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POIncrementing values in a search tree after insertion of a key-value pair
 

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  1. POIncrementing values in a search tree after insertion of a key-value pair
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    <p>I'm working on a programming problem and am running into a roadblock. I'm trying to come up with a data structure to map an arbitrary integer to another integer. You may be inclined to say "Hash Table!" or "Search Tree!", and I have in fact thought of these (and even tried a dirty implementation). But, there is a catch!</p> <p>Every time I insert or remove a value from the mapping, I want to also increment/decrement (by one or some arbitrary offset) all values greater than or equal to the inserted/removed value. </p> <p>Here's an example.</p> <p>Say I have two lists of integers that I will use for my keys and values in this map:</p> <pre><code>Keys: (1, 6, 18, 21, 24) Vals: (2, 1, 3, 0, 4) </code></pre> <p>Now if I add a key-value pair (7, 1), I want to increment all values greater than or equal to 1 resulting in this: </p> <pre><code>Keys: (1, 6, 7, 18, 21, 24) Vals: (3, 2, 1, 4, 0, 5) </code></pre> <p>And subsequently if I delete the key-value pair (21, 0), this is the result:</p> <pre><code>Keys: (1, 6, 7, 18, 24) Vals: (2, 1, 0, 3, 4) </code></pre> <p>This is rather trivial to do with a couple of lists/arrays and some processing after each insertion/deletion (i.e., going through the values and changing them one-by-one). </p> <p>But, I'm looking for a way to do it more efficiently, perhaps without having to go through the entire list of values and increment/decrementing them. Perhaps by even delaying the increment/decrement until a value (that should have been incremented/decremented) has been requested. </p> <p>Any thoughts? </p>
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