Fibonacci Series Generation

21 Questions

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

n == 0 || n == 1

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

What is the purpose of the Euclidean algorithm?

To compute the greatest common divisor of two integers

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

gcd(m, n)

Who is credited with first describing the Euclidean algorithm?

Euclid of Alexandria

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

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

Modulus

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

To compute the greatest common divisor

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

Using a loop

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

int

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

Using a pointer operator

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

To handle the base case of the recursion

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

Hearts

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

What is the purpose of the gcd function?

To find the greatest common divisor

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

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

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

To subtract the smaller number from the larger number

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

The remainder of a divided by b

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

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

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 (*).

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.

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