Find the Suffix Array of given String with no repeating character

Given a string str of size N, the task is to find the suffix array of the given string.

Note: A suffix array is a sorted array of all suffixes of a given string.

Examples: 

Input: str = "prince"
Output: 4 5 2 3 0 1
Explanation: The suffixes are
0 prince                                    4 ce
1 rince      Sort the suffixes       5 e  
2 ince         ---------------->    2 ince  
3 nce          alphabetically        3 nce    
4 ce                                          0 prince
5 e                                           1 rince

Input: str = "abcd"
Output: 0 1 2 3

Approach: The methods of suffix array finding for any string are discussed here. In this article, the focus is on finding suffix array for strings with no repeating character. It is a simple implementation based problem. Follow the steps mentioned below to solve the problem:

• Count occurrence of each character.
• Find prefix sum of it.
• Find start array by start[0] = 0, start[i+1] = prefix[i] for all i > 0 .
• Find start array containing the index of the substring (suffix) with starting character of the respective column.

Follow the illustration below for better understanding.

Illustration:

Consider string "prince":
Given below is the suffix table 

char	a	b	c	d	e	f	g	h	i	j	k	l	m	n	o	p	q	r	s	t	u	v	w	x	y	z
count	0	0	1	0	1	0	0	0	1	0	0	0	0	1	0	1	0	1	0	0	0	0	0	0	0	0
prefix	0	0	1	1	2	2	2	2	3	3	3	3	3	4	4	5	5	6	6	6	6	6	6	6	6	6
start	0	0	0	1	1	2	2	2	2	3	3	3	3	3	4	4	5	5	6	6	6	6	6	6	6	6

For char 'r' start value is 5 . 
Implies substring (suffix) starting with char 'r' i.e. "rince" has rank 5 .
Rank is position in suffix array.  ( 1 "rince" ) implies 5th position in suffix array ), refer first table.
Similarly, start value of char 'n' is 3 . Implies ( 3 "nce" ) 3rd position in suffix array .

  Below is the implementation of the above approach

4 5 2 3 0 1 

Time Complexity: O(N)
Auxiliary Space: O(N)