Word Pattern

Identifying Problem Isomorphism

“Word Pattern” has an approximate isomorph: “Isomorphic Strings”.

In “Word Pattern”, you are given a pattern and a string, and you have to determine if the string follows the same pattern. Here a pattern is a sequence of characters without any repetition and the string contains words separated by a single space.

“Isomorphic Strings” requires you to determine if two strings s and t are isomorphic. Two strings are isomorphic if the characters in s can be replaced to get t, and all occurrences of a character must be replaced with another character while preserving the order of characters.

Both problems require a mapping from one set of items (characters or words) to another, and checking for a one-to-one correspondence.

“Isomorphic Strings” is simpler because it only involves characters, whereas “Word Pattern” is more complex because it operates on words.

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class Solution:
    def wordPattern(self, pattern: str, s: str) -> bool:
        words, w_to_p = s.split(' '), dict()

        if len(pattern) != len(words): return False
        if len(set(pattern)) != len(set(words)): return False

        for i in range(len(words)):
            if words[i] not in w_to_p: 
                w_to_p[words[i]] = pattern[i]
            elif w_to_p[words[i]] != pattern[i]: 
                return False

        return True

Problem Classification

This problem can be classified into the following categories:

  1. Pattern Matching: The problem essentially requires matching a pattern provided as a string to another string.

  2. String Manipulation: We are dealing with strings and their manipulation, such as splitting the string into words.

  3. Mapping/Dictionary Usage: We need to establish a one-to-one correspondence (bijection) between the letters in the pattern and the words in the string s. This typically involves using a map or dictionary data structure to maintain the relationship.

  4. Comparative Analysis: The problem involves comparing if the string s follows the same pattern. This is a comparison-based problem.

Language Agnostic Coding Drills

Let’s break down the code into smaller units and describe the problem-solving approach for the final solution.

  1. String Splitting: The first drill here is learning how to split a string into individual words. In the given problem, we are given a sentence which we need to split into words. Most modern languages provide in-built methods to split strings based on a delimiter. The delimiter in this case would be a space ’ ‘.

  2. Dictionary Creation: The second drill is about creating and using dictionaries (or associative arrays, or hash maps). This is a fundamental aspect of the solution, as we need to create a mapping (or bijection) from words to pattern characters. Most modern languages have in-built support for dictionaries.

  3. Iteration: The next drill is iteration, specifically, iterating over the words in the sentence. This is crucial for checking whether each word maps to the appropriate pattern character.

  4. Dictionary Manipulation and Lookup: The fourth drill is learning how to perform dictionary manipulations - adding new entries to the dictionary, and looking up values based on keys. In the context of the problem, this involves adding words and their corresponding pattern characters to the dictionary, and looking up whether a word has already been associated with a pattern character.

  5. Comparisons and Condition Checking: The final drill is about learning how to do comparisons and check conditions. This is necessary for checking whether the words in the string match the pattern.

When integrating these drills into a solution, the steps would be as follows:

  1. Split the string into words.
  2. Initialize an empty dictionary.
  3. Start iterating over the words.
  4. For each word, check if it is in the dictionary.
  5. If it is not in the dictionary, add an entry mapping the word to the corresponding pattern character.
  6. If it is in the dictionary, check if the mapped pattern character matches the current pattern character. If they do not match, return False.
  7. If we have iterated over all words without returning False, return True. This indicates that the string follows the pattern.

Targeted Drills in Python

These drills will focus on understanding and implementing the core skills needed for the problem.

Drill 1: String Splitting

Python has a built-in method for splitting a string into a list of substrings, based on a specified delimiter.

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s = "the quick brown fox"
words = s.split(' ')
print(words)  # Output: ['the', 'quick', 'brown', 'fox']

Drill 2: Dictionary Creation

Python dictionaries can be created using {} or the dict() function. They map keys to values.

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# Using {}
dict1 = {"apple": 1, "banana": 2}
print(dict1)  # Output: {'apple': 1, 'banana': 2}

# Using dict()
dict2 = dict(orange=3, mango=4)
print(dict2)  # Output: {'orange': 3, 'mango': 4}

Drill 3: Iteration

Python lists and other iterable objects can be iterated using the for loop.

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fruits = ["apple", "banana", "orange", "mango"]
for fruit in fruits:
    print(fruit)

Drill 4: Dictionary Manipulation and Lookup

In Python, new entries can be added to a dictionary, and existing entries can be retrieved using the [] operator.

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dict1 = {}
dict1["apple"] = 1  # Add a new entry
print(dict1["apple"])  # Retrieve an entry, Output: 1

Drill 5: Comparisons and Condition Checking

Python supports a variety of comparison and logical operators such as ==, !=, <, >, <=, >=, and, or, and not.

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a = 5
b = 10
if a < b:
    print("a is less than b")  # Output: a is less than b

After understanding these core concepts and practicing them with these drills, you should be able to integrate them to solve the problem at hand, i.e., to check if a given string follows a specified pattern.