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89 lines
2.6 KiB
Python
89 lines
2.6 KiB
Python
# Ugly Number 2 Problem
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# LeetCode Problem: https://leetcode.com/problems/ugly-number-ii/
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"""
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Prints the nth ugly number n being the user input.
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Ugly numbers are a sequence of positive integers that are defined as numbers whose only prime factors are 2, 3, and 5.
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The sequence 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, … shows the first 11 ugly numbers. By convention, 1 is included
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Parameters:
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n (int): The index of the desired ugly number.
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Returns:
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int: The nth ugly number.
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Algorithm:
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The nth ugly number is generated by multiplying previous ugly numbers with 2, 3, or 5.
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The ugly numbers are stored in an array k, and the algorithm uses three pointers ptr1, ptr2, and ptr3
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to keep track of the positions in the array for multiplying with 2, 3, and 5 respectively.
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Time Complexity:
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O(n) - The algorithm generates the nth ugly number in linear time.
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Space Complexity:
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O(n) - The algorithm uses an array of size n to store the ugly numbers.
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Sources:
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- Dynamic Programming and Ugly Numbers: https://www.geeksforgeeks.org/ugly-numbers/
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"""
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def nth_ugly_number(n: int) -> int:
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"""
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Return the nth ugly number.
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>>> nth_ugly_number(5)
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5
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>>> nth_ugly_number(7)
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8
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>>> nth_ugly_number(1)
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1
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>>> nth_ugly_number(-1)
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Traceback (most recent call last):
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ValueError: Index for nth ugly number should be ≥ 0
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"""
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if n < 0:
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raise ValueError("Index for nth ugly number should be ≥ 0")
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dp = [1] * (n + 1)
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ptr1 = 0
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ptr2 = 0
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ptr3 = 0
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for i in range(1, n):
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two = dp[ptr1] * 2
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three = dp[ptr2] * 3
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five = dp[ptr3] * 5
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dp[i] = min(two, three, five)
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if dp[i] == two:
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ptr1 += 1
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if dp[i] == three:
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ptr2 += 1
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if dp[i] == five:
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ptr3 += 1
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return dp[n - 1]
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if __name__ == "__main__":
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# User input to find the nth Ugly Number
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print("\n********* Ugly Numbers Using Dynamic Programming ************\n")
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print("\n*** Enter -1 to quit ***")
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print("\nEnter the index (≥ 0) of the Ugly number to find: ", end="")
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try:
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while True:
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n = int(input().strip())
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if n < 0:
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print("\n********* END ************")
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break
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else:
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ugly_number = nthUglyNumber(n)
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print(f"The {n}th Ugly Number is: {ugly_number}")
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print("Try another index to find a Ugly Number: ", end="")
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except (NameError, ValueError):
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print("\n********* Invalid input, END ************\n")
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import doctest
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# Test cases for nthUglyNumber function
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doctest.testmod()
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