Palindrome Pairs

shitgpt

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class Solution:
    class TrieNode:
        def __init__(self):
            self.next = [None] * 26
            self.index = -1
            self.list = []

    def palindromePairs(self, words: List[str]) -> List[List[int]]:
        def is_palindrome(s):
            return s == s[::-1]

        def addWord(root, word, index):
            for i in range(len(word) - 1, -1, -1):
                j = ord(word[i]) - ord('a')

                if not root.next[j]:
                    root.next[j] = Solution.TrieNode()

                if is_palindrome(word[:i + 1]):
                    root.list.append(index)

                root = root.next[j]

            root.list.append(index)
            root.index = index

        def search(words, i, root, res):
            for j in range(len(words[i])):
                if root.index >= 0 and root.index != i and is_palindrome(words[i][j:]):
                    res.append([i, root.index])

                root = root.next[ord(words[i][j]) - ord('a')]
                if not root:
                    return

            for j in root.list:
                if i == j:
                    continue
                res.append([i, j])

        result = []
        root = Solution.TrieNode()

        for i, word in enumerate(words):
            addWord(root, word, i)

        for i, word in enumerate(words):
            search(words, i, root, result)

        return result

Identifying Problem Isomorphism

“Palindrome Pairs” asks you to find all pairs of unique words from a list that form a palindrome when concatenated.

A simpler problem is “Valid Palindrome”, where the goal is to determine if a given string is a palindrome, considering only alphanumeric characters and ignoring cases. This problem forms the basis of the “Palindrome Pairs” as it tests the fundamental concept of identifying palindromes.

A more complex problem related to this is “Longest Palindromic Substring”, which not only requires identifying a palindrome, but also the longest one within a given string. This adds an extra layer of complexity by asking for the longest possible palindrome.

Though not exactly isomorphic, they share the core concept of identifying palindromes. The main difference lies in the complexity and specificity of the problems. Here is the hierarchy:

1. “Valid Palindrome” - tests the basic concept of identifying palindromes.
2. “Palindrome Pairs” - takes this concept further by concatenating words to form palindromes.
3. “Longest Palindromic Substring” - escalates complexity by asking for the longest possible palindrome within a string.

This makes the mapping an approximation, as the problems differ in terms of problem statement and complexity, but they share the central theme of working with palindromes.

10 Prerequisite LeetCode Problems

“Palindrome Pairs” involves string manipulation, palindromes and efficient search in a collection of items. Here are some problems as preparation:

1. “Valid Palindrome” (LeetCode 125): This problem gives you the fundamental understanding of palindromes.

2. “Valid Palindrome II” (LeetCode 680): An extension of the previous problem that introduces some complexity.

3. “Reverse String” (LeetCode 344): This problem will provide practice with string manipulation, which is necessary for the “Palindrome Pairs” problem.

4. “Longest Palindromic Substring” (LeetCode 5): This problem gives you practice on identifying palindromes within a larger string.

5. “Shortest Palindrome” (LeetCode 214): This problem is a variation of identifying palindromes.

6. “Palindrome Linked List” (LeetCode 234): This problem introduces the concept of palindromes in a different data structure, which can help in broadening your understanding.

7. “Longest Palindromic Subsequence” (LeetCode 516): This is another problem focusing on palindromes, but from the angle of dynamic programming.

8. “Implement strStr()” (LeetCode 28): This problem will help you understand the concepts of searching for a substring within a string, which is a necessary skill for the “Palindrome Pairs” problem.

9. “Two Sum” (LeetCode 1): Although this problem is about numbers, not strings, the pattern of looking for pairs that meet a certain condition is common with the “Palindrome Pairs” problem.

10. “Longest Common Prefix” (LeetCode 14): This problem involves string comparison and manipulation, which is beneficial for the “Palindrome Pairs” problem.

