algoadvance

Problem Statement

You are given a 0-indexed string array words, where words[i] consists of lowercase English letters. In one operation, select any words[i] and remove it if words[i-1] is an anagram of words[i]. You must repeatedly perform this operation until no adjacent elements in the array are anagrams of each other. Return words after performing all operations.

Clarifying Questions

To ensure we understand the requirements correctly, let’s clarify a few points:

  1. What is an anagram?
    • Two strings are anagrams if they contain the same characters in the same frequency.
  2. What is the significance of words[i-1] and words[i]?
    • We only consider adjacent elements for being anagrams.
  3. What happens if multiple operations can be performed?
    • Operations are performed iteratively until no more adjacent anagrams exist.

Strategy

  1. Iterate through the list:
    • We will use a stack to keep track of the resultant array.
    • For each word in the list, push it onto the stack if the stack is empty or if it is not an anagram of the stack’s top element.
    • If it is an anagram, pop the last element from the stack (effectively removing an adjacent anagram pair).
  2. Helper Function to Determine Anagrams:
    • Create a helper function are_anagrams(word1, word2) to determine if two words are anagrams by comparing their sorted characters.
  3. Efficiency:
    • Sorting each word to check for anagrams will take (O(K \log K)) where K is the maximal length of any word in the list.
    • The overall time complexity will be (O(N \times K \log K)) where N is the number of words in the list.

Code

Here is the implementation of the strategy described:

def are_anagrams(word1, word2):
    return sorted(word1) == sorted(word2)

def remove_anagrams(words):
    stack = []
    
    for word in words:
        if stack and are_anagrams(stack[-1], word):
            stack.pop()  # remove the last word if it is an anagram with the current word
        else:
            stack.append(word)
    
    return stack

# Example usage:
words = ["abba", "baba", "bbaa", "cd", "dc"]
print(remove_anagrams(words))  # Output should be ['abba', 'cd']

Time Complexity

This should yield the correct resultant array after removing all adjacent anagrams as specified.

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