Python: Find the nth ugly number using Heap queue algorithm

Python heap queue algorithm: Exercise-18 with Solution

Write a Python program to find the nth ugly number using Heap queue algorithm.

Ugly numbers are positive numbers whose only prime factors are 2, 3 or 5. The sequence 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, ... shows the first 10 ugly numbers.
Note: 1 is typically treated as an ugly number.

Sample Solution:

Python Code:

import heapq
class Solution(object):      
      #:type n: integer
      #:return type: integer      
   def nth_Ugly_Number(self, n):
       ugly_num = 0
       heap = []
       heapq.heappush(heap, 1)
       for _ in range(n):
           ugly_num = heapq.heappop(heap)
           if ugly_num % 2 == 0:
               heapq.heappush(heap, ugly_num * 2)
           elif ugly_num % 3 == 0:
               heapq.heappush(heap, ugly_num * 2)
               heapq.heappush(heap, ugly_num * 3)
           else:
               heapq.heappush(heap, ugly_num * 2)
               heapq.heappush(heap, ugly_num * 3)
               heapq.heappush(heap, ugly_num * 5)
               return ugly_num
n = 7
S = Solution()
result = S.nth_Ugly_Number(n)
print("7th Ugly number:")
print(result)
n = 10
result = S.nth_Ugly_Number(n)
print("\n10th Ugly number:")
print(result)

Sample Output:

7th Ugly number:
1

10th Ugly number:
1

Flowchart:

Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:

Python Code Editor:

Have another way to solve this solution? Contribute your code (and comments) through Disqus.

Previous: You are given two integer arrays sorted in ascending order and an integer k. Write a Python program to find k number of pairs (u, v) which consists of one element from the first array and one element from the second array using Heap queue algorithm.
Next: Write a Python program to print a heap as a tree-like data structure.