Find Lexicographically Smallest String in Python

Suppose we have an array A of n numbers, where A[i] indicates the number of distinct characters in the prefix of length (i + 1) of a string s, we have to find the lexicographically smallest string that satisfies the given prefix array. All characters will be lowercase English alphabets [a-z]. If there is no such string then return -1.

So, if the input is like A = [1,1,2,3,4], then the output will be aabcd as prefix[0] has 1 distinct character, prefix[1] has 1 distinct character, prefix[2] has 2 distinct characters, prefix[3] has 3 distinct characters, prefix[4] has 4 distinct characters and the string is smallest.

To solve this, we will follow these steps −

• n := size of A

• character := 'a'

• string := blank string

• if n < 1 or A[0] is not 1, then

  • return -1

• string := string concatenate character

• character := next character of this current character

• for i in range 1 to n, do

  • difference := A[i] - A[i - 1]

  • if difference > 1 or difference < 0 or A[i] > 26, then

    • return -1

  • otherwise when difference is same as 0, then

    • string := string concatenate 'a'

  • otherwise,

    • string := string concatenate character

    • character := next character of this current character

• return string

Example 

Let us see the following implementation to get better understanding −

 Live Demo

def get_smallest_string(A):
   n = len(A)
   character = 'a'
   string = ""
   if (n < 1 or A[0] != 1):
      return -1
   string += str(character)
   character = chr(ord(character) + 1)
   for i in range(1, n):
      difference = A[i] - A[i - 1]
      if (difference > 1 or difference < 0 or A[i] > 26):
         return -1
      elif (difference == 0):
         string += 'a'
      else:
         string += character
         character = chr(ord(character) + 1)
return string

A = [1, 1, 2, 3, 4]
print(get_smallest_string(A))

Input

[1, 1, 2, 3, 4]

Output

aabcd