[Verse 1] Started with an array, numbers in a line Need the longest sequence that's climbing all the time Not consecutive elements, just increasing order Dynamic programming gonna help us cross that border Break it down to subproblems, that's the key insight Every element could be the end of something right Build up from the bottom, let the patterns emerge Optimal substructure, watch the solution converge [Chorus] LIS, LIS, longest increasing subsequence DP table holding all the evidence N squared time, but the logic's so clean Memoize the max length, build the optimal scene LIS, LIS, from left to right we go Each position stores the best that we know [Verse 2] Initialize the table, every cell gets one Single elements count, that's where we begun For each position, look at everything before If it's smaller than current, we can build some more Take the maximum length, add one to the count That's the longest sequence with current as amount Fill the table completely, left to right we scan N log N exists too, but let's master this plan [Chorus] LIS, LIS, longest increasing subsequence DP table holding all the evidence N squared time, but the logic's so clean Memoize the max length, build the optimal scene LIS, LIS, from left to right we go Each position stores the best that we know [Bridge] Binary search optimization when you need that speed Patience sorting concept, that's the advanced feed But the classic DP version teaches intuition State transitions clear, mathematical precision Applications everywhere, from biology to stocks Scheduling algorithms, building stronger blocks [Verse 3] Reconstruction phase if you need the actual path Keep parent pointers, do the backtracking math Start from maximum position, trace it to the source Print the subsequence, show the optimal course Overlapping subproblems solved just once and stored Bottom-up approach, efficiency restored This is how we conquer optimization games Dynamic programming setting algorithmic flames [Chorus] LIS, LIS, longest increasing subsequence DP table holding all the evidence N squared time, but the logic's so clean Memoize the max length, build the optimal scene LIS, LIS, from left to right we go Each position stores the best that we know [Outro] From simple recurrence to the final solution LIS algorithm, computational evolution Master this pattern, you'll see it everywhere Dynamic programming showing how much we care
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