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Oct 26, 2022
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48 changes: 48 additions & 0 deletions dynamic_programming/minimum_squares_to_represent_a_number.py
Original file line number Diff line number Diff line change
@@ -0,0 +1,48 @@
import math
import sys


def minimum_squares_to_represent_a_number(number: int) -> int:
"""
Count the number of minimum squares to represent a number
>>> minimum_squares_to_represent_a_number(25)
1
>>> minimum_squares_to_represent_a_number(37)
2
>>> minimum_squares_to_represent_a_number(21)
3
>>> minimum_squares_to_represent_a_number(58)
2
>>> minimum_squares_to_represent_a_number(-1)
Traceback (most recent call last):
...
ValueError: the value of input must not be a negative number
>>> minimum_squares_to_represent_a_number(0)
1
>>> minimum_squares_to_represent_a_number(12.34)
Traceback (most recent call last):
...
ValueError: the value of input must be a natural number
"""
if number != int(number):
raise ValueError("the value of input must be a natural number")
if number < 0:
raise ValueError("the value of input must not be a negative number")
if number == 0:
return 1
answers = [-1] * (number + 1)
answers[0] = 0
for i in range(1, number + 1):
answer = sys.maxsize
root = int(math.sqrt(i))
for j in range(1, root + 1):
current_answer = 1 + answers[i - (j**2)]
answer = min(answer, current_answer)
answers[i] = answer
return answers[number]


if __name__ == "__main__":
import doctest

doctest.testmod()