Reversing LCP Matrices with Java and Dynamic Programming

#100DaysOfLeetcode journey 🚀 Day 48/100 — Reversing LCP Matrices! Today’s Problem: 2573. Find the String with LCP (Hard) 🔹 The Goal: Given an $n \times n$ matrix representing the Longest Common Prefix (LCP) for every possible pair of suffixes, reconstruct the lexicographically smallest string that generates this exact matrix. 🔹 The Insight: This problem is a beautiful mix of Greedy Construction and Dynamic Programming. The "lexicographically smallest" constraint tells us exactly how to group indices. If lcp[i][j] > 0, indices $i$ and $j$ must share the same character. By processing indices from left to right and assigning the smallest available letter ('a' through 'z'), we build our candidate string. 🔹 The Logic: Grouping: We use the matrix to cluster indices that are forced to be identical. Transitivity Check: The matrix might be a "trap"—it could define relationships that are logically impossible. Verification: The only way to be sure is a full $O(n^2)$ verification. We use the DP relation LCP[i][j] = (s[i] == s[j]) ? LCP[i+1][j+1] + 1 : 0 to regenerate the matrix from our candidate string and compare it to the input. ✨ Achievement: Day 48! Tackled a Hard-level string reconstruction problem. It’s a fantastic exercise in understanding the internal properties of LCP arrays and how to use greedy logic to satisfy lexicographical requirements. 🔍 Steps followed: ✔ Greedy Character Assignment: Clustered indices based on positive LCP values. ✔ Alphabetical Minimization: Prioritized 'a' for the earliest possible unassigned groups. ✔ $O(n^2)$ Consistency Validation: Verified every single cell in the matrix using DP to ensure the matrix was valid. 🔧 Complexity Analysis: Time Complexity: $O(n^2)$ Space Complexity: $O(n)$ 48 days down! The intersection of string algorithms and mathematical consistency is where the most rewarding challenges live. 🛠️ #Java #DSA #LeetCode #CodingJourney #100DaysOfCode #SoftwareEngineer #InternshipBound #Programming #StringAlgorithms #DP #LCP #Day48

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