Fibonacci Series Generation

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Questions and Answers

What is the base case for the Fibonacci function in the provided code?

n == 0 || n == 1 (correct)

n == 2

n == 10

n > 1

What is the output of the Fibonacci function when the input is 5?

5 (correct)

What is the purpose of the Euclidean algorithm?

To compute the greatest common divisor of two integers (correct)

To find the smallest number in a sequence

To find the middle number in a sequence

To find the largest number in a sequence

What is the notation for the greatest common divisor of two integers m and n?

gcd(m, n) Signup and view all the answers

Who is credited with first describing the Euclidean algorithm?

Euclid of Alexandria Signup and view all the answers

What is the result of gcd(60, 24)?

6 Signup and view all the answers

What operation is used to calculate the remainder in the Euclidean Algorithm?

Modulus Signup and view all the answers

What is the purpose of the while loop in the GCD algorithm?

To compute the greatest common divisor Signup and view all the answers

How is the variable 'next' assigned in the Fibonacci sequence algorithm?

Using a loop Signup and view all the answers

What is the data type of the variable 'first' in the Fibonacci sequence algorithm?

int Signup and view all the answers

How is the 'suit' member of the 'card' structure accessed?

Using a pointer operator Signup and view all the answers

What is the purpose of the 'if' statement in the GCD algorithm?

To handle the base case of the recursion Signup and view all the answers

What is the output of the statement 'printf( "%s", cardPtr->suit );'?

Hearts Signup and view all the answers

What is the result of gcd(60,24) according to the Euclidean Algorithm?

12 Signup and view all the answers

What is the purpose of the gcd function?

To find the greatest common divisor Signup and view all the answers

What is the difference between the subtraction-based version and the recursive version of the Euclidean Algorithm?

The subtraction-based version is more efficient than the recursive version Signup and view all the answers

What is the result of gcd(80,20) using the subtraction-based version of the Euclidean Algorithm?

20 Signup and view all the answers

What is the purpose of the while loop in the Euclidean Algorithm?

To subtract the smaller number from the larger number Signup and view all the answers

What is the result of a mod b in the recursive version of the Euclidean Algorithm?

The remainder of a divided by b Signup and view all the answers

What is the role of the temporary variable in the recursive version of the Euclidean Algorithm?

To store the remainder of the division of a by b Signup and view all the answers

What is the difference between the using the mod operation and the subtraction operation in the Euclidean Algorithm?

The mod operation is used in the recursive version while the subtraction operation is used in the subtraction-based version Signup and view all the answers

Study Notes

Fibonacci Sequence

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones.
The Fibonacci sequence is defined recursively as f(n) = f(n-1) + f(n-2) with f(0) = 0 and f(1) = 1.
The sequence starts with 0 and 1, and each subsequent number is the sum of the previous two.

Fibonacci Algorithm

The Fibonacci algorithm is a recursive function that calculates the Fibonacci sequence.
The algorithm uses the formula f(n) = f(n-1) + f(n-2) to calculate the n-th Fibonacci number.
The algorithm has a base case of n == 0 or n == 1, where it returns n directly.

Euclidean Algorithm

The Euclidean algorithm is an efficient method for computing the Greatest Common Divisor (GCD) of two integers.
The GCD is defined as the largest integer that divides both integers without a remainder.
The algorithm has three implementations: subtraction-based, using a mod operation, and recursive.

Subtraction-Based Euclidean Algorithm

The subtraction-based algorithm uses a loop to repeatedly subtract the smaller number from the larger one until they are equal.
The GCD is the final value of the loop.

Mod Operation Euclidean Algorithm

The mod operation algorithm uses the modulo operator to calculate the remainder of the division of the two numbers.
The algorithm repeatedly applies the mod operation until the remainder is 0, and the GCD is the final value of the divisor.

Recursive Euclidean Algorithm

The recursive algorithm uses a recursive function to calculate the GCD.
The function calls itself with the smaller number and the remainder of the division of the two numbers until the remainder is 0, and the GCD is the final value of the divisor.

Exercises

The exercises ask to trace the three implementations of the Euclidean algorithm using different values of a and b.
The exercises also ask to rewrite the Fibonacci algorithm using a loop and compare it with the recursive algorithm.

Accessing Members of an Array of Structures

The example shows how to access the members of an array of structures using pointer notation.
The example defines a structure Card and creates an array of Card structures.
The example shows how to access the members of the structure using the arrow operator (->) and the dereference operator (*).

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Description

Write a program to generate the Fibonacci series for a given number of terms. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones.