Memoization Top Down DP in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare the memo array for storing computed Fibonacci values.

DSA C

int memo[[1]];

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

A10

B0

C1000

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using zero or negative size for the array.

Using too small size causing out of bounds.

The memo array size should be large enough to store Fibonacci values up to the maximum input. 1000 is a common safe size.

2fill in blank

medium

Complete the code to initialize the memo array with -1 to indicate uncomputed values.

DSA C

for (int i = 0; i < n; i++) {
    memo[i] = [1];
}

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

A-1

B0

C1

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing with 0 which is a valid Fibonacci number.

Using positive numbers that can confuse computed and uncomputed states.

We use -1 to mark that the Fibonacci value for that index is not computed yet.

3fill in blank

hard

Fix the error in the memoization check to return the stored value if already computed.

DSA C

if (memo[n] != [1]) {
    return memo[n];
}

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

A-1

B1

Cn

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Checking for 0 which is a valid Fibonacci number.

Checking for 1 which is also a valid Fibonacci number.

We check if memo[n] is not -1, meaning it is already computed, so we return it directly.

4fill in blank

hard

Fill both blanks to complete the recursive Fibonacci function with memoization.

DSA C

int fib(int n) {
    if (n <= 1) return n;
    if (memo[n] != -1) return memo[n];
    memo[n] = fib(n [1] 1) + fib(n [2] 2);
    return memo[n];
}

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or multiplication instead of subtraction for indices.

Using wrong operators causing wrong recursion.

We calculate fib(n-1) and fib(n-2) and add them to get fib(n).

5fill in blank

hard

Fill all three blanks to complete the memoization initialization and function call.

DSA C

for (int i = 0; i < [1]; i++) {
    memo[i] = [2];
}
int result = fib([3]);

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

An

B-1

C10

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing with 0 instead of -1.

Calling fib with 0 which returns trivial result.

Initialize memo for all n elements with -1, then call fib(10) to compute the 10th Fibonacci number.

Practice

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

easy

A. To convert recursive code into iterative code

B. To sort the input data before processing

C. To store results of subproblems to avoid repeated calculations

D. To increase the number of recursive calls

Solution

1. Step 1: Understand memoization concept

   Memoization saves answers of smaller problems so they don't get solved again.

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

   It stores subproblem results during recursion to speed up the process.

3. Final Answer:

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

4. Quick Check:

   Memoization = Store subproblem results [OK]

Hint: Memoization means saving answers to reuse later [OK]

Common Mistakes:

• Confusing memoization with sorting
• Thinking memoization converts recursion to iteration
• Believing memoization increases recursive calls

2. Which of the following is the correct way to declare a memoization array for Fibonacci numbers in C?

easy

A. int memo[] = new int[100];

B. int memo[100] = {0};

C. int memo = new int[100];

D. int memo(100);

Solution

1. Step 1: Recall C array declaration syntax

   In C, arrays are declared with fixed size and optional initialization like int memo[100] = {0};

2. Step 2: Check each option

   int memo[100] = {0}; uses correct C syntax. Options A and C use Java/C++ style. int memo(100); is invalid in C.

3. Final Answer:

   int memo[100] = {0}; -> Option B

4. Quick Check:

   C array declaration = int memo[100] = {0}; [OK]

Hint: C arrays use fixed size with square brackets [OK]

Common Mistakes:

• Using Java or C++ style array declarations in C
• Forgetting to initialize memo array to zero
• Using parentheses instead of brackets for arrays

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

int memo[10] = {0};
int fib(int n) {
  if (n <= 1) return n;
  if (memo[n] != 0) return memo[n];
  memo[n] = fib(n-1) + fib(n-2);
  return memo[n];
}

int main() {
  printf("%d", fib(5));
  return 0;
}

medium

A. 0

B. 8

C. 3

D. 5

Solution

1. Step 1: Trace fib(5) calls and memo usage

   fib(5) calls fib(4) + fib(3), and so on. Memo stores results to avoid repeats.

2. Step 2: Calculate fib(5)

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

3. Final Answer:

   5 -> Option D

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 memoization effect
• Assuming memo array starts with all ones

4. Identify the error in this memoized Fibonacci function in C:

int memo[10];
int fib(int n) {
  if (n <= 1) return n;
  if (memo[n] != -1) return memo[n];
  memo[n] = fib(n-1) + fib(n-2);
  return memo[n];
}

int main() {
  printf("%d", fib(5));
  return 0;
}

medium

A. memo array is not initialized to -1

B. fib function should return void

C. Base case should be n == 0 only

D. memo array size is too small

Solution

1. Step 1: Check memo array initialization

   Memo is checked for -1 but never initialized, so contains garbage values.

2. Step 2: Understand impact on memoization

   Without initialization, memo[n] != -1 may be true incorrectly, causing wrong returns.

3. Final Answer:

   memo array is not initialized to -1 -> Option A

4. Quick Check:

   Initialize memo to -1 before use [OK]

Hint: Always initialize memo array before use [OK]

Common Mistakes:

• Forgetting to initialize memo array
• Changing base case incorrectly
• Assuming default zero initialization in C

5. Given the following top-down memoized code to count ways to climb stairs (1 or 2 steps), what is the output of countWays(4)? Assume memo array is initialized with -1.

int memo[100];
int countWays(int n) {
  if (n == 0) return 1;
  if (n < 0) return 0;
  if (memo[n] != -1) return memo[n];
  memo[n] = countWays(n-1) + countWays(n-2);
  return memo[n];
}

int main() {
  for(int i=0; i<100; i++) memo[i] = -1;
  printf("%d", countWays(4));
  return 0;
}

hard

A. 5

B. 7

C. 8

D. 4

Solution

1. Step 1: Understand problem and base cases

   Ways to climb 0 steps = 1, negative steps = 0, ways(n) = ways(n-1)+ways(n-2).

2. Step 2: Calculate countWays(4)

   countWays(1)=1, countWays(2)=2, countWays(3)=3, countWays(4)=5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   Ways to climb 4 steps = 5 [OK]

Hint: Count ways follow Fibonacci pattern starting with 1,1 [OK]

Common Mistakes:

• Confusing base cases for counting ways
• Not initializing memo array
• Mixing up countWays with Fibonacci values