How do you optimize the space and time complexity of a trie using compression or pruning techniques?

1 What is compression?

Compression is a technique that reduces the number of nodes in a trie by merging nodes that have only one child. For example, if you have a trie that stores the words "dog", "dot", and "doe", you can compress it by removing the nodes that represent "d" and "o", and replacing them with a single node that represents "do". This way, you save two nodes and two edges, and you still preserve the information of the trie.

2 What is pruning?

Pruning is a technique that removes nodes that are not needed for the trie functionality. For example, if you have a trie that stores the words "apple", "apply", and "app", you can prune it by removing the nodes that represent "apple" and "apply", and marking the node that represents "app" as a terminal node. This way, you save four nodes and four edges, and you still maintain the ability to search and autocomplete the words.

3 How to compress a trie?

To compress a trie, you need to traverse it in a bottom-up manner, starting from the leaf nodes and moving up to the root. For each node, you need to check if it has only one child, and if so, you need to merge it with its child by concatenating their labels and deleting the child node. You need to repeat this process until you reach the root or a node that has more than one child.

4 How to prune a trie?

To prune a trie, you need to traverse it in a top-down manner, starting from the root and moving down to the leaf nodes. For each node, you need to check if it is a terminal node, and if so, you need to mark it as such and delete all its descendants. You need to repeat this process until you reach the leaf nodes or a node that is not a terminal node.

5 What are the benefits of compression and pruning?

Compression and pruning can improve the space and time complexity of a trie by reducing the number of nodes and edges. This means that you need less memory to store the trie, and less time to search, sort, or autocomplete the strings. Compression and pruning can also make the trie more compact and readable, which can help with debugging and visualization.

6 What are the drawbacks of compression and pruning?

Compression and pruning can also have some disadvantages, depending on the use case and the data set. Compression can make the trie less flexible and adaptable, as it can be harder to insert or delete strings without affecting the existing structure. Pruning can make the trie less comprehensive and informative, as it can lose some information about the frequency or diversity of the strings. Compression and pruning can also introduce some overhead in terms of computation and maintenance, as they require additional operations and checks on the trie.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?