Fibonacci Using DP in DSA C - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the first two Fibonacci numbers in the array.

DSA C

int fib[100];
fib[0] = 0;
fib[1] = [1];

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A1

B2

C0

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Setting fib[1] to 0 instead of 1.

Using a number greater than 1 for fib[1].

The first two Fibonacci numbers are 0 and 1. So fib[1] should be 1.

2fill in blank

medium

Complete the for loop header to iterate from 2 to n.

DSA C

for (int i = [1]; i <= n; i++) {
    fib[i] = fib[i-1] + fib[i-2];
}

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An

B2

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Starting loop from 0 or 1 causing overwriting of initial values.

Starting loop from n causing no iterations.

The loop starts from 2 because the first two Fibonacci numbers are already set.

3fill in blank

hard

Fix the error in the return statement to return the nth Fibonacci number.

DSA C

return [1];

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Afib[n]

Bfib[n+1]

Cfib[n-1]

Dfib[n-2]

Attempts:

3 left

💡 Hint

Common Mistakes

Returning fib[n-1] which is the previous Fibonacci number.

Returning fib[n+1] which is out of bounds.

The nth Fibonacci number is stored at fib[n].

4fill in blank

hard

Fill both blanks to complete the function header and declare the fib array size.

DSA C

int fibonacci([1] n) {
    int fib[[2]];
    fib[0] = 0;
    fib[1] = 1;
    for (int i = 2; i <= n; i++) {
        fib[i] = fib[i-1] + fib[i-2];
    }
    return fib[n];
}

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Aint

Bfloat

C50

D100

Attempts:

3 left

💡 Hint

Common Mistakes

Using float for n which is not suitable for indexing.

Declaring array size too small causing out of bounds.

The function parameter should be an integer 'int n'. The array size should be large enough, here 100.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps numbers to their Fibonacci values if the number is greater than 5.

DSA C

for (int [1] = 0; [1] <= [2]; [1]++) {
    if ([1] > 5) {
        fib[[1]] = fib[[1]-1] + fib[[1]-2];
    }
}

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Ai

Bn

C10

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong loop variable names.

Incorrect loop range causing errors.

The loop variable is i, iterating from 0 to n (which can be 10). The condition checks if i > 5.

Practice

1. What is the main advantage of using Dynamic Programming (DP) to calculate Fibonacci numbers compared to a simple recursive approach?

easy

A. It stores intermediate results to avoid repeated calculations

B. It uses more memory without improving speed

C. It calculates Fibonacci numbers randomly

D. It only works for small Fibonacci numbers

Solution

1. Step 1: Understand recursion vs DP

   Simple recursion recalculates the same Fibonacci numbers many times, causing slow performance.

2. Step 2: Role of DP in Fibonacci

   DP saves previously calculated Fibonacci values in a table (memoization or tabulation), avoiding repeated work.

3. Final Answer:

   It stores intermediate results to avoid repeated calculations -> Option A

4. Quick Check:

   DP = stores results to save time [OK]

Hint: DP saves past answers to speed up Fibonacci [OK]

Common Mistakes:

• Thinking DP uses more memory without speed benefit
• Believing DP calculates numbers randomly
• Assuming DP only works for small inputs

2. Which of the following is the correct way to initialize the base cases in a bottom-up DP approach for Fibonacci in C?

easy

A. int fib[2] = {0, 0};

B. int fib[2] = {1, 1};

C. int fib[2] = {0, 1};

D. int fib[2] = {1, 0};

Solution

1. Step 1: Identify Fibonacci base cases

   Fibonacci sequence starts with fib(0) = 0 and fib(1) = 1.

2. Step 2: Match initialization with base cases

   Array fib[2] = {0, 1} correctly sets fib(0) = 0 and fib(1) = 1.

3. Final Answer:

   int fib[2] = {0, 1}; -> Option C

4. Quick Check:

   Base fib = 0,1 [OK]

Hint: Start fib with 0 and 1 for base cases [OK]

Common Mistakes:

• Swapping the order of 0 and 1
• Setting both base cases to 1
• Initializing both to zero

3. What is the output of the following C code snippet using bottom-up DP to find fib(5)?

int fib[6];
fib[0] = 0;
fib[1] = 1;
for(int i = 2; i <= 5; i++) {
    fib[i] = fib[i-1] + fib[i-2];
}
printf("%d", fib[5]);

medium

A. 5

B. 8

C. 3

D. 13

Solution

1. Step 1: Calculate Fibonacci values step-by-step

   fib[0]=0, fib[1]=1 fib[2]=1, fib[3]=2, fib[4]=3, fib[5]=5

2. Step 2: Identify fib[5]

   fib[5] is 5 after the loop completes.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   fib(5) = 5 [OK]

Hint: Calculate fib stepwise from 0 and 1 [OK]

Common Mistakes:

• Confusing fib(5) with fib(6)
• Starting loop from wrong index
• Off-by-one errors in array indexing

4. Identify the error in this DP Fibonacci code snippet and select the correct fix:

int fib[10];
fib[0] = 0;
fib[1] = 1;
for(int i = 1; i < 10; i++) {
    fib[i] = fib[i-1] + fib[i-2];
}

medium

A. Initialize fib[2] before loop

B. Change loop to start from i = 2

C. Change loop condition to i <= 10

D. No error, code is correct

Solution

1. Step 1: Analyze loop start index

   The loop starts at i=1, but fib[1] is already initialized, so fib[1] gets overwritten incorrectly.

2. Step 2: Correct loop start

   Loop should start at i=2 to use fib[0] and fib[1] for calculation without overwriting base cases.

3. Final Answer:

   Change loop to start from i = 2 -> Option B

4. Quick Check:

   Loop start = 2 fixes overwrite [OK]

Hint: Start loop after base cases to avoid overwrite [OK]

Common Mistakes:

• Starting loop at 1 overwrites fib[1]
• Not initializing base cases properly
• Using wrong loop end condition

5. You want to find the 10th Fibonacci number using DP but with optimized space using only two variables instead of an array. Which code snippet correctly implements this?

hard

A. int a = 0, b = 1, c, n = 10;
for(int i = 0; i < n; i++) {
c = a + b;
a = c;
b = a;
}
printf("%d", c);

B. int a = 0, b = 1, c, n = 10;
for(int i = 1; i < n; i++) {
c = a + b;
b = a;
a = c;
}
printf("%d", a);

C. int a = 1, b = 1, c, n = 10;
for(int i = 2; i <= n; i++) {
c = a + b;
a = b;
b = c;
}
printf("%d", c);

D. int a = 0, b = 1, c, n = 10;
for(int i = 2; i <= n; i++) {
c = a + b;
a = b;
b = c;
}
printf("%d", b);

Solution

1. Step 1: Understand space optimization

   Only two variables (a, b) track last two Fibonacci numbers; c stores current sum.

2. Step 2: Check loop and updates

   Loop from 2 to n, update c = a + b, then shift a = b, b = c correctly to move forward.

3. Final Answer:

   Code snippet A correctly implements optimized Fibonacci calculation -> Option D

4. Quick Check:

   Two vars + sum update = correct [OK]

Hint: Use two vars and update in loop for space optimization [OK]

Common Mistakes:

• Swapping updates of a and b incorrectly
• Wrong loop range causing off-by-one errors
• Initializing variables incorrectly