mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-23 21:11:08 +00:00
403d3b8a29
* Add Integer Square Root Algorithm * Update integer_square_root.py * Update integer_square_root.py --------- Co-authored-by: Christian Clauss <cclauss@me.com>
74 lines
2.2 KiB
Python
74 lines
2.2 KiB
Python
"""
|
|
Integer Square Root Algorithm -- An efficient method to calculate the square root of a
|
|
non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
|
|
approach to find the integer square root without using any built-in exponent functions
|
|
or operators.
|
|
* https://en.wikipedia.org/wiki/Integer_square_root
|
|
* https://docs.python.org/3/library/math.html#math.isqrt
|
|
Note:
|
|
- This algorithm is designed for non-negative integers only.
|
|
- The result is rounded down to the nearest integer.
|
|
- The algorithm has a time complexity of O(log(x)).
|
|
- Original algorithm idea based on binary search.
|
|
"""
|
|
|
|
|
|
def integer_square_root(num: int) -> int:
|
|
"""
|
|
Returns the integer square root of a non-negative integer num.
|
|
Args:
|
|
num: A non-negative integer.
|
|
Returns:
|
|
The integer square root of num.
|
|
Raises:
|
|
ValueError: If num is not an integer or is negative.
|
|
>>> [integer_square_root(i) for i in range(18)]
|
|
[0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
|
|
>>> integer_square_root(625)
|
|
25
|
|
>>> integer_square_root(2_147_483_647)
|
|
46340
|
|
>>> from math import isqrt
|
|
>>> all(integer_square_root(i) == isqrt(i) for i in range(20))
|
|
True
|
|
>>> integer_square_root(-1)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: num must be non-negative integer
|
|
>>> integer_square_root(1.5)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: num must be non-negative integer
|
|
>>> integer_square_root("0")
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: num must be non-negative integer
|
|
"""
|
|
if not isinstance(num, int) or num < 0:
|
|
raise ValueError("num must be non-negative integer")
|
|
|
|
if num < 2:
|
|
return num
|
|
|
|
left_bound = 0
|
|
right_bound = num // 2
|
|
|
|
while left_bound <= right_bound:
|
|
mid = left_bound + (right_bound - left_bound) // 2
|
|
mid_squared = mid * mid
|
|
if mid_squared == num:
|
|
return mid
|
|
|
|
if mid_squared < num:
|
|
left_bound = mid + 1
|
|
else:
|
|
right_bound = mid - 1
|
|
|
|
return right_bound
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|