Fibonacci. In 1202, Fibonacci published his sequence. The Fibonacci sequence helped with bookkeeping and charging interest on loans.
Algorithms. We can compute this sequence iteratively, with no recursion. To display a list of Fibonacci numbers, we can make just one iteration through them.
First program. To compute the Fibonacci sequence, we must sum the previous two numbers. This value becomes the next number for the sequence.
Info A temporary variable "temp" is used to store the previous value for later use.
Note We use range() to loop over the entire numeric range to the desired Fibonacci number.
Note 2 We do not need recursion for a Fibonacci sequence. Iteration, with a temporary variable, works as well—and is likely faster.
def fibonacci(n):
a = 0
b = 1
for i in range(0, n):
temp = a
a = b
b = temp + b
return a
# Display the first 15 Fibonacci numbers.
for c in range(0, 15):
print(fibonacci(c))0
1
1
2
3
5
8
13
21
34
55
89
144
233
377
Display. This method displays Fibonacci numbers as it goes along. For creating a list of Fibonacci numbers, this approach is faster. Just change the "print" statement to a list append call.
Tip Using lookup tables or "memoizing" math computations is usually faster for nontrivial requirements.
def fibonacci2(n):
a = 0
b = 1
for i in range(0, n):
# Display the current Fibonacci number.
print(a)
temp = a
a = b
b = temp + b
return a
# Directly display the numbers.
fibonacci2(15)0
1
1
2
3
5
8
13
21
34
55
89
144
233
377
A summary. Fibonacci sequences are often used to predict financial markets. Whether anyone can predict financial markets reliably is debatable.
The sequence itself, though, is simple and easy to iteratively compute. Recursion is not necessary. Using a cache (like a list) of numbers would be worthwhile for performance.
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This page was last updated on Mar 20, 2023 (edit).