Fibonacci Using DP in DSA C++ - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the base case for Fibonacci DP array.

DSA C++

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

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

A0

B1

C-1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Setting fib[0] to 1 instead of 0

Using negative numbers for base case

The first Fibonacci number is 0, so fib[0] should be set to 0.

2fill in blank

medium

Complete the code to initialize the second base case for Fibonacci DP array.

DSA C++

fib[1] = [1];

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A1

B0

C2

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting fib[1] to 0 instead of 1

Using numbers greater than 1 for base case

The second Fibonacci number is 1, so fib[1] should be set to 1.

3fill in blank

hard

Fix the error in the loop condition to correctly compute Fibonacci numbers using DP.

DSA C++

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

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A>

B>=

C<=

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>=' which causes no iterations

Using '<=' which goes one step too far

The loop should run while i is less than n to fill fib array up to n-1 index.

4fill in blank

hard

Fill both blanks to complete the function header and return statement for Fibonacci DP.

DSA C++

int fibonacci([1] n) {
    int fib[100];
    fib[0] = 0;
    fib[1] = 1;
    for (int i = 2; i < n; i++) {
        fib[i] = fib[i-1] + fib[i-2];
    }
    return fib[[2]];
}

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Aint

Bfloat

Cn-1

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using float as parameter type

Returning fib[n] which is out of bounds

The function takes an integer n and returns fib[n-1] because array indexing starts at 0.

5fill in blank

hard

Fill all three blanks to complete the main function that reads input, calls Fibonacci DP, and prints result.

DSA C++

#include <iostream>
using namespace std;

int fibonacci(int n) {
    int fib[100];
    fib[0] = 0;
    fib[1] = 1;
    for (int i = 2; i < n; i++) {
        fib[i] = fib[i-1] + fib[i-2];
    }
    return fib[n-1];
}

int main() {
    int [1];
    cin >> [2];
    int result = fibonacci([3]);
    cout << result << endl;
    return 0;
}

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

Anum

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names causing errors

Forgetting to read input before calling function

The variable name for input and function argument should be consistent, here 'num'.

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 uses less memory by not storing any results.

B. It avoids repeated calculations by storing intermediate results.

C. It calculates Fibonacci numbers using only addition.

D. It uses a recursive function without any loops.

Solution

1. Step 1: Understand recursion vs DP

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

2. Step 2: Role of DP in Fibonacci

   DP stores previously calculated Fibonacci numbers in a table (memoization or tabulation) to avoid repeated work.

3. Final Answer:

   It avoids repeated calculations by storing intermediate results. -> Option B

4. Quick Check:

   DP = store results to avoid repeats [OK]

Hint: DP saves results to skip repeated work [OK]

Common Mistakes:

• Thinking DP uses less memory than recursion
• Confusing DP with simple recursion
• Believing DP avoids addition operations

2. Which of the following C++ code snippets correctly initializes the base cases for Fibonacci using bottom-up DP?

easy

A. int fib[10]; fib[0] = 0; fib[1] = 1;

B. int fib[10]; fib[1] = 0; fib[2] = 1;

C. int fib[10]; fib[0] = 1; fib[1] = 1;

D. int fib[10]; fib[0] = 1; fib[2] = 0;

Solution

1. Step 1: Identify Fibonacci base cases

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

2. Step 2: Check initialization correctness

   int fib[10]; fib[0] = 0; fib[1] = 1; correctly sets fib[0] = 0 and fib[1] = 1, matching the base cases.

3. Final Answer:

   int fib[10]; fib[0] = 0; fib[1] = 1; -> Option A

4. Quick Check:

   fib[0]=0, fib[1]=1 base cases [OK]

Hint: Base cases: fib[0]=0 and fib[1]=1 [OK]

Common Mistakes:

• Starting fib from index 1 instead of 0
• Swapping values of fib[0] and fib[1]
• Initializing wrong indices

3. What is the output of the following C++ code snippet?

int fib[6];
fib[0] = 0; fib[1] = 1;
for(int i = 2; i < 6; i++) {
    fib[i] = fib[i-1] + fib[i-2];
}
std::cout << fib[5];

medium

A. 5

B. 8

C. 13

D. 21

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 output

   The code prints fib[5], which is 5.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   fib[5]=5 [OK]

Hint: Calculate fib stepwise from base cases [OK]

Common Mistakes:

• Confusing fib[5] with fib[6]
• Off-by-one errors in loop
• Incorrect addition order

4. Identify the error in the following Fibonacci DP code and choose 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];
}
std::cout << fib[9];

medium

A. Change loop condition to i <= 10

B. Initialize fib[2] before the loop

C. Change fib[0] to 1

D. Change loop start to i = 2

Solution

1. Step 1: Analyze loop start index

   The loop starts at i=1, but fib[1] is already initialized. Calculating fib[1] again causes fib[-1] access (invalid).

2. Step 2: Correct loop start

   Loop should start at i=2 to use fib[i-1] and fib[i-2] safely.

3. Final Answer:

   Change loop start to i = 2 -> Option D

4. Quick Check:

   Loop from i=2 avoids invalid index [OK]

Hint: Start loop at 2 to avoid negative index [OK]

Common Mistakes:

• Starting loop at 1 causing invalid access
• Changing base case values incorrectly
• Extending loop beyond array size

5. You want to find the 50th Fibonacci number using DP in C++. Which approach is best to handle large Fibonacci numbers efficiently and why?

hard

A. Use bottom-up DP with int array since int can hold large numbers.

B. Use simple recursion without memoization for clarity.

C. Use a vector of unsigned long long and bottom-up DP to avoid recursion overhead.

D. Use recursion with memoization but store results in int array.

Solution

1. Step 1: Consider data type size

   50th Fibonacci number is very large; int cannot hold it, unsigned long long can hold bigger values.

2. Step 2: Choose DP approach

   Bottom-up DP avoids recursion overhead and stack issues, making it efficient for large n.

3. Final Answer:

   Use a vector of unsigned long long and bottom-up DP to avoid recursion overhead. -> Option C

4. Quick Check:

   Big number + bottom-up DP = efficient and safe [OK]

Hint: Use big data type and bottom-up DP for large n [OK]

Common Mistakes:

• Using int causing overflow
• Using recursion causing stack overflow
• Ignoring data type limits