Camelcase Matching

Here’s a Python function that takes an array of strings queries and a string pattern, and returns a boolean array indicating whether each query matches the pattern according to the given rules.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12

class Solution:
    def camelMatch(self, queries: List[str], pattern: str) -> List[bool]:
        def is_match(query, pattern):
            j = 0
            for char in query:
                if j < len(pattern) and char == pattern[j]:
                    j += 1
                elif char.isupper():
                    return False
            return j == len(pattern)

        return [is_match(query, pattern) for query in queries]

Explanation:

  • is_match is a helper function that checks if a single query matches the pattern.
  • It iterates through the query characters, and if the character matches the current pattern character, it moves to the next pattern character.
  • If an uppercase letter is encountered that does not match the current pattern character, the function returns False.
  • The function returns True if all pattern characters are matched.
  • The main function uses a list comprehension to apply is_match to all queries, returning the result.

For example, if the queries are ["FooBar","FooBarTest","FootBall","FrameBuffer","ForceFeedBack"] and the pattern is "FB", the function will return [true,false,true,true,false].

Identifying Problem Isomorphism

“Camelcase Matching” has an isomorphism in “Word Subsets”. Both problems are concerned with the idea of matching strings based on specific conditions.

In “Camelcase Matching”, the task is to find if queries are camelcase versions of a pattern. The problem “Word Subsets” is about finding all universal words in a string list that contain all the characters of words from another list.

The problems are not exactly the same, but they share a similar structure in matching specific string patterns. Both problems require a detailed understanding of string manipulation and comparison.

“Camelcase Matching” is simpler as it only involves one pattern and query at a time, whereas “Word Subsets” requires analyzing multiple words at once.

The problems are approximately isomorphic, they share a similar theme of string matching based on certain conditions. The degree of isomorphism can vary and often depends on interpreting the essence of the problem rather than the specific details.

10 Prerequisite LeetCode Problems

For this, the following are a good preparation:

  1. “28. Implement strStr()” - This problem involves finding a needle in a haystack, which is a string search that can help with matching patterns.

  2. “10. Regular Expression Matching” - This problem is very much related to pattern matching and will provide a more nuanced understanding of such tasks.

  3. “392. Is Subsequence” - This problem is about determining whether a string is a subsequence of another, similar to how we have to find if a pattern is a subsequence of a query in Camelcase Matching.

  4. “125. Valid Palindrome” - This problem requires string manipulation and checking of conditions in a string.

  5. “409. Longest Palindrome” - This problem involves creating new strings from given conditions, which can be useful in the pattern manipulation part of the Camelcase Matching problem.

  6. “917. Reverse Only Letters” - This problem requires you to manipulate strings in specific ways, which can be beneficial when matching camelcase strings.

  7. “680. Valid Palindrome II” - This problem adds some complexity by allowing some errors, much like the Camelcase Matching problem allows additional letters.

  8. “521. Longest Uncommon Subsequence I” - This problem involves manipulating and comparing sequences, which can be helpful in understanding how to compare the pattern and the query.

  9. “686. Repeated String Match” - This problem involves finding patterns in repeated strings, which is similar to finding the pattern in a Camelcase Matching problem.

  10. “657. Robot Return to Origin” - This problem deals with movement according to commands, which can be thought of as a form of pattern matching.

These cover string manipulation and pattern matching, making them useful to solve the Camelcase Matching problem.

Problem Classification

The problem falls under the domain of “String Manipulation” and “Array Processing.”

What

  1. An array of strings called queries.
  2. A single string called pattern.
  3. A boolean array answer, where each element corresponds to whether the string from queries can be formed by inserting lowercase letters into pattern.

Classification

This is essentially a pattern matching problem. It involves traversing through the array of strings and the pattern string to check if each string in the array can be constructed by inserting lowercase letters into the pattern. Therefore, it combines elements of string manipulation and array processing.

The problem also requires a good understanding of string operations like traversal and character comparison. It further demands an efficient way to collect and return the boolean results for each query in the array.

