Trie | (Delete)

In the previous post on trie we have described how to insert and search a node in trie. Here is an algorithm how to delete a node from trie.
During delete operation we delete the key in bottom up manner using recursion. The following are possible conditions when deleting key from trie, 

1. Key may not be there in trie. Delete operation should not modify trie.
2. Key present as unique key (no part of key contains another key (prefix), nor the key itself is prefix of another key in trie). Delete all the nodes.
3. Key is prefix key of another long key in trie. Unmark the leaf node.
4. Key present in trie, having atleast one other key as prefix key. Delete nodes from end of key until first leaf node of longest prefix key.

The below code presents algorithm to implement above conditions. 

C++

// C++ implementation of delete
// operations on Trie
#include <bits/stdc++.h>
using namespace std;

const int ALPHABET_SIZE = 26;

// trie node
struct TrieNode {
    struct TrieNode* children[ALPHABET_SIZE];

    // isEndOfWord is true if the node represents
    // end of a word
    bool isEndOfWord;
};

// Returns new trie node (initialized to NULLs)
struct TrieNode* getNode(void)
{
    struct TrieNode* pNode = new TrieNode;

    pNode->isEndOfWord = false;

    for (int i = 0; i < ALPHABET_SIZE; i++)
        pNode->children[i] = NULL;

    return pNode;
}

// If not present, inserts key into trie
// If the key is prefix of trie node, just
// marks leaf node
void insert(struct TrieNode* root, string key)
{
    struct TrieNode* pCrawl = root;

    for (int i = 0; i < key.length(); i++) {
        int index = key[i] - 'a';
        if (!pCrawl->children[index])
            pCrawl->children[index] = getNode();

        pCrawl = pCrawl->children[index];
    }

    // mark last node as leaf
    pCrawl->isEndOfWord = true;
}

// Returns true if key presents in trie, else
// false
bool search(struct TrieNode* root, string key)
{
    struct TrieNode* pCrawl = root;

    for (int i = 0; i < key.length(); i++) {
        int index = key[i] - 'a';
        if (!pCrawl->children[index])
            return false;

        pCrawl = pCrawl->children[index];
    }

    return (pCrawl != NULL && pCrawl->isEndOfWord);
}

// Returns true if root has no children, else false
bool isEmpty(TrieNode* root)
{
    for (int i = 0; i < ALPHABET_SIZE; i++)
        if (root->children[i])
            return false;
    return true;
}

// Recursive function to delete a key from given Trie
TrieNode* remove(TrieNode* root, string key, int depth = 0)
{
    // If tree is empty
    if (!root)
        return NULL;

    // If last character of key is being processed
    if (depth == key.size()) {

        // This node is no more end of word after
        // removal of given key
        if (root->isEndOfWord)
            root->isEndOfWord = false;

        // If given is not prefix of any other word
        if (isEmpty(root)) {
            delete (root);
            root = NULL;
        }

        return root;
    }

    // If not last character, recur for the child
    // obtained using ASCII value
    int index = key[depth] - 'a';
    root->children[index] =
          remove(root->children[index], key, depth + 1);

    // If root does not have any child (its only child got
    // deleted), and it is not end of another word.
    if (isEmpty(root) && root->isEndOfWord == false) {
        delete (root);
        root = NULL;
    }

    return root;
}

// Driver
int main()
{
    // Input keys (use only 'a' through 'z'
    // and lower case)
    string keys[] = { "the", "a", "there",
                      "answer", "any", "by",
                      "bye", "their", "hero", "heroplane" };
    int n = sizeof(keys) / sizeof(keys[0]);

    struct TrieNode* root = getNode();

    // Construct trie
    for (int i = 0; i < n; i++)
        insert(root, keys[i]);

    // Search for different keys
    search(root, "the") ? cout << "Yes\n" : cout << "No\n";
    search(root, "these") ? cout << "Yes\n" : cout << "No\n";

    remove(root, "heroplane");
    search(root, "hero") ? cout << "Yes\n" : cout << "No\n";
    return 0;
}

Java

// Java implementation of delete
// operations on Trie
import java.util.*;

public class GFG{

    static int ALPHABET_SIZE = 26;

    // trie node
    static class TrieNode {
        TrieNode children[] = new TrieNode[ALPHABET_SIZE];

        // isEndOfWord is true if the node represents
        // end of a word
        boolean isEndOfWord;
    }


    // If not present, inserts key into trie
    // If the key is prefix of trie node, just
    // marks leaf node
    static void insert(TrieNode root, String key)
    {
        TrieNode pCrawl = root;

        for (int i = 0; i < key.length(); i++) {
            int index = key.charAt(i) - 'a';
            if (pCrawl.children[index] == null)
                pCrawl.children[index] = new TrieNode();

            pCrawl = pCrawl.children[index];
        }

        // mark last node as leaf
        pCrawl.isEndOfWord = true;
    }

    // Returns true if key presents in trie, else
    // false
    static boolean search(TrieNode root, String key)
    {
        TrieNode pCrawl = root;

        for (int i = 0; i < key.length(); i++) {
            int index = key.charAt(i) - 'a';
            if (pCrawl.children[index] == null)
                return false;

            pCrawl = pCrawl.children[index];
        }

        return (pCrawl != null && pCrawl.isEndOfWord);
    }

    // Returns true if root has no children, else false
    static boolean isEmpty(TrieNode root)
    {
        for (int i = 0; i < ALPHABET_SIZE; i++)
            if (root.children[i] != null)
                return false;
        return true;
    }