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class Solution:
    def palindromePairs(self, words: List[str]) -> List[List[int]]:
        backward, res = {}, []
        for i, word in enumerate(words):
            backward[word[::-1]] = i

        for i, word in enumerate(words):
            
            if word in backward and backward[word] != i:
                res.append([i, backward[word]])
                
            if word != "" and "" in backward and word == word[::-1]:
                res.append([i, backward[""]])
                res.append([backward[""], i])
                
            for j in range(len(word)):
                if word[j:] in backward and word[:j] == word[j-1::-1]:
                    res.append([backward[word[j:]], i])
                if word[:j] in backward and word[j:] == word[:j-1:-1]:
                    res.append([i, backward[word[:j]]])
                    
        return res

Problem Classification

Palindrome Pairs - The problem asks to find pairs of words that form a palindrome when concatenated. This is a Palindrome Pair Identification Problem.

Language Agnostic Coding Drills

The given Python code is a solution to finding all palindrome pairs in a given list of words. Let’s break it down into simpler concepts and processes, listing them in order of increasing complexity.

1. Understanding Data Structures: Basic knowledge about list and dictionary data structures in Python is essential. Lists are used to store the words and resultant pairs. Dictionaries are used for efficient look-up of reversed words.

2. String Manipulation and Reversal: This problem uses the concept of reversing strings and checking for palindromes. The string slicing technique is used to reverse the strings.

3. Loops and Iterations: Iterating over the list of words using a for loop. You need to understand how to loop over a list and process each element.

4. Indexing in Python: Understanding of 0-based indexing in Python is crucial. This is because we are storing and returning indices of words in the list.

5. Dictionary Manipulation: Creating a dictionary that stores the reversed words as keys and their indices as values.

6. Conditions and Edge Cases: Checks are made to ensure that the same word is not being paired with itself, and cases of empty strings are handled separately. Also, there are two different checks for possible palindrome pairs: one where the first part of the word is a palindrome and the other where the last part is.

7. Appending to List: Append the pairs of indices to the result list.

8. Nested Loops: There are nested loops in the code, one looping over the words and the other looping over the length of the individual word.

To combine these elements into a solution, you’d start by creating the reversed dictionary. Then you’d loop through the words and perform the necessary checks and operations to identify palindrome pairs and store their indices. For each word, you’d also loop over its length to find possible palindrome pairs and append them to the result. Finally, you’d return the list of all found pairs. This combines all the concepts and drills into the final solution.

Targeted Drills in Python

Let’s create some drills that can be implemented separately and then eventually be combined for the final solution. Each code snippet below corresponds to the steps outlined previously:

1. Understanding Data Structures:

   • Lists: Create a list of integers and print it.
   • Dictionaries: Create a dictionary with string keys and integer values, and print it.

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   # List list_of_numbers = [1, 2, 3, 4, 5] print(list_of_numbers) # Dictionary dict_of_strings = {"one": 1, "two": 2, "three": 3} print(dict_of_strings)

2. String Manipulation and Reversal: Reverse a string and check if a string is a palindrome.

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   word = "hello" reversed_word = word[::-1] print(reversed_word) palindrome_word = "racecar" print(palindrome_word == palindrome_word[::-1])

3. Loops and Iterations: Iterate over a list of words and print each one.

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   words = ["hello", "world", "python"] for word in words: print(word)

4. Indexing in Python: Print the first and last word from the list of words.

   1 2	print(words[0]) # First word print(words[-1]) # Last word

5. Dictionary Manipulation: Create a dictionary of reversed words from the list of words.

   1 2	reversed_words_dict = {word[::-1]: i for i, word in enumerate(words)} print(reversed_words_dict)

6. Conditions and Edge Cases: Check if a word is in the dictionary and not at the same index.

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   for i, word in enumerate(words): if word in reversed_words_dict and reversed_words_dict[word] != i: print(f"Found a match for {word} at a different index.")

7. Appending to List: Append a pair of indices to a list.

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   pairs = [] pairs.append([0, 1]) print(pairs)

8. Nested Loops: Loop over the length of a word and print each character.

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   for word in words: for i in range(len(word)): print(word[i])

In the final solution, you would create the reversed words dictionary first, then loop over the list of words to find matching reversed words at different indices, and loop over the length of each word to find palindromic pairs. You would append each pair of indices to the results list.