Clarification Questions

  1. Can the pattern string contain both uppercase and lowercase letters, or is it limited to uppercase only?
  2. Are the strings in queries case-sensitive?
  3. Is it allowed to use a character from pattern more than once for a single query?
  4. What should be the output if the queries array is empty?
  5. Can the pattern string be empty? If so, what would be the expected output?
  6. Can there be duplicate strings in the queries array? If so, should the output reflect those duplicates accordingly?
  7. Should the program handle special characters or is it strictly alphabetic characters?
  8. Is the order of the boolean values in the output array important? Should they strictly correspond to the order of strings in the queries array?
  9. What is the expected time complexity for solving this problem?
  10. Can we assume that all strings in queries and pattern contain only English alphabets?

These questions can help clarify any ambiguities and make sure you fully understand the problem constraints and requirements before starting with the implementation.

Problem Analysis and Key Insights

  1. Matching Mechanism: The problem essentially asks whether a given pattern can be reconstructed by inserting lowercase English letters into a query string. The order of characters in the pattern should be maintained.

  2. Case Sensitivity: The problem statement specifies that the pattern consists of English letters, but it doesn’t mention case sensitivity. An assumption is made that the pattern’s case should match exactly with the corresponding letters in the query strings.

  3. Array of Queries: The task is to return a boolean array that answers the matching question for each query string. This means the solution needs to be efficient to handle multiple queries.

  4. Boolean Output: The output is straightforward; for each query, it’s either a match (true) or not a match (false).

  5. Constraints: The size constraint for both pattern and each query string is 100 characters, indicating that a brute-force solution could be feasible but not efficient for a large number of queries.

  6. Insertion, Not Deletion: It’s important to note that you can only insert characters into the pattern to match the query. You can’t remove any characters from the query to make it fit the pattern.

By understanding these key insights, you can better approach the coding solution, ensuring that all aspects of the problem are considered.

Problem Boundary

The scope of the problem is limited to string matching under specific conditions:

  1. The strings involved are limited to English letters.

  2. The length constraints are clearly defined, with the length of pattern and each string in queries not exceeding 100 characters.

  3. The task is to determine if each string in an array of queries can be formed by inserting lowercase English letters into a given pattern string.

  4. The output must be a boolean array corresponding to each query string, indicating whether it matches the given pattern or not.

The problem doesn’t extend to any more complex string operations, like rearrangements or deletions. It’s confined to the simple task of string pattern matching as defined in the problem statement.

Establishing the boundary of the problem involves clarifying the limitations and assumptions that are defined by the problem statement:

  1. Input Constraints:
  • pattern.length and queries.length must be at least 1 and at most 100.
  • Each string in queries must have a length between 1 and 100.
  • All characters in queries and pattern are English letters.
  1. Output Constraints:
  • The output is a boolean array, where each element represents whether the corresponding string in queries can be formed by the pattern.
  1. Functional Constraints:
  • Pattern matching allows only insertion of lowercase English letters.
  • No deletions or rearrangements are allowed.
  1. Context Constraints:
  • The problem is focused on string matching, so issues like string encoding or other language-specific considerations are not relevant here.
  1. Objective:
  • The goal is to determine if each string in queries can be created by inserting lowercase English letters into the pattern.

By understanding these boundaries, we can focus on solving the problem without worrying about external factors or edge cases that fall outside these constraints.

Distilling the Problem to Its Core Elements

  1. Fundamental Concept:

    • The fundamental concept this problem relies upon is “Pattern Matching” within strings. The task is to match each query string with a given pattern, following a specific set of rules for insertion.

  2. Simplest Description:

    • You have a pattern string and a list of other strings. You can only insert lowercase letters into the pattern to make it match the other strings. Find out which of those strings can be made by doing this.

  3. Core Problem:

    • The core problem is identifying whether each string in a list can be created by inserting lowercase letters into a given pattern.

  4. Key Components:

    • Input pattern string
    • List of query strings
    • Rules for allowable transformations (inserting lowercase letters)
    • Output list of boolean values representing match or no match

  5. Minimal Set of Operations:

    • Loop through each query string.
    • Loop through each character in both the pattern and the query string to check for a match.
    • Insert lowercase letters where necessary to keep the pattern intact.
    • Return True if the entire pattern is found within the query string, otherwise return False.

By understanding these aspects, we can create a focused and efficient solution to the problem.

