What is the best way to create a binary trie with nodes that can process 4 bits simultaneously?

I am currently exploring ways to organize a binary trie in a more streamlined manner. Typically, a binary trie consists of nodes for each slot in a binary number, branching left on 0 and right on 1. Is it possible to read 4 bits at a time instead of just 1? One idea is to have 16 slots in each trie node, but visualizing this concept proves to be challenging; how would the process of reading binary input like 10101010 4-bits at a time actually work with this approach? What would the structure look like?

[  left    , right   ,   left,  right  ,  left,   right   ...]
  (goto2)    (goto5)   (goto7)  (goto8)   (goto9), (goto10)

Alternatively, could there be an algorithm that cross-checks 4 bits against 16 slots in an array efficiently?

While it appears that 4 bits can fit into 16 slots logically, developing an algorithm to interpret these connections without having to manually visualize each step remains a challenge. There must be some equation or method to simplify this process.

Answer №1

What you are talking about is a data structure known as a radix trie implemented using base 16 encoding. By extracting 4 bits from the key provided, you can obtain a number ranging from 0 to 15 (inclusive). This number serves as an index for accessing nodes within the trie:

struct Node {
    Node *children[16];
    Value value;
};

Value *search(const char *key, int nkey, Node *node) {
    int i = 0;
    while(i < 2*nkey && node) {
        int digit = (key[i/2] >> (i%2==0 ? 0 : 4)) & 0xf;
        node = node->children[digit];
        ++i;
    }
    return node ? &node->value : nullptr;
}

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