Python: Find the nth ugly number using Heap queue algorithm

Last update on December 21 2024 07:30:30 (UTC/GMT +8 hours)

Write a Python program to find the n^th ugly number using the 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:
8
10th Ugly number:
12

Flowchart:

Python Code Editor:

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