关于将对象数组（array of objects）拆分至最少固定容量分桶（buckets）的优化方案咨询

Hey there! Totally get where you're coming from—self-taught admins hacking things together out of necessity deal with so many practical, messy problems that formal CS classes often rebrand into abstract jargon first. Let's untangle this "pretzel in your head" together.

First off, you're describing the Bin Packing Problem—a classic combinatorial optimization problem that's actually way trickier than it sounds (so don't beat yourself up over it!). It's classified as NP-hard, which means there's no known fast (polynomial-time) algorithm that guarantees an optimal solution for large datasets (unless one of the biggest unsolved problems in CS gets answered). But that's okay—for real-world use cases, we use "good enough" heuristic algorithms that are fast and get results very close to the optimal minimum number of buckets.

Let's break down what you've already tried, and how those fit into standard approaches, plus some next steps:

What You've Already Built (And What They're Called) #

You're already using common heuristic approaches without even knowing it:

• Round-Robin with Descending Sort: Your first method (sort biggest to smallest, then cycle through buckets) is a simplified take on load balancing. It's super easy to code and fast, but it often leaves wasted space in buckets because it doesn't check if an item could fit into an existing partially filled bucket instead of cycling to the next one.
• First Fit (FF): Your second method—fill a bucket until it's full, then check existing buckets for space before making a new one—is exactly the First Fit algorithm. If you add a pre-sort step (descending order), this becomes First Fit Decreasing (FFD), which is one of the most widely used heuristics for this problem. FFD usually gets within ~2% of the optimal solution, which is great for real-world tasks.

Better Heuristics to Explore (High-Level) #

If you want to tweak your approach for better bucket utilization, here are two popular alternatives:

• Best Fit (BF): Instead of picking the first bucket that can fit the item, pick the bucket with the smallest remaining capacity that can still hold the item. This minimizes wasted space by "filling in the gaps" as much as possible. Again, sorting descending first turns this into Best Fit Decreasing (BFD), which often outperforms FFD slightly (but with a tiny bit more computation).
• Worst Fit (WF): The opposite of Best Fit—pick the bucket with the largest remaining capacity to place the item. This is meant to keep larger gaps available for future big items, but in practice, it usually doesn't perform as well as FFD/BFD.

For Small Datasets (If You Need Absolute Optimal) #

If you're working with a small number of items (like hundreds instead of thousands), you can use exact methods to get the true minimum number of buckets:

• Dynamic Programming: Define a state like dp[i][j] = minimum buckets needed to pack the first i items with a total remaining capacity of j. This works for small datasets but becomes impossible for large ones because the state space explodes.
• Branch and Bound: This uses a "smart search" approach—you start by calculating the theoretical minimum number of buckets (total sum of values divided by bucket capacity, rounded up). As you explore possible bucket combinations, you discard any paths where the number of buckets already exceeds this theoretical minimum, cutting down on unnecessary computation.

Practical Implementation Tips #

For your use case (like 100k items), stick with FFD or BFD—they're fast, easy to code, and more than good enough:

1. Sort first: Always sort your items in descending order of their numerical value. This is the single biggest factor in improving bucket utilization.
2. Optimize bucket lookup: If you're dealing with tons of buckets, looping through every single one to find a fit can get slow. For FFD, you can keep buckets in a list and stop at the first valid one. For BFD, you can use a priority queue (min-heap) that keeps track of bucket remaining capacities—this lets you quickly grab the smallest valid bucket without looping through all of them.

You're not stupid for struggling with this—this is a problem that stumps even seasoned CS folks when they first encounter it. The key is that for real-world tasks, you don't need the perfect solution—you just need one that works efficiently and doesn't waste too many buckets.

备注：内容来源于stack exchange，提问作者thisismyname