Visual Model of the Problem

Visualizing the problem can be achieved using a few methods:

  1. Two-Pointer Diagram: Imagine two pointers, one for the query string and one for the pattern. Move these pointers along their respective strings to find the match. A diagram would show the pointers’ positions during each step.

    Pattern: F B
Query:   F o o B a r
Pointers: ↑         ↑

  2. Flowchart: A flowchart can help outline the process of traversing each query string and pattern. It will show the decision points, such as whether to move a pointer or whether a match is found.

  3. Table: Create a table with rows as the query strings and columns with step-by-step changes to the pattern, marking where the pattern fits into the query string.

    StepQuery StringPatternMatch
    1F o o B a rFYes
    2F o o B a rF o oYes
    3F o o B a rF o o BYes
    …………

  4. Text-based Visuals: Create a simple text-based representation to track the pattern within the query. For example, use uppercase letters for pattern letters and lowercase for inserted letters.

    Query: FooBar
Visual: F--B--

  5. Color Coding: If this visualization is digital, color-coding the matching and non-matching characters can make it easier to track the process.

By visualizing the problem in these ways, you can more easily track the logic and flow of a potential solution.

Problem Restatement

Given a list of words and a specific pattern, determine if each word in the list can be formed by inserting lowercase letters into the pattern. Return a list of boolean values, where each value indicates whether the corresponding word in the list can be formed using the given pattern. The pattern and words will consist only of English letters. The length of the pattern and each word in the list will be between 1 and 100.

You have an array of strings called “queries” and a single string called “pattern.” Your task is to check if each string in “queries” can be formed by inserting lowercase English letters into the “pattern” string. You can insert each character at any position, and you may not insert any characters that aren’t lowercase English letters.

Return an array of boolean values where each value corresponds to a string in “queries.” A value will be true if the string can be formed based on the pattern and false otherwise.

Constraints:

  • Both the pattern and the queries will contain only English letters.
  • The length of the pattern and each string in queries will be between 1 and 100.

Abstract Representation of the Problem

Given a sequence of elements queries and another sequence pattern, determine if each element in queries can be generated by inserting additional elements into pattern while keeping the existing elements in pattern in their relative order. Return a boolean array, where each index i contains true if queries[i] can be generated in this way, and false otherwise. All elements in both sequences are taken from a finite alphabet. The sequences are bounded in length.

Terminology

  1. Pattern Matching: This is the process of checking a given sequence of elements for the presence of the constituents of some pattern. In this problem, pattern matching is used to check if pattern can be inserted into each string in queries.

  2. Boolean Array: An array containing boolean values (true or false). In this problem, the boolean array represents whether each string in queries can be formed using the given pattern.

  3. Queries: A list of strings that we will check against the pattern. Each string in queries is a candidate for pattern matching.

  4. Insert Operation: The act of adding additional elements into a sequence. In this problem, we are inserting lowercase English letters into the pattern to make it match with the strings in queries.

  5. Alphabet: A set of symbols or characters. In this case, the alphabet consists of English letters.

  6. Constraints: The limitations or boundaries set for the problem. Here, they specify the length of the pattern and queries.

Understanding these terms is essential for grasping how to approach solving the problem and what each part of the code is aiming to accomplish.

Problem Simplification and Explanation

Certainly. In simple terms, you have a word (the pattern) and a list of other words (the queries). You want to find out if you can rearrange the letters in your pattern and add some extra lower-case letters so it spells out each of the words in the list. If it works, you note that as ’true’, otherwise ‘false’.

Key Concepts:

  1. Pattern: Think of it as a skeleton key.
  2. Queries: These are the locks you’re trying to open.
  3. Insert Operation: Imagine you have additional small keys (lowercase letters) that can be attached to your skeleton key to make it fit into each lock.

Interaction:

You take your skeleton key (pattern) and try to make it fit into each lock (each word in queries) by adding or rearranging smaller keys (inserting lower-case letters).

Metaphor:

Let’s think of this as a puzzle game where you have a base puzzle piece (the pattern) and a set of puzzle slots (the queries). You can attach extra tiny pieces (lowercase letters) to your base puzzle piece to make it fit into each slot. If it fits, you mark it as a win (’true’). If not, it’s a loss (‘false’).

By understanding this interaction, you’ll get a clearer picture of how to approach solving the problem.

