diff --git a/DIRECTORY.md b/DIRECTORY.md
index 384ce1b2209d..be5fa3584a58 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -573,9 +573,7 @@
* [Fermat Little Theorem](maths/fermat_little_theorem.py)
* [Fibonacci](maths/fibonacci.py)
* [Find Max](maths/find_max.py)
- * [Find Max Recursion](maths/find_max_recursion.py)
* [Find Min](maths/find_min.py)
- * [Find Min Recursion](maths/find_min_recursion.py)
* [Floor](maths/floor.py)
* [Gamma](maths/gamma.py)
* [Gamma Recursive](maths/gamma_recursive.py)
diff --git a/maths/find_max.py b/maths/find_max.py
index 684fbe8161e8..729a80ab421c 100644
--- a/maths/find_max.py
+++ b/maths/find_max.py
@@ -1,23 +1,23 @@
from __future__ import annotations
-def find_max(nums: list[int | float]) -> int | float:
+def find_max_iterative(nums: list[int | float]) -> int | float:
"""
>>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
- ... find_max(nums) == max(nums)
+ ... find_max_iterative(nums) == max(nums)
True
True
True
True
- >>> find_max([2, 4, 9, 7, 19, 94, 5])
+ >>> find_max_iterative([2, 4, 9, 7, 19, 94, 5])
94
- >>> find_max([])
+ >>> find_max_iterative([])
Traceback (most recent call last):
...
- ValueError: find_max() arg is an empty sequence
+ ValueError: find_max_iterative() arg is an empty sequence
"""
if len(nums) == 0:
- raise ValueError("find_max() arg is an empty sequence")
+ raise ValueError("find_max_iterative() arg is an empty sequence")
max_num = nums[0]
for x in nums:
if x > max_num:
@@ -25,6 +25,59 @@ def find_max(nums: list[int | float]) -> int | float:
return max_num
+# Divide and Conquer algorithm
+def find_max_recursive(nums: list[int | float], left: int, right: int) -> int | float:
+ """
+ find max value in list
+ :param nums: contains elements
+ :param left: index of first element
+ :param right: index of last element
+ :return: max in nums
+
+ >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
+ ... find_max_recursive(nums, 0, len(nums) - 1) == max(nums)
+ True
+ True
+ True
+ True
+ >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+ >>> find_max_recursive(nums, 0, len(nums) - 1) == max(nums)
+ True
+ >>> find_max_recursive([], 0, 0)
+ Traceback (most recent call last):
+ ...
+ ValueError: find_max_recursive() arg is an empty sequence
+ >>> find_max_recursive(nums, 0, len(nums)) == max(nums)
+ Traceback (most recent call last):
+ ...
+ IndexError: list index out of range
+ >>> find_max_recursive(nums, -len(nums), -1) == max(nums)
+ True
+ >>> find_max_recursive(nums, -len(nums) - 1, -1) == max(nums)
+ Traceback (most recent call last):
+ ...
+ IndexError: list index out of range
+ """
+ if len(nums) == 0:
+ raise ValueError("find_max_recursive() arg is an empty sequence")
+ if (
+ left >= len(nums)
+ or left < -len(nums)
+ or right >= len(nums)
+ or right < -len(nums)
+ ):
+ raise IndexError("list index out of range")
+ if left == right:
+ return nums[left]
+ mid = (left + right) >> 1 # the middle
+ left_max = find_max_recursive(nums, left, mid) # find max in range[left, mid]
+ right_max = find_max_recursive(
+ nums, mid + 1, right
+ ) # find max in range[mid + 1, right]
+
+ return left_max if left_max >= right_max else right_max
+
+
if __name__ == "__main__":
import doctest
diff --git a/maths/find_max_recursion.py b/maths/find_max_recursion.py
deleted file mode 100644
index 629932e0818f..000000000000
--- a/maths/find_max_recursion.py
+++ /dev/null
@@ -1,58 +0,0 @@
-from __future__ import annotations
-
-
-# Divide and Conquer algorithm
-def find_max(nums: list[int | float], left: int, right: int) -> int | float:
- """
- find max value in list
- :param nums: contains elements
- :param left: index of first element
- :param right: index of last element
- :return: max in nums
-
- >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
- ... find_max(nums, 0, len(nums) - 1) == max(nums)
- True
- True
- True
- True
- >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
- >>> find_max(nums, 0, len(nums) - 1) == max(nums)
- True
- >>> find_max([], 0, 0)
- Traceback (most recent call last):
- ...
- ValueError: find_max() arg is an empty sequence
- >>> find_max(nums, 0, len(nums)) == max(nums)
- Traceback (most recent call last):
- ...
- IndexError: list index out of range
- >>> find_max(nums, -len(nums), -1) == max(nums)
- True
- >>> find_max(nums, -len(nums) - 1, -1) == max(nums)
- Traceback (most recent call last):
- ...
