[Verse 1] Got an array and I'm looking for the pattern Numbers climbing up, that's what really matters Not consecutive, just strictly increasing Find the longest chain, that's what I'm seeking Dynamic programming gonna solve this right Building up solutions from left to right Each position holds the best we've seen Longest sequence ending at that scene [Chorus] LIS, LIS, longest increasing subsequence Dynamic table, optimal reference Bottom up, we build the solution clean N squared time, but the logic's pristine LIS, LIS, find the maximum length Patience sorting gives us extra strength Remember the path, trace it back with care Longest climb is waiting for us there [Verse 2] Start with base case, every single stands alone Length of one at every position shown For each element, scan what came before If it's smaller, we can add one more Take the maximum from all valid picks That's the recurrence relation that clicks Fill the table left to right with grace Each cell holds the best case for that place [Chorus] LIS, LIS, longest increasing subsequence Dynamic table, optimal reference Bottom up, we build the solution clean N squared time, but the logic's pristine LIS, LIS, find the maximum length Patience sorting gives us extra strength Remember the path, trace it back with care Longest climb is waiting for us there [Bridge] Binary search can make it faster still N log N time if you've got the skill Active list of tails, replace with care Patience game strategy, winners everywhere But sometimes you need the actual sequence Not just length, but full coherence Parent pointers help you reconstruct The path that made your algorithm struck [Verse 3] Applications everywhere you look around Scheduling tasks where time constraints abound Version control and file comparisons too DNA sequencing, bioinformatics crew Box stacking problems, nested rectangles Investment planning, profit trajectles Any time you need the optimal chain LIS algorithm breaks the coding strain [Chorus] LIS, LIS, longest increasing subsequence Dynamic table, optimal reference Bottom up, we build the solution clean N squared time, but the logic's pristine LIS, LIS, find the maximum length Patience sorting gives us extra strength Remember the path, trace it back with care Longest climb is waiting for us there [Outro] From the simple to the optimized Every subsequence gets analyzed Build your table, trace your path LIS mastery, that's the aftermath
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