Solution Explanation

This problem asks us to verify if a list of words is lexicographically sorted according to a given alien alphabet. The solution involves comparing pairs of consecutive words to check their lexicographical order based on the provided alphabet order.

Approach

1. Create a mapping: Construct a mapping from each character in the alien alphabet to its index. This allows for efficient comparison of characters based on their order in the alien alphabet. We can use a hash map (dictionary in Python) or an array for this purpose.

2. Iterate through word pairs: Iterate through consecutive pairs of words in the input list.

3. Compare characters: For each pair of words, compare their characters one by one, using the created mapping to determine the order.

4. Handle unequal length words: Special handling is needed when comparing words of unequal length. If a shorter word precedes a longer word and the shorter word is a prefix of the longer one (e.g., "apple" and "app"), then it violates the lexicographical order.

5. Return the result: If any pair of words violates the lexicographical order, return false. Otherwise, return true after checking all pairs.

Time and Space Complexity Analysis

Time Complexity: O(N*M), where N is the number of words and M is the maximum length of a word. This is because we iterate through each word once (O(N)) and potentially compare all characters in each word (O(M) in the worst case).

Space Complexity: O(1). The space used by the mapping is constant since the alphabet size is fixed (26 characters). We use a fixed amount of additional space for temporary variables irrespective of input size.

Code Explanation (Python)

The Python code implements the approach efficiently using a dictionary for mapping and a concise loop structure:

class Solution:
    def isAlienSorted(self, words: List[str], order: str) -> bool:
        m = {c: i for i, c in enumerate(order)}  # Create character mapping
        for i in range(len(words) - 1):  # Iterate through word pairs
            word1, word2 = words[i], words[i + 1]
            min_len = min(len(word1), len(word2))
            diff = False #Flag to indicate different char found
            for j in range(min_len): #Compare chars
                if m[word1[j]] < m[word2[j]]:
                    diff = True
                    break
                elif m[word1[j]] > m[word2[j]]:
                    return False #Lexicographical order violated
            if not diff and len(word1) > len(word2): #Handle unequal length
                return False
        return True #All pairs are lexicographically sorted

The other languages follow a similar approach with the data structures and control flow adjusted to their specific syntax. The core logic remains consistent across all implementations.