Problem: Given the starting and ending integers representing…
Problem: Given the starting and ending integers representing a range of numbers, count the number of integers in that range, inclusive of the endpoints, which are a part of the Fibonacci sequence of numbers. Example Execution #1: Enter the starting value: 2 Enter the ending value: 22
Answer
The problem at hand requires counting the number of integers within a given range that are part of the Fibonacci sequence. The Fibonacci sequence is a series of numbers in which each number after the first two is the sum of the two preceding ones. It begins with 0 and 1, so the sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, …
To solve this problem, we need to first determine the Fibonacci numbers within the given range. Then, we count the total number of Fibonacci numbers in that range.
To start, we require a method to generate the Fibonacci sequence. One common approach is to use an iterative method, in which we add the last two Fibonacci numbers to obtain the next one. We can implement this method as a loop, iterating through the range until we reach the maximum number in our range. Here is an example code snippet:
“`python
def generate_fibonacci(range_max):
fibonacci_sequence = [0, 1]
while fibonacci_sequence[-1] <= range_max:
next_number = fibonacci_sequence[-1] + fibonacci_sequence[-2]
fibonacci_sequence.append(next_number)
return fibonacci_sequence
```
Using this method, we can now generate the Fibonacci sequence up to the maximum value within our range. For example, if the range's endpoint is 22, the Fibonacci sequence up to that point would be: 0, 1, 1, 2, 3, 5, 8, 13, 21.
Next, we need to count the number of Fibonacci numbers within the given range. To do this, we iterate through the Fibonacci sequence we generated earlier and check if each number falls within the range. If it does, we increment a counter. Here is an example code snippet:
```python
def count_fibonacci_in_range(start_value, end_value):
fibonacci_sequence = generate_fibonacci(end_value)
count = 0
for number in fibonacci_sequence:
if start_value <= number <= end_value:
count += 1
return count
```
Using this method, we can provide the starting and ending values to calculate the count of Fibonacci numbers within the specified range. For example, if the starting value is 2 and the ending value is 22, the count would be 6.
In conclusion, the problem of counting Fibonacci numbers within a given range can be solved by generating the Fibonacci sequence up to the maximum value in the range and then counting the numbers falling within that range. By using the proposed methods, we can easily calculate the count of Fibonacci numbers for any given range.