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    <p>+1 to the kind-of binary search idea. It's simple and gives good performance for 600000 buckets. That being said, if it's not good enough, you could create an array with MAX BUCKET VALUE - MIN BUCKET VALUE = RANGE elements, and have each element in this array reference the appropriate bucket. Then, you get a lookup in guaranteed constant [O(1)] time, at the cost of using a <em>huge</em> amount of memory.</p> <p>If A) the probability of accessing buckets is not uniform and B) you knew / could figure out how likely a given set of buckets were to be accessed, you could probably combine these two approaches to create a kind of cache. For example, say bucket {0, 3} were accessed all the time, as was {7, 13}, then you can create an array CACHE. . .</p> <p>int cache_low_value = 0;</p> <p>int cache_hi_value = 13;</p> <p>CACHE[0] = BUCKET_1</p> <p>CACHE[1] = BUCKET_1</p> <p>...</p> <p>CACHE[6] = BUCKET_2</p> <p>CACHE[7] = BUCKET_3</p> <p>CACHE[8] = BUCKET_3</p> <p>...</p> <p>CACHE[13] = BUCKET_3</p> <p>. . . which will allow you to find a bucket in O(1) time assuming the value you're trying to associate a value with a bucket is between cache_low_value and cache_hi_value (if Y &lt;= cache_hi_value &amp;&amp; Y >= cache_low_value; then BUCKET = CACHE[Y]). On the up side, this approach wouldn't use all the memory on your machine; on the downside, it'd add the equivalent of an additional operation or two to your bsearch in the case you can't find your number / bucket pair in the cache (since you had to check the cache in the first place).</p>
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    1. POStoring a bucket of numbers in an efficient data structure
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    1. UScubic1271
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