Created ugly_numbers.py in Python/maths

maths/ugly_numbers.py

@@ -0,0 +1,54 @@
+"""
+Ugly numbers are numbers whose only prime factors are 2, 3 or 5. The sequence
+1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, … shows the first 11 ugly numbers. By convention,
+1 is included.
+Given an integer n, we have to find the nth ugly number.
+
+For more details, refer this article
+https://www.geeksforgeeks.org/ugly-numbers/
+"""
+
+
+def ugly_numbers(n: int) -> int:
+    """
+    Returns the nth ugly number.
+    >>> ugly_numbers(100)
+    1536
+    >>> ugly_numbers(0)
+    1
+    >>> ugly_numbers(20)
+    36
+    >>> ugly_numbers(-5)
+    1
+    >>> ugly_numbers(-5.5)
+    Traceback (most recent call last):
+        ...
+    TypeError: 'float' object cannot be interpreted as an integer
+    """
+    ugly_nums = [1]
+
+    i2, i3, i5 = 0, 0, 0
+    next_2 = ugly_nums[i2] * 2
+    next_3 = ugly_nums[i3] * 3
+    next_5 = ugly_nums[i5] * 5
+
+    for i in range(1, n):
+        next_num = min(next_2, next_3, next_5)
+        ugly_nums.append(next_num)
+        if next_num == next_2:
+            i2 += 1
+            next_2 = ugly_nums[i2] * 2
+        if next_num == next_3:
+            i3 += 1
+            next_3 = ugly_nums[i3] * 3
+        if next_num == next_5:
+            i5 += 1
+            next_5 = ugly_nums[i5] * 5
+    return ugly_nums[-1]
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod(verbose=True)
+    print(f"{ugly_numbers(200) = }")