GATE-CS-2004 Question 5

This is a programming problem that requires the implementation of a data structure known as a "suffix tree". The problem statement asks us to write a function that finds the longest repeated substring in a given string.

A suffix tree is a specialized data structure that is used to efficiently search for patterns in a given text. It represents all the suffixes of the given text as leaves of a tree, with the internal nodes representing common substrings. By traversing this tree, we can quickly locate all the occurrences of a given substring, and also find the longest repeated substring.

To solve this problem, we can first construct the suffix tree for the given string. This can be done efficiently using Ukkonen's algorithm, which has a time complexity of O(n). Once we have the suffix tree, we can traverse it in a depth-first manner to find the longest repeated substring.

Here's some sample code to illustrate the basic idea:

class SuffixTree:
    def __init__(self, text):
        self.root = {}
        self.text = text
        self.construct_tree()

    def construct_tree(self):
        # TODO: implement Ukkonen's algorithm to construct the suffix tree
        pass

    def find_longest_repeated_substring(self):
        # TODO: traverse the suffix tree to find the longest repeated substring
        pass

text = "banana"
suffix_tree = SuffixTree(text)
longest_repeated_substring = suffix_tree.find_longest_repeated_substring()
print(longest_repeated_substring)

In this code, we define a class called SuffixTree that represents the suffix tree for a given string. The construct_tree method is left empty for now, as it's an implementation detail that depends on Ukkonen's algorithm. The find_longest_repeated_substring method will be used to traverse the suffix tree and find the longest repeated substring in the text.

Note that this is just a skeleton code, and you'll need to fill in the details to make it work. Also, there are many different ways to implement a suffix tree, so you may need to adjust the code to fit your specific implementation.