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 −
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