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Optimize a dynamic programming solution

#1
10-06-2024, 03:30 AM
You often hit walls when your DP runs too slow for bigger inputs. I keep telling you to rethink the states you track right away. But you might cut down redundant calculations by storing only what matters next. And that shift saves time without much extra effort. Perhaps you test smaller cases first to spot the waste.

I see you struggling with memory piles in those tables. You should swap to rolling arrays instead of full grids. But I tried that once and it trimmed space by half almost instantly. And your code runs smoother when you reuse the same spots. Maybe you experiment with one dimension at a time to see gains. Then you notice patterns where old values get dropped early.

You can prune states that never lead anywhere useful. I always start by listing what each step really needs from prior ones. But you avoid full recomputes by updating just the active parts. And that keeps things fast even on larger sets. Perhaps you merge similar states into one slot. Or you check if some transitions repeat and skip them. Now you build up from the base without extra layers.

I think you benefit from bottom up builds over recursive calls. You lose stack overhead that way and gain speed. But your loops must hit only necessary indices each pass. And partial fills help when you know limits ahead. Maybe you reorder computations to hit cache better. Then results pop out quicker without all the fluff.

You find space savings by dropping dimensions one by one. I often replace two arrays with a single one that flips back and forth. But you watch for overlaps that break correctness. And testing small runs confirms it works fine. Perhaps you compress states further if bits allow it. Or you drop unused variables mid process. Now the whole thing fits in tighter memory.

I notice you gain from early stops when values stabilize. You skip loops once maxes are reached in subproblems. But careful checks prevent missing edge paths. And that tweak cuts time on average cases. Maybe you add simple bounds to avoid full scans. Then overall performance jumps without fancy tricks.

You handle overlapping subproblems better by tracking only frontiers. I shift focus to what changes between steps. But you verify no info gets lost in the cut. And experiments show big wins on repeated queries. Perhaps you batch updates to reduce access counts. Or you reuse buffers across multiple runs. Now your solution scales without blowing up resources.

You tweak the recurrence itself sometimes for fewer operations. I look for ways to combine steps into single passes. But you must keep the logic sound or answers twist wrong. And small changes here multiply across all sizes. Maybe you precompute constants that repeat often. Then loops shorten naturally in practice.

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ron74
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Optimize a dynamic programming solution - by ron74 - 10-06-2024, 03:30 AM

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Optimize a dynamic programming solution

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