Program to find kth lexicographic sequence from 1 to n of size k Python

PythonServer Side ProgrammingProgramming

Suppose we have two values n and k. Now consider a list of numbers in range 1 through n [1, 2, ..., n] and generating every permutation of this list in lexicographic sequence. For example, if n = 4 we have [1234, 1243, 1324, 1342, 1423, 1432, 2134, 2143, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 3412, 3421, 4123, 4132, 4213, 4231, 4312, 4321]. We have to find the kth value of this permutation sequence as a string.

So, if the input is like n = 4 k = 5, then the output will be "1432"

To solve this, we will follow these steps −

  • Define a function factors() . This will take num

  • quo := num

  • res := a double ended queue and insert 0 at beginning

  • i := 2

  • while quo is not empty, do

    • quo := quotient of (quo / i), rem := quo mod i

    • insert rem at the left of res

    • i := i + 1

  • return res

  • From the main method do the following −

  • numbers := a list with values 1 through n

  • res := blank string

  • k_fact := factors(k)

  • while size of k_fact < size of numbers, do

    • res := res concatenate first element of numbers as string, then delete first element of numbers

  • for each index in k_fact, do

    • number := index−th element of numbers, then remove that element

    • res := res concatenate number

  • return res

Let us see the following implementation to get better understanding −

Example

 Live Demo

from collections import deque
def factors(num):
   quo = num
   res = deque([0])
   i = 2
   while quo:
      quo, rem = divmod(quo, i)
      res.appendleft(rem)
      i += 1
   return res
class Solution:
   def solve(self, n, k):
      numbers = [num for num in range(1, n + 1)]
      res = ""
      k_fact = factors(k)
      while len(k_fact) < len(numbers):
         res += str(numbers.pop(0))
      for index in k_fact:
         number = numbers.pop(index)
         res += str(number)
      return res
ob = Solution()
n = 4
k = 5
print(ob.solve(n, k))

Input

4, 5

Output

1432
raja
Published on 26-Dec-2020 10:56:56
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