diff --git a/dynamic_programming/minimum_squares_to_represent_a_number.py b/dynamic_programming/minimum_squares_to_represent_a_number.py new file mode 100644 index 000000000..bf5849f5b --- /dev/null +++ b/dynamic_programming/minimum_squares_to_represent_a_number.py @@ -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()