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Poosarla Sai Karthik
Tech guy with a busi...ย โขย 6m
Collapse Theory: Knapsack in a smarter way :) Just came across a fascinating idea that rethinks how we approach optimization, especially the classic Knapsack Problem. In short, youโre packing items with different weights and values into a limited space. The goal is to get maximum value without exceeding the limit. Traditionally, solving this takes O(nยฒ) time. Collapse Theory offers a new route. It uses the golden ratio (ฯ = 1.618โฆ) and Fibonacci sequences to assign a โcollapse scoreโ to each item: ฮถ(i) = 1 / |ฯ trace(i)|^0.5 That score measures how much complexity an item introduces. Instead of brute force combinations, it ranks items based on this entropy based score. Items are encoded using Zeckendorf representation, which is Fibonacci based. The payoff is that you get around 78.6 percent of the optimal value in O(n log n) time. And it works for bounded, unbounded, and multi dimensional knapsack problems. Whatโs deeper is the idea that complex systems collapse into simpler efficient forms. This pattern shows up in markets, neural networks, team dynamics, and even evolution. Collapse Theory doesnโt just speed things up, it aligns with how real systems behave. P.S. I saw this diversion coming from X.
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