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    <p>Hashtables (usually) perform search operations (look up) bounded within the complexity of <code>O(n)&lt;=T(n)&lt;=O(1)</code>, with an average case complexity of <code>O(1 + n/k)</code>; however, binary search trees, (BST's), perform search operations (lookup) bounded within the complexity of <code>O(n)&lt;=T(n)&lt;=O(log_2(n))</code>, with an average case complexity of <code>O(log_2(n))</code>. The implementation for each (and every) data structure should be known (by you), to understand the advantages, drawbacks, time complexity of operations, and code complexity. </p> <p>For example, the number of entries in a hashtable often have some fixed number of entries (some part of which may not be filled at all) with lists of collisions. Trees, on the other hand, usually have two pointers (references) per node, but this can be more if the implementation allows more than two child nodes per node, and this allows the tree to grow as nodes are added, but may not allow duplicates. (The default implementation of a Java TreeMap does not allow for duplicates)</p> <p>There are special cases to consider as well, for example, what if the number of elements in a particular data structure increases without bound or approaches the limit of an underlying part of the data structure? What about amortized operations that perform some rebalancing or cleanup operation? </p> <p>For example, in a hashtable, when the number of elements in the table become sufficiently large, and arbitrary number of collisions can occur. On the other hand, trees usually require come re-balancing procedure after an insertion (or deletion). </p> <p>So, if you have something like a cache (Ex. the number of elements in bounded, or size is known) then a hashtable is probably your best bet; however, if you have something more like a dictionary (Ex. populated once and looked up many times) then I'd use a tree. </p> <p>This is only in the general case, however, (no information was given). You have to understand process that happen how they happen to make the right choice in deciding which data structure to use. </p> <p>When I need a multi-map (ranged lookup) or sorted flattening of a collection, then it can't be a hashtable. </p>
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    1. USIvan
    1. USony
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    1. COI disagree with your example of using a tree for a structure that will be populated once and referenced many times. In this scenario you can create an appropriately sized Hashtable that has an O(1) lookup performance vs. O(log n) for a tree based structure. Furthermore you'll never use the linear operations of a `Hashtable`.
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      1. USChris Kerekes
    2. CO@ChrisKerekes, You can create hashtable that will suite perfectly and there will be no collisions that makes it O(m) and get that promised O(1). But you'll need to generate good hash function specific for you data (not always you can spend few empty extra-entries to change hash function behavior). Otherwise general hashtables is more suited for fast peace cache, I think.
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    3. COIs that `O(n)<=T(n)<=O(1)` correct?
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      1. USf.ardelian
 

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