(40));

medium

A. It will cause a stack overflow error for large n.

B. It returns wrong Fibonacci numbers for n > 2.

C. It uses memoization incorrectly.

D. It has a syntax error in the return statement.

Solution

1. Step 1: Analyze recursion depth for fib(40)

   Without memoization, fib(40) causes many repeated calls, leading to deep recursion.

2. Step 2: Understand consequences

   Deep recursion can cause stack overflow or very slow execution, but no syntax or logic errors.

3. Final Answer:

   It will cause a stack overflow error for large n. -> Option A

4. Quick Check:

   Deep recursion without memo causes stack overflow [OK]

Hint: Large n without memo causes stack overflow [OK]

Common Mistakes:

• Thinking it returns wrong values
• Assuming syntax error exists
• Confusing memoization usage

5. You want to find the minimum number of coins to make a sum using recursion. Why is dynamic programming necessary here instead of plain recursion?

function minCoins(coins: number[], sum: number): number {
  if (sum === 0) return 0;
  let res = Infinity;
  for (let coin of coins) {
    if (coin <= sum) {
      let subRes = minCoins(coins, sum - coin);
      if (subRes !== Infinity && subRes + 1 < res) {
        res = subRes + 1;
      }
    }
  }
  return res;
}

hard

A. Because recursion cannot handle arrays as input parameters.

B. Because recursion alone recalculates the same sums multiple times, causing slow performance.

C. Because dynamic programming uses loops instead of recursion.

D. Because recursion always returns Infinity for large sums.

Solution

1. Step 1: Identify repeated subproblems in recursion

   The function calls itself with the same sums multiple times, recalculating results.

2. Step 2: Explain dynamic programming benefit

   DP stores results for sums already computed, avoiding repeated work and speeding up solution.

3. Final Answer:

   Because recursion alone recalculates the same sums multiple times, causing slow performance. -> Option B

4. Quick Check:

   DP saves repeated sum calculations [OK]

Hint: DP caches results to avoid repeated sum calculations [OK]

Common Mistakes:

• Thinking recursion can't handle arrays
• Believing DP replaces recursion with loops
• Assuming recursion returns Infinity always