    // Recursive function to delete a key from given Trie
    static TrieNode remove(TrieNode root, String key, int depth)
    {
        // If tree is empty
        if (root == null)
            return null;

        // If last character of key is being processed
        if (depth == key.length()) {

            // This node is no more end of word after
            // removal of given key
            if (root.isEndOfWord)
                root.isEndOfWord = false;

            // If given is not prefix of any other word
            if (isEmpty(root)) {
                root = null;
            }

            return root;
        }

        // If not last character, recur for the child
        // obtained using ASCII value
        int index = key.charAt(depth) - 'a';
        root.children[index] =
            remove(root.children[index], key, depth + 1);

        // If root does not have any child (its only child got
        // deleted), and it is not end of another word.
        if (isEmpty(root) && root.isEndOfWord == false){
            root = null;
        }

        return root;
    }

    // Driver
    public static void main(String args[])
    {
        // Input keys (use only 'a' through 'z'
        // and lower case)
        String keys[] = { "the", "a", "there",
                        "answer", "any", "by",
                        "bye", "their", "hero", "heroplane" };
        int n = keys.length;

        TrieNode root = new TrieNode();

        // Construct trie
        for (int i = 0; i < n; i++)
            insert(root, keys[i]);

        // Search for different keys
        if(search(root, "the"))
            System.out.println("Yes");
        else
            System.out.println("No");

        if(search(root, "these"))
            System.out.println("Yes");
        else
            System.out.println("No");

        remove(root, "heroplane", 0);

        if(search(root, "hero"))
            System.out.println("Yes");
        else
            System.out.println("No");

    }
}

// This code is contributed by aditypande88.

Python3

class TrieNode:
    def __init__(self):
        self.children = [None] * 26
        self.isEndOfWord = False

def getNode():
    pNode = TrieNode()
    pNode.isEndOfWord = False
    return pNode

def insert(root, key):
    pCrawl = root
    for i in range(len(key)):
        index = ord(key[i]) - ord('a')
        if not pCrawl.children[index]:
            pCrawl.children[index] = getNode()
        pCrawl = pCrawl.children[index]
    pCrawl.isEndOfWord = True

def search(root, key):
    pCrawl = root
    for i in range(len(key)):
        index = ord(key[i]) - ord('a')
        if not pCrawl.children[index]:
            return False
        pCrawl = pCrawl.children[index]
    return pCrawl and pCrawl.isEndOfWord

def isEmpty(root):
    for i in range(26):
        if root.children[i]:
            return False
    return True

def remove(root, key, depth = 0):
    if not root:
        return None

    if depth == len(key):
        if root.isEndOfWord:
            root.isEndOfWord = False
        if isEmpty(root):
            del root
            root = None
        return root

    index = ord(key[depth]) - ord('a')
    root.children[index] = remove(root.children[index], key, depth + 1)

    if isEmpty(root) and not root.isEndOfWord:
        del root
        root = None
    return root

if __name__ == '__main__':
    keys = ["the", "a", "there", "answer", "any", "by", "bye", "their", "hero", "heroplane"]
    root = getNode()
    for i in range(len(keys)):
        insert(root, keys[i])
    if search(root, "the"):
        print("Yes")
    else:
        print("No")
    if search(root, "these"):
        print("Yes")
    else:
        print("No")
    root = remove(root, "heroplane")
    if search(root, "hero"):
        print("Yes")
    else:
        print("No")

C#

// C# implementation of delete
// operations on Trie
using System;

namespace GFG
{
    class TrieNode
    {
        // An array of children nodes.
        public TrieNode[] children = new TrieNode[26];

        // A flag to represent end of a word.
        public bool isEndOfWord;
    }

    class Program
    {
        static int ALPHABET_SIZE = 26;

        static void Insert(TrieNode root, string key)
        {
            // Start from root node.
            TrieNode pCrawl = root;

            for (int i = 0; i < key.Length; i++)
            {
                int index = key[i] - 'a';

                // Create a new node if the path doesn't exist.
                if (pCrawl.children[index] == null)
                    pCrawl.children[index] = new TrieNode();

                // Move to the next node.
                pCrawl = pCrawl.children[index];
            }

            // Mark the last node as the end of a word.
            pCrawl.isEndOfWord = true;
        }

        static bool Search(TrieNode root, string key)
        {
            // Start from the root node.
            TrieNode pCrawl = root;

            for (int i = 0; i < key.Length; i++)
            {
                int index = key[i] - 'a';

                // If the path doesn't exist, return false.
                if (pCrawl.children[index] == null)
                    return false;

                // Move to the next node.
                pCrawl = pCrawl.children[index];
            }