- IndexError: list index out of range
- """
- if len(nums) == 0:
- raise ValueError("find_max() arg is an empty sequence")
- if (
- left >= len(nums)
- or left < -len(nums)
- or right >= len(nums)
- or right < -len(nums)
- ):
- raise IndexError("list index out of range")
- if left == right:
- return nums[left]
- mid = (left + right) >> 1 # the middle
- left_max = find_max(nums, left, mid) # find max in range[left, mid]
- right_max = find_max(nums, mid + 1, right) # find max in range[mid + 1, right]
-
- return left_max if left_max >= right_max else right_max
-
-
-if __name__ == "__main__":
- import doctest
-
- doctest.testmod(verbose=True)
diff --git a/maths/find_min.py b/maths/find_min.py
index 2eac087c6388..762562e36ef9 100644
--- a/maths/find_min.py
+++ b/maths/find_min.py
@@ -1,33 +1,86 @@
from __future__ import annotations
-def find_min(nums: list[int | float]) -> int | float:
+def find_min_iterative(nums: list[int | float]) -> int | float:
"""
Find Minimum Number in a List
:param nums: contains elements
:return: min number in list
>>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
- ... find_min(nums) == min(nums)
+ ... find_min_iterative(nums) == min(nums)
True
True
True
True
- >>> find_min([0, 1, 2, 3, 4, 5, -3, 24, -56])
+ >>> find_min_iterative([0, 1, 2, 3, 4, 5, -3, 24, -56])
-56
- >>> find_min([])
+ >>> find_min_iterative([])
Traceback (most recent call last):
...
- ValueError: find_min() arg is an empty sequence
+ ValueError: find_min_iterative() arg is an empty sequence
"""
if len(nums) == 0:
- raise ValueError("find_min() arg is an empty sequence")
+ raise ValueError("find_min_iterative() arg is an empty sequence")
min_num = nums[0]
for num in nums:
min_num = min(min_num, num)
return min_num
+# Divide and Conquer algorithm
+def find_min_recursive(nums: list[int | float], left: int, right: int) -> int | float:
+ """
+ find min value in list
+ :param nums: contains elements
+ :param left: index of first element
+ :param right: index of last element
+ :return: min in nums
+
+ >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
+ ... find_min_recursive(nums, 0, len(nums) - 1) == min(nums)
+ True
+ True
+ True
+ True
+ >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+ >>> find_min_recursive(nums, 0, len(nums) - 1) == min(nums)
+ True
+ >>> find_min_recursive([], 0, 0)
+ Traceback (most recent call last):
+ ...
+ ValueError: find_min_recursive() arg is an empty sequence
+ >>> find_min_recursive(nums, 0, len(nums)) == min(nums)
+ Traceback (most recent call last):
+ ...
+ IndexError: list index out of range
+ >>> find_min_recursive(nums, -len(nums), -1) == min(nums)
+ True
+ >>> find_min_recursive(nums, -len(nums) - 1, -1) == min(nums)
+ Traceback (most recent call last):
+ ...
+ IndexError: list index out of range
+ """
+ if len(nums) == 0:
+ raise ValueError("find_min_recursive() arg is an empty sequence")
+ if (
+ left >= len(nums)
+ or left < -len(nums)
+ or right >= len(nums)
+ or right < -len(nums)
+ ):
+ raise IndexError("list index out of range")
+ if left == right:
+ return nums[left]
+ mid = (left + right) >> 1 # the middle
+ left_min = find_min_recursive(nums, left, mid) # find min in range[left, mid]
+ right_min = find_min_recursive(
+ nums, mid + 1, right
+ ) # find min in range[mid + 1, right]
+
+ return left_min if left_min <= right_min else right_min
+
+
if __name__ == "__main__":
import doctest
diff --git a/maths/find_min_recursion.py b/maths/find_min_recursion.py
deleted file mode 100644
index 4d11015efcd5..000000000000
--- a/maths/find_min_recursion.py
+++ /dev/null
@@ -1,58 +0,0 @@
-from __future__ import annotations
-
-
-# Divide and Conquer algorithm
-def find_min(nums: list[int | float], left: int, right: int) -> int | float:
- """
- find min value in list
- :param nums: contains elements
- :param left: index of first element
- :param right: index of last element
- :return: min in nums
-
- >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
- ... find_min(nums, 0, len(nums) - 1) == min(nums)
- True
- True
- True
- True
- >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
- >>> find_min(nums, 0, len(nums) - 1) == min(nums)
- True
- >>> find_min([], 0, 0)
- Traceback (most recent call last):
- ...
- ValueError: find_min() arg is an empty sequence
- >>> find_min(nums, 0, len(nums)) == min(nums)
- Traceback (most recent call last):
- ...
- IndexError: list index out of range
- >>> find_min(nums, -len(nums), -1) == min(nums)
- True
- >>> find_min(nums, -len(nums) - 1, -1) == min(nums)
- Traceback (most recent call last):
- ...
- IndexError: list index out of range
- """
- if len(nums) == 0:
- raise ValueError("find_min() arg is an empty sequence")
- if (
- left >= len(nums)
- or left < -len(nums)
- or right >= len(nums)
- or right < -len(nums)
- ):
- raise IndexError("list index out of range")
- if left == right:
- return nums[left]
- mid = (left + right) >> 1 # the middle
- left_min = find_min(nums, left, mid) # find min in range[left, mid]
- right_min = find_min(nums, mid + 1, right) # find min in range[mid + 1, right]
-
- return left_min if left_min <= right_min else right_min
-
-
-if __name__ == "__main__":
- import doctest
-
- doctest.testmod(verbose=True)