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POOptimally reordering cards in a wallet?
 

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    <p>I was out buying groceries the other day and needed to search through my wallet to find my credit card, my customer rewards (loyalty) card, and my photo ID. My wallet has dozens of other cards in it (work ID, other credit cards, etc.), so it took me a while to find everything.</p> <p>My wallet has six slots in it where I can put cards, with only the first card in each slot initially visible at any one time. If I want to find a specific card, I have to remember which slot it's in, then look at all the cards in that slot one at a time to find it. The closer it is to the front of a slot, the easier it is to find it.</p> <p>It occurred to me that this is pretty much a data structures question. Suppose that you have a data structure consisting of k linked lists, each of which can store an arbitrary number of elements. You want to distribute elements into the linked lists in a way that minimizes looking up. You can use whatever system you want for distributing elements into the different lists, and can reorder lists whenever you'd like. Given this setup, is there an optimal way to order the lists, under any of the assumptions:</p> <ol> <li>You are given the probabilities of accessing each element in advance and accesses are independent, or</li> <li>You have no knowledge in advance what elements will be accessed when?</li> </ol> <p>The informal system I use in my wallet is to "hash" cards into different slots based on use case (IDs, credit cards, loyalty cards, etc.), then keep elements within each slot roughly sorted by access frequency. However, maybe there's a better way to do this (for example, storing the k most frequently-used elements at the front of each slot regardless of their use case).</p> <p>Is there a known system for solving this problem? Is this a well-known problem in data structures? If so, what's the optimal solution?</p> <p>(In case this doesn't seem programming-related: I could imagine an application in which the user has several drop-down lists of commonly-used items, and wants to keep those items ordered in a way that minimizes the time required to find a particular item.)</p>
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    1. COSearching through a list to find a specific item is an O(n) operation - which is about as optimal as it gets. Dividing it into k list (providing you can know which list to look in) makes it O(n)/k which is insignificant for n>>k. Putting more frequently accessed items at the front of the list effectively reduces n.
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    2. CO@Dale- While that's true, you could imagine some sort of splay-tree like algorithm that gives good *amortized* performance even if individual lookups are slow. You could also design a data structure that makes high-priority elements accessible very quickly by making sure they're not too deep in the linked lists. The fact that you can't do better than O(n / k) in the worst-case doesn't necessarily mean that it's the best that you can do for all access patterns.
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    3. CO@templatetypedef- Sure, however, you have to work out if the overhead of maintaining the list is less than the saving.
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