String Sorting

Keywords and Synonyms

Sorting of multi-dimensional keys; Vector sorting    

Problem Definition

The problem is to sort a set of strings into lexicographical order. More formally: A string over an alphabet Σ is a finite sequence ${ x_1 x_2 x_3 \dots x_k }$ where ${ x_i \in \Sigma }$ for ${ i = 1,\dots,k }$. The x _i 's are called the characters of the string, and k is the length of the string. If the alphabet Σ is ordered, the lexicographical order on the set of strings over Σ is defined by declaring a string ${ x = x_1 x_2 x_3 \dots x_k }$ smaller than a string ${ y = y_1 y_2 y_3 \dots y_l }$ if either there exists a ${ j \ge 1 }$ such that ${ x_i = y_i }$ for ${ 1 \le i < j }$ and ${ x_j < y_j }$, or if ${ k < l }$ and ${ x_i = y_i }$ for ${ 1 \le i \le k }$. Given a set S of strings over some ordered alphabet, the problem is to sort S according to lexicographical order.

The input to the string sorting problem consists of an array of pointers...