Time Complexity: O(N), where N is the length of the word or prefix being processed. Each method (inserting a word, counting words equal to a given word, counting words starting with a prefix, and erasing a word) involves traversing the Trie for each character of the input word or prefix. Thus, the time complexity is linear relative to the length of the word or prefix being processed.

Space Complexity: O(N), where N is the total number of characters across all words inserted into the Trie. The space complexity depends on the number of unique words added to the Trie and the average length of these words.