Create minimums_squares_to_represent_a_number.py (#7595)

* Create minimums_squares_to_represent_a_number.py

added a dynamic programming approach of finding the minimum number of square to represent a number.
eg : 
25 = 5*5
37 = 6*6 + 1*1
21 = 4*4 + 2*2 + 1*1

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* Update and rename minimums_squares_to_represent_a_number.py to minimum_squares_to_represent_a_number.py

updated the code

* Update minimum_squares_to_represent_a_number.py

I have added the appropriate checks for 0 and 12.34. 
It would be great if you could suggest a name for the dp array

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* Update minimum_squares_to_represent_a_number.py

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

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* Update minimum_squares_to_represent_a_number.py

updated

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

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* Update minimum_squares_to_represent_a_number.py

updated

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

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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()