What is the best way to implement a trie?

1 Basic structure

A trie consists of a root node that has zero or more child nodes, each representing a character. The root node does not store any character itself, but acts as a placeholder. Each node can also have a boolean flag that indicates whether it marks the end of a valid string or not. For example, the trie below stores the strings "cat", "car", and "cart".

root
/   c   ...
/  a   ...
/  t*  r*
    /
   t*        

The asterisk (*) denotes that the node is the end of a string.

2 Implementation in Python

One of the simplest ways to implement a trie in Python is to use a dictionary to store the child nodes and the boolean flag. Each node is a dictionary that maps characters to other nodes, and has a special key "_end" that stores the flag. For example, the root node of the previous trie would be:

root = {
  "c": {
    "a": {
      "t": {"_end": True},
      "r": {
        "_end": True,
        "t": {"_end": True}
      }
    }
  }
}        

To insert a string into the trie, you can iterate over its characters and create or update the corresponding nodes. To search for a string or a prefix, you can also iterate over its characters and check if the nodes exist.

3 Implementation in Java

In Java, you can implement a trie using a class that represents a node, with an array of child nodes and a boolean flag as fields. Each node has a fixed size array of 26 child nodes, one for each letter of the alphabet. For example, the root node of the previous trie would be:

class Node {
  Node[] children;
  boolean isEnd;
  public Node() {
    children = new Node[26];
    isEnd = false;
  }
}
Node root = new Node();
root.children[2] = new Node(); // c
root.children[2].children[0] = new Node(); // a
root.children[2].children[0].children[19] = new Node(); // t
root.children[2].children[0].children[19].isEnd = true;
root.children[2].children[0].children[17] = new Node(); // r
root.children[2].children[0].children[17].isEnd = true;
root.children[2].children[0].children[17].children[19] = new Node(); // t
root.children[2].children[0].children[17].children[19].isEnd = true;        

To insert a string into the trie, you can use a loop or a recursion to traverse the array and create or update the nodes. To search for a string or a prefix, you can also use a loop or a recursion to traverse the array and check if the nodes exist.

4 Implementation in C++

In C++, you can implement a trie using a struct that represents a node, with a map of child nodes and a boolean flag as members. Each node has a map that associates characters to other nodes, and a flag that indicates if it is the end of a string. For example, the root node of the previous trie would be:

struct Node {
  map<char, Node*> children;
  bool isEnd;
  Node() {
    isEnd = false;
  }
};
Node* root = new Node();
root->children['c'] = new Node();
root->children['c']->children['a'] = new Node();
root->children['c']->children['a']->children['t'] = new Node();
root->children['c']->children['a']->children['t']->isEnd = true;
root->children['c']->children['a']->children['r'] = new Node();
root->children['c']->children['a']->children['r']->isEnd = true;
root->children['c']->children['a']->children['r']->children['t'] = new Node();
root->children['c']->children['a']->children['r']->children['t']->isEnd = true;        

To insert a string into the trie, you can use a pointer and a loop to traverse the map and create or update the nodes. To search for a string or a prefix, you can also use a pointer and a loop to traverse the map and check if the nodes exist.

5 Advantages and disadvantages

When deciding whether to implement a trie, you should consider the advantages and disadvantages. One of the benefits is fast and easy lookup of strings and prefixes, since you only need to follow the path of the characters. Additionally, trie is space-efficient for storing many strings that share common prefixes, as it avoids duplication. It is also flexible for adding and deleting strings as you only need to modify the nodes along the path. However, trie is memory-intensive for storing many strings that have few or no common prefixes, as it requires creating many nodes. Furthermore, some operations such as sorting or finding the longest common prefix are complex to implement with a trie, since you need to traverse the whole structure. Lastly, language-dependence is an issue when choosing the best way to store the child nodes, since different languages have different data types and features.

6 Tips and tricks

To improve your trie implementation, you can use some tips and tricks that can help optimize your code and performance. For instance, a hash table instead of an array or a map for storing the child nodes can reduce the space and time complexity. Additionally, a bit vector instead of a boolean flag for marking the end of a string can save some memory and allow more information to be stored. A compressed trie rather than a regular trie can merge the nodes that have one child and reduce the height of the trie. Furthermore, a ternary search tree instead of a trie can balance the space and time trade-off by using three pointers (left, middle, and right) for each node.