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Suffix Array: Introduction
What is a Suffix Array?
A suffix array is a data structure that provides a sorted array of all suffixes of a given string. It is used in various applications such as pattern matching, data compression, and bioinformatics.
Why Use Suffix Arrays?
Suffix arrays offer a space-efficient alternative to suffix trees while maintaining the ability to perform efficient pattern matching and other operations.
Example 1: Basic Suffix Array Construction
Constructing a Suffix Array
Given the string "banana", the suffixes are ["banana", "anana", "nana", "ana", "na", "a"]. The sorted suffixes are ["a", "ana", "anana", "banana", "na", "nana"]. The suffix array is [5, 3, 1, 0, 4, 2].
String text = "banana";
int[] suffixArray = buildSuffixArray(text);
System.out.println(Arrays.toString(suffixArray)); // Output: [5, 3, 1, 0, 4, 2]
Example 2: Pattern Matching with Suffix Arrays
Using Suffix Arrays for Pattern Matching
To find if a pattern exists in a text, use binary search on the suffix array. For example, to find "ana" in "banana", check the sorted suffixes using the suffix array.
boolean patternExists = patternMatching("banana", "ana", suffixArray);
System.out.println(patternExists); // Output: true
Example 3: Longest Repeated Substring
Finding the Longest Repeated Substring
Using the suffix array and the longest common prefix (LCP) array, identify the longest repeated substring in a string.
String longestRepeatedSubstring = findLongestRepeatedSubstring("banana");
System.out.println(longestRepeatedSubstring); // Output: "ana"
Example 4: Suffix Array for Lexicographical Order
Sorting Substrings Lexicographically
Use the suffix array to sort all substrings of a string lexicographically. This is useful in problems involving lexicographical order.
List sortedSubstrings = getSortedSubstrings("banana");
System.out.println(sortedSubstrings); // Output: ["a", "ana", "anana", "banana", "na", "nana"]
Example 5: Space Optimization with Suffix Arrays
Efficient Space Usage
Suffix arrays use O(n) space, which is more efficient than the O(n log n) space used by suffix trees. This makes them suitable for large-scale data processing.
int[] optimizedSuffixArray = buildOptimizedSuffixArray("large_text_input");
System.out.println(Arrays.toString(optimizedSuffixArray));