            // Return true if the last node represents the end of a word.
            return (pCrawl != null && pCrawl.isEndOfWord);
        }

        static bool IsEmpty(TrieNode root)
        {
            for (int i = 0; i < ALPHABET_SIZE; i++)
                if (root.children[i] != null)
                    return false;

            return true;
        }

        static TrieNode Remove(TrieNode root, string key, int depth)
        {
            // If tree is empty.
            if (root == null)
                return null;

            // If last character of key is being processed.
            if (depth == key.Length)
            {
                // This node is no more end of word after
                // removal of given key.
                if (root.isEndOfWord)
                    root.isEndOfWord = false;

                // If given key is not a prefix of any other word.
                if (IsEmpty(root))
                    root = null;

                return root;
            }

            // If not last character, recur for the child obtained by
            // indexing into the children array using the current character.
            int index = key[depth] - 'a';
            root.children[index] = Remove(root.children[index], key, depth + 1);

            // If root does not have any children (its only child got
            // deleted), and it is not the end of a word.
            if (IsEmpty(root) && !root.isEndOfWord)
                root = null;

            return root;
        }

        static void Main(string[] args)
        {
            // Test cases.
            string[] keys = { "the", "a", "there", "answer", "any",
                               "by", "bye", "their", "hero", "heroplane" };
            int n = keys.Length;

            // Construct the Trie.
            TrieNode root = new TrieNode();
            for (int i = 0; i < n; i++)
                Insert(root, keys[i]);

            // Test search function.

            if (Search(root, "the"))
                Console.WriteLine("Yes");
            else
                Console.WriteLine("No");

            if (Search(root, "these"))
                Console.WriteLine("Yes");
            else
                Console.WriteLine("No");

            Remove(root, "heroplane", 0);

            if (Search(root, "hero"))
                Console.WriteLine("Yes");
            else
                Console.WriteLine("No");

            Console.ReadLine();
        }
    }
}

Javascript

<script>
// Javascript implementation of delete
// operations on Trie

let ALPHABET_SIZE = 26;

// trie node
class TrieNode
{
    constructor()
    {
        this.children=new Array(ALPHABET_SIZE);
        this.isEndOfWord=false;
    }
}

// If not present, inserts key into trie
    // If the key is prefix of trie node, just
    // marks leaf node
function insert(root,key)
{
    let pCrawl = root;

        for (let i = 0; i < key.length; i++) {
            let index = key[i].charCodeAt(0) - 'a'.charCodeAt(0);
            if (pCrawl.children[index] == null)
                pCrawl.children[index] = new TrieNode();

            pCrawl = pCrawl.children[index];
        }

        // mark last node as leaf
        pCrawl.isEndOfWord = true;
}

// Returns true if key presents in trie, else
    // false
function search(root,key)
{
    let pCrawl = root;

        for (let i = 0; i < key.length; i++) {
            let index = key[i].charCodeAt(0) - 'a'.charCodeAt(0);
            if (pCrawl.children[index] == null)
                return false;

            pCrawl = pCrawl.children[index];
        }

        return (pCrawl != null && pCrawl.isEndOfWord);
}

// Returns true if root has no children, else false
function isEmpty(root)
{
    for (let i = 0; i < ALPHABET_SIZE; i++)
            if (root.children[i] != null)
                return false;
        return true;
}

// Recursive function to delete a key from given Trie
function remove(root,key,depth)
{
    // If tree is empty
        if (root == null)
            return null;

        // If last character of key is being processed
        if (depth == key.length) {

            // This node is no more end of word after
            // removal of given key
            if (root.isEndOfWord)
                root.isEndOfWord = false;

            // If given is not prefix of any other word
            if (isEmpty(root)) {
                root = null;
            }

            return root;
        }

        // If not last character, recur for the child
        // obtained using ASCII value
        let index = key[depth].charCodeAt(0) - 'a'.charCodeAt(0);
        root.children[index] =
            remove(root.children[index], key, depth + 1);

        // If root does not have any child (its only child got
        // deleted), and it is not end of another word.
        if (isEmpty(root) && root.isEndOfWord == false){
            root = null;
        }

        return root;
}

// Driver
// Input keys (use only 'a' through 'z'
// and lower case)
let keys = [ "the", "a", "there",
                 "answer", "any", "by",
                 "bye", "their", "hero", "heroplane" ];
let n = keys.length;

let root = new TrieNode();

// Construct trie
for (let i = 0; i < n; i++)
    insert(root, keys[i]);

// Search for different keys
if(search(root, "the"))
    document.write("Yes<br>");
else
    document.write("No<br>");

if(search(root, "these"))
    document.write("Yes<br>");
else
    document.write("No<br>");

remove(root, "heroplane", 0);

if(search(root, "hero"))
    document.write("Yes<br>");
else
    document.write("No<br>");


// This code is contributed by patel2127
</script>

Output:

Yes
No
Yes

Time Complexity: The time complexity of the deletion operation is O(n) where n is the key length.

Auxiliary Space: O(n*m), where n is the key length of the longest word and m is the total no of words.

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