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Finding unique substrings & LCS Problems

Finding unique substrings & LCS Problems This video explores algorithms for counting unique substrings and finding the longest common substring (LCS) using longest common prefix (LCP) arrays. It discusses the mathematical formula for calculating unique substrings and compares naive and efficient methods for LCS problems, illustrating the concepts with examples such as 'abracadabra' and 'ababaa'. Key Points: Counting Unique Substrings The presenter explains how to count unique substrings in a string using the longest common prefix (LCP) array. The formula derived indicates that the total number of substrings is given by n * (n + 1) / 2, from which the sum of the LCP array (representing duplicates) is subtracted to find the count of unique substrings. Longest Repeated Substring Algorithm The video introduces the longest repeated substring problem, discussing its naive method, which is inefficient (O(n²) time complexity). It then presents a more efficient algorithm that utilizes the LCP array to find the maximum length of the longest repeated substring. Real-World Examples Examples are used to illustrate both topics, with specific cases like the string 'abracadabra' being analyzed to demonstrate how to identify unique substrings and the longest repeated substring through their respective algorithms. Discussion on Algorithm Complexity The presenter highlights the inefficiencies of the naive approach to finding unique substrings and discusses the performance benefits of using an algorithm based on LCP arrays for both unique substrings and longest repeated substrings. Learning and Application The discussion touches on the presenter's studies in algorithms, including courses related to suffix arrays and practical applications in Python, suggesting a balance of theory and practical programming.