Check if the given Trie contains words starting from every alphabet

Given a Trie, the task is to check if it contains words starting from every alphabet from [a – z].

Examples:

Input: keys[] = {“element”, “fog”, “great”, “hi”,
“ok”, “ios”, “parrot”, “quiz”, “kim”, “mango”, “nature”, “apple”,
“ball”, “cat”, “dog”, “lime”, “ruby”, “shine”, “tinkter”,
“ultra”, “volly”, “wow”, “xerox”, “yak”, “zenon”, “joke”}
Output: Yes

Input: keys[] = {“geeks”, “for”, “geeks”}
Output: No

Approach: We just need to focus on the root node of the given Trie and no need to traverse other nodes. We simply check if Trie has all its child pointers pointing to valid nodes i.e. there are words starting from every character of the alphabet.

Below is the implementation of the above approach:

// C++ implementation of the approach
#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 NULL)
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;
}

// Function to check if Trie contains words
// starting from all the alphabets
bool containsAll(TrieNode* root)
{
    // We check if root node has all childs
    // if None of them is NULL then we return true
    for (int i = 0; i < 26; i++) {

        // If there is no word in the trie starting
        // from the current alphabet
        if (root->children[i] == NULL)
            return false;
    }
    return true;
}

// Driver code
int main()
{

    string keys[] = { "element", "fog", "great", "hi", "ok",
                      "ios", "parrot", "quiz", "kim", "mango", "nature",
                      "apple", "ball", "cat", "dog", "lime", "ruby",
                      "shine", "tinkter", "ultra", "volly", "wow",
                      "xerox", "yak", "zenon", "joke" };
    int n = sizeof(keys) / sizeof(keys[0]);

    // Create the Trie
    struct TrieNode* root = getNode();
    for (int i = 0; i < n; i++)
        insert(root, keys[i]);

    // If trie contains words starting
    // from every alphabet
    if (containsAll(root))
        cout << "Yes";
    else
        cout << "No";

    return 0;
}

Output:

Yes