[Add]: Code for nth ugly number

dynamic_programming/nth_ugly_number.py

@@ -0,0 +1,88 @@
+# Ugly Number 2 Problem
+# LeetCode Problem: https://leetcode.com/problems/ugly-number-ii/
+"""
+Prints the nth ugly number n being the user input.
+
+Ugly numbers are a sequence of positive integers that are defined as numbers whose only prime factors are 2, 3, and 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
+
+Parameters:
+n (int): The index of the desired ugly number.
+
+Returns:
+int: The nth ugly number.
+
+Algorithm:
+The nth ugly number is generated by multiplying previous ugly numbers with 2, 3, or 5.
+The ugly numbers are stored in an array k, and the algorithm uses three pointers ptr1, ptr2, and ptr3
+to keep track of the positions in the array for multiplying with 2, 3, and 5 respectively.
+
+Time Complexity:
+O(n) - The algorithm generates the nth ugly number in linear time.
+
+Space Complexity:
+O(n) - The algorithm uses an array of size n to store the ugly numbers.
+
+
+Sources:
+- Dynamic Programming and Ugly Numbers: https://www.geeksforgeeks.org/ugly-numbers/
+"""
+def nth_ugly_number(n: int) -> int:
+    
+    """
+    Return the nth ugly number.
+    >>> nth_ugly_number(5)
+    5
+    >>> nth_ugly_number(7)
+    8
+    >>> nth_ugly_number(1)
+    1
+    >>> nth_ugly_number(-1)
+    Traceback (most recent call last):
+    ValueError: Index for nth ugly number should be ≥ 0
+    
+    """
+    if n < 0:
+         raise ValueError("Index for nth ugly number should be ≥ 0")
+    dp = [1] * (n + 1)
+    ptr1 = 0
+    ptr2 = 0
+    ptr3 = 0
+    for i in range(1, n):
+        two = dp[ptr1] * 2
+        three = dp[ptr2] * 3
+        five = dp[ptr3] * 5
+        dp[i] = min(two, three, five)
+        if dp[i] == two:
+            ptr1 += 1
+        if dp[i] == three:
+            ptr2 += 1
+        if dp[i] == five:
+            ptr3 += 1
+            
+    return dp[n - 1]
+
+if __name__ == "__main__":
+
+    # User input to find the nth Ugly Number
+    print("\n********* Ugly Numbers Using Dynamic Programming ************\n")
+    print("\n*** Enter -1 to quit ***")
+    print("\nEnter the index (≥ 0) of the Ugly number to find: ", end="")
+    try:
+        while True:
+            n = int(input().strip())
+            if n < 0:
+                print("\n********* END ************")
+                break
+            else:
+                
+                ugly_number = nthUglyNumber(n)
+                print(f"The {n}th Ugly Number is: {ugly_number}")
+                print("Try another index to find a Ugly Number: ", end="")
+    except (NameError, ValueError):
+        print("\n********* Invalid input, END ************\n")
+        
+import doctest
+    
+# Test cases for nthUglyNumber function
+doctest.testmod()