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Asked: 2026-06-16T01:21:14+00:00

I’ve implemented my own AVL tree and I’m using it as a dictionary. I’m

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I’ve implemented my own AVL tree and I’m using it as a dictionary. I’m wondering, what would be the fastest way to count all the words that starts with some string.

eg:

string prefix = "fa";

enter image description here

output: 4

I’ve got it working in O(n) however, I’ve heard it can be done much faster.
I can of course hold in nodes additional information, like nodes that are below and other things like that.

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1 Answer

  1. Editorial Team

    If you want to reduce the memory footprint as much as possible while keeping the same asymptotic time bounds, you can suffice with one integer per node and still achieve O(log n) time (assuming constant-time key comparison).

    Store with each node the size of its subtree. This can be easily updated during tree modifications.

    To find the number of keys with a given range:

    • Find the top element in this range. That is, the unique node that is in the range but none of its ancestors is. Call the element “top”.
    • If no such element exists, return 0
    • Initialise sum = 1 (representing the top).
    • Find the start of the range in the left subtree of “top”:
      • If you descend left from a node, add the size of its entire right subtree to the sum, and add one.
      • If you descend right, add nothing.
    • Find the end of the range in the right subtree of “top”:
      • If you descend right from a node, add the size of its entire left subtree to the sum, and add one.
      • If you descend left, add nothing.
    • return the sum.

    The range for a given prefix contains all elements that have the prefix. It is important to note that the set of strings with a given prefix is consecutive w.r.t. its sorting order – that is, it’s indeed a range.

    The start of a prefix range is the position just before the prefix itself.

    The end of a prefix range is the position just before the lexicographically first disjoint prefix after this one (FA=>FB; FZ=>GA when only A-Z are in the alphabet).

    Unicode simplifies this by introducing a ‘top’ character that may not actually occur in a text, and compares above all other characters. That is, end = prefix + "\uFFFF".

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