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Python: Find the nth super ugly number from a given prime list of size k using Heap queue algorithm

Python heap queue algorithm: Exercise-13 with Solution

Write a Python program to find the nth super ugly number from a given prime list of size k using Heap queue algorithm.

Super ugly numbers are positive numbers whose all prime factors are in the given prime list primes of size k. For example, [1, 2, 4, 7, 8, 13, 14, 16, 19, 26, 28, 32] is the sequence of the first 12 super ugly numbers given primes = [2, 7, 13, 19] of size 4.

Sample Solution:

Python Code:

import heapq
#Ref.: https://bit.ly/32c9P3A
def nth_Super_Ugly_Number(n, primes):
    uglies = [1]

    def gen(prime):
        for ugly in uglies:
            yield ugly * prime

    merged = heapq.merge(*map(gen, primes))
    while len(uglies) < n:
        ugly = next(merged)
        if ugly != uglies[-1]:
            uglies.append(ugly)
    return uglies[-1]
n = 12
primes = [2,7,13,19]
print(nth_Super_Ugly_Number(n, primes))

Sample Output:

32

Flowchart:

Python heap queue algorithm: Find the nth super ugly number from a given prime list of size k using Heap queue algorithm.

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Previous: Given a n x n matrix where each of the rows and columns are sorted in ascending order, write a Python program to find the kth smallest element in the matrix.
Next: Write a Python program to get the k most frequent elements from a given non-empty list of words using Heap queue algorithm.

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Python: Tips of the Day

Find current directory and file's directory:

To get the full path to the directory a Python file is contained in, write this in that file:

import os 
dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os
cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

  • The os and os.path modules.
  • The __file__ constant
  • os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")
  • os.path.dirname(path) (returns "the directory name of pathname path")
  • os.getcwd() (returns "a string representing the current working directory")
  • os.chdir(path) ("change the current working directory to path")

Ref: https://bit.ly/3fy0R6m