add a yield method to fibonaci (#10826)

* add a yiled method to fibonaci

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* fibonaci

* Update fibonacci.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update fibonacci.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

maths/fibonacci.py

@@ -1,4 +1,3 @@
-# fibonacci.py
 """
 Calculates the Fibonacci sequence using iteration, recursion, memoization,
 and a simplified form of Binet's formula
@@ -9,14 +8,12 @@ the Binet's formula function because the Binet formula function  uses floats
 NOTE 2: the Binet's formula function is much more limited in the size of inputs
 that it can handle due to the size limitations of Python floats
 
-RESULTS: (n = 20)
-fib_iterative runtime: 0.0055 ms
-fib_recursive runtime: 6.5627 ms
-fib_memoization runtime: 0.0107 ms
-fib_binet runtime: 0.0174 ms
+See benchmark numbers in __main__ for performance comparisons/
+https://en.wikipedia.org/wiki/Fibonacci_number for more information
 """
 
 import functools
+from collections.abc import Iterator
 from math import sqrt
 from time import time
 
@@ -35,6 +32,31 @@ def time_func(func, *args, **kwargs):
     return output
 
 
+def fib_iterative_yield(n: int) -> Iterator[int]:
+    """
+    Calculates the first n (1-indexed) Fibonacci numbers using iteration with yield
+    >>> list(fib_iterative_yield(0))
+    [0]
+    >>> tuple(fib_iterative_yield(1))
+    (0, 1)
+    >>> tuple(fib_iterative_yield(5))
+    (0, 1, 1, 2, 3, 5)
+    >>> tuple(fib_iterative_yield(10))
+    (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55)
+    >>> tuple(fib_iterative_yield(-1))
+    Traceback (most recent call last):
+        ...
+    ValueError: n is negative
+    """
+    if n < 0:
+        raise ValueError("n is negative")
+    a, b = 0, 1
+    yield a
+    for _ in range(n):
+        yield b
+        a, b = b, a + b
+
+
 def fib_iterative(n: int) -> list[int]:
     """
     Calculates the first n (0-indexed) Fibonacci numbers using iteration
@@ -49,10 +71,10 @@ def fib_iterative(n: int) -> list[int]:
     >>> fib_iterative(-1)
     Traceback (most recent call last):
         ...
-    Exception: n is negative
+    ValueError: n is negative
     """
     if n < 0:
-        raise Exception("n is negative")
+        raise ValueError("n is negative")
     if n == 0:
         return [0]
     fib = [0, 1]
@@ -75,7 +97,7 @@ def fib_recursive(n: int) -> list[int]:
     >>> fib_iterative(-1)
     Traceback (most recent call last):
         ...
-    Exception: n is negative
+    ValueError: n is negative
     """
 
     def fib_recursive_term(i: int) -> int:
@@ -95,13 +117,13 @@ def fib_recursive(n: int) -> list[int]:
         Exception: n is negative
         """
         if i < 0:
-            raise Exception("n is negative")
+            raise ValueError("n is negative")
         if i < 2:
             return i
         return fib_recursive_term(i - 1) + fib_recursive_term(i - 2)
 
     if n < 0:
-        raise Exception("n is negative")
+        raise ValueError("n is negative")
     return [fib_recursive_term(i) for i in range(n + 1)]
 
 
@@ -119,7 +141,7 @@ def fib_recursive_cached(n: int) -> list[int]:
     >>> fib_iterative(-1)
     Traceback (most recent call last):
         ...
-    Exception: n is negative
+    ValueError: n is negative
     """
 
     @functools.cache
@@ -128,13 +150,13 @@ def fib_recursive_cached(n: int) -> list[int]:
         Calculates the i-th (0-indexed) Fibonacci number using recursion
         """
         if i < 0:
-            raise Exception("n is negative")
+            raise ValueError("n is negative")
         if i < 2:
             return i
         return fib_recursive_term(i - 1) + fib_recursive_term(i - 2)
 
     if n < 0:
-        raise Exception("n is negative")
+        raise ValueError("n is negative")
     return [fib_recursive_term(i) for i in range(n + 1)]
 
 
@@ -152,10 +174,10 @@ def fib_memoization(n: int) -> list[int]:
     >>> fib_iterative(-1)
     Traceback (most recent call last):
         ...
-    Exception: n is negative
+    ValueError: n is negative
     """
     if n < 0:
-        raise Exception("n is negative")
+        raise ValueError("n is negative")
     # Cache must be outside recursuive function
     # other it will reset every time it calls itself.
     cache: dict[int, int] = {0: 0, 1: 1, 2: 1}  # Prefilled cache
@@ -193,29 +215,30 @@ def fib_binet(n: int) -> list[int]:
     >>> fib_binet(-1)
     Traceback (most recent call last):
         ...
-    Exception: n is negative
+    ValueError: n is negative
     >>> fib_binet(1475)
     Traceback (most recent call last):
         ...
-    Exception: n is too large
+    ValueError: n is too large
     """
     if n < 0:
-        raise Exception("n is negative")
+        raise ValueError("n is negative")
     if n >= 1475:
-        raise Exception("n is too large")
+        raise ValueError("n is too large")
     sqrt_5 = sqrt(5)
     phi = (1 + sqrt_5) / 2
     return [round(phi**i / sqrt_5) for i in range(n + 1)]
 
 
 if __name__ == "__main__":
-    import doctest
-
-    doctest.testmod()
+    from doctest import testmod
 
+    testmod()
+    # Time on an M1 MacBook Pro -- Fastest to slowest
     num = 30
-    time_func(fib_iterative, num)
-    time_func(fib_recursive, num)  # Around 3s runtime
-    time_func(fib_recursive_cached, num)  # Around 0ms runtime
-    time_func(fib_memoization, num)
-    time_func(fib_binet, num)
+    time_func(fib_iterative_yield, num)  # 0.0012 ms
+    time_func(fib_iterative, num)  # 0.0031 ms
+    time_func(fib_binet, num)  # 0.0062 ms
+    time_func(fib_memoization, num)  # 0.0100 ms
+    time_func(fib_recursive_cached, num)  # 0.0153 ms
+    time_func(fib_recursive, num)  # 257.0910 ms