In this lecture, we will learn about the Trie<\/strong> data structure and solve algorithmic problems using the Trie.<\/p>\n The problem is as follows:<\/p>\n A Trie is a tree structure optimized for storing and searching strings. Each node in the Trie represents a path to the next character, making it useful for storing strings like phone numbers. To implement a Trie, we define a node class and design the Trie as a structure that includes node objects.<\/p>\n We implement the Next, we implement the Finally, we insert all phone numbers into the Trie for the given list of phone numbers and call The time complexity of this algorithm using a Trie is O(N * M), where N is the number of phone numbers and M is the maximum length of the phone numbers. In this lecture, we explored how to solve the problem of determining prefix relationships among a list of phone numbers using the Trie data structure. <\/body><\/p>\n","protected":false},"excerpt":{"rendered":"\nProblem:<\/strong> Phone Number List\nWrite a function to check if any phone number in a given list is a prefix of another phone number.\nIf any of the consecutive phone numbers have a prefix relationship, return false<\/strong>, \notherwise return true<\/strong>.\n\nInput:<\/strong>\n- An array of phone number strings, numbers. (1 \u2264 numbers.length \u2264 1000, 1 \u2264 numbers[i].length \u2264 30)\n\nOutput:<\/strong>\n- Return false<\/strong> if phone numbers have a prefix relationship, otherwise return true<\/strong>.\n<\/pre>\n
Problem Solving Process<\/h2>\n
1. Understanding the Trie Data Structure<\/h3>\n
\nA key feature of the Trie is that it can effectively save memory when there are strings that share a common prefix<\/strong>.<\/p>\n2. Implementing the Trie<\/h3>\n
class TrieNode {\n var children: [Character: TrieNode] = [:]\n var isEndOfNumber: Bool = false\n}<\/code><\/pre>\n3. Implementing the insert Method<\/h3>\n
insert<\/code> method to insert a new phone number into the Trie. This method adds each character of the phone number to the node, and sets isEndOfNumber<\/code> to true<\/code> at the end of the phone number.<\/p>\nclass Trie {\n var root: TrieNode\n \n init() {\n root = TrieNode()\n }\n \n func insert(_ number: String) {\n var currentNode = root\n for char in number {\n if currentNode.children[char] == nil {\n currentNode.children[char] = TrieNode()\n }\n currentNode = currentNode.children[char]!\n }\n currentNode.isEndOfNumber = true\n }\n}<\/code><\/pre>\n4. Implementing the checkPrefix Method<\/h3>\n
checkPrefix<\/code> method to check if a phone number in the list is a prefix of another phone number.
\nThis method traverses the Trie and checks if the current string is the end of a phone number before reaching the end of another phone number to determine the prefix relationship.<\/p>\nfunc checkPrefix(_ number: String) -> Bool {\n var currentNode = root\n for (index, char) in number.enumerated() {\n if let node = currentNode.children[char] {\n currentNode = node\n \/\/ If the current node is an ending phone number\n if currentNode.isEndOfNumber {\n return false\n }\n } else {\n break\n }\n \/\/ If there are nodes existing beyond the last character\n if index < number.count - 1 && currentNode.isEndOfNumber {\n return false\n }\n }\n return true\n}<\/code><\/pre>\n5. Overall Solution<\/h3>\n
checkPrefix<\/code> for each phone number to return the result.<\/p>\nfunc solution(_ numbers: [String]) -> Bool {\n let trie = Trie()\n \n for number in numbers {\n \/\/ Check if it is a prefix of an already registered phone number\n if !trie.checkPrefix(number) {\n return false\n }\n \/\/ Register the current phone number\n trie.insert(number)\n }\n return true\n}<\/code><\/pre>\n6. Time Complexity and Space Complexity<\/h3>\n
\nThe space complexity is O(N * M), representing the space needed to store the phone numbers.<\/p>\nConclusion<\/h2>\n
\nTries are a powerful tool for string processing and can be applied to various string-related problems.
\nEspecially when dealing with a large number of strings, considering space complexity allows for efficient design.<\/p>\n