Constraints

Here are some specific characteristics or conditions that could be exploited for an efficient solution:

  1. Case Sensitivity: The pattern and queries consist of English letters where case matters. Capital letters in the pattern must appear in the same order in the queries. This reduces the number of places where we can “fit” our pattern.

  2. Length Constraints: Both pattern and queries have a length constraint of 1 to 100 characters. Knowing the upper limits can help in optimizing the solution, knowing it doesn’t have to scale beyond this.

  3. Insert Only: You can only insert lowercase letters into the pattern to match it with a query. You can’t remove or rearrange letters from the pattern, so this simplifies what operations you have to consider.

  4. Sequence Order: The sequence of the uppercase letters in the query should match the sequence in the pattern. This allows for direct comparison without having to sort or rearrange letters.

  5. Queries Array: Since you’re working with an array of queries, any pre-processing or post-processing steps can be applied across the board. This might be useful for batch operations or parallelization.

By exploiting these characteristics, you can reduce the number of operations needed and thereby make your solution more efficient.

From analyzing the constraints, the key insights are:

  1. Fixed Lengths: Both the pattern and each query in the queries array have a maximum length of 100 characters. This sets an upper limit for computational complexity.

  2. Limited Alphabet: The problem involves only English letters, meaning the character set is fixed and limited, reducing the complexity involved in string manipulations.

  3. Case Sensitivity: Uppercase letters in the pattern must match exactly with those in the queries. This simplifies the search problem, as we only need to match uppercase letters in the exact order they appear.

  4. Insert Operations Only: The pattern can be transformed into a query only by inserting lowercase letters. This eliminates the need to consider deletions or substitutions, thereby simplifying the transformation rules.

  5. Array of Queries: Multiple queries must be checked against the same pattern. This allows for the possibility of reusing some computation across multiple queries, which could lead to efficiency gains.

These insights help in tailoring an efficient algorithm, allowing us to focus only on what’s necessary to solve the problem.

Case Analysis

Certainly, let’s delve into additional examples that cover various dimensions of the problem. I will name and categorize these cases to highlight different aspects.

Edge Cases

  1. Empty Queries List (Edge Case)

    • Input: queries = [], pattern = "FB"
    • Output: []
    • Reasoning: Since there are no queries, the output is an empty list.

  2. Single-Character Pattern (Edge Case)

    • Input: queries = ["A", "B", "C"], pattern = "A"
    • Output: [true, false, false]
    • Reasoning: Only the query that exactly matches the single character of the pattern returns true.

Boundary Cases

  1. Case Sensitivity (Boundary Case)

    • Input: queries = ["FooBar"], pattern = "fB"
    • Output: [false]
    • Reasoning: Case sensitivity matters. ‘F’ and ‘f’ are not the same.

  2. All Lowercase Pattern (Boundary Case)

    • Input: queries = ["foobar", "foobartest"], pattern = "fbt"
    • Output: [false, false]
    • Reasoning: Uppercase letters in queries must match exactly, so an all-lowercase pattern can’t match any queries with uppercase letters.

  3. Disorder in Uppercase Letters (Boundary Case)

    • Input: queries = ["FooBar"], pattern = "BF"
    • Output: [false]
    • Reasoning: Uppercase letters must appear in the same order as in the pattern.

  4. Missing Uppercase Letters (Boundary Case)

    • Input: queries = ["Foobar"], pattern = "FB"
    • Output: [false]
    • Reasoning: All uppercase letters in the pattern must be present in the query.

  5. Longest Pattern and Query (Boundary Case)

    • Input: queries = ["A"*100], pattern = "A"*100
    • Output: [true]
    • Reasoning: Both pattern and query are at their maximum lengths and identical, hence true.

  6. Multiple Matches (Boundary Case)

    • Input: queries = ["FooBar", "FooBat", "FooBasket"], pattern = "FB"
    • Output: [true, true, true]
    • Reasoning: All queries can be transformed to the pattern by inserting lowercase letters.

  7. Multiple Queries, Single Pattern (Boundary Case)

    • Input: queries = ["FooBar", "FootBall", "Fumble"], pattern = "FB"
    • Output: [true, true, false]
    • Reasoning: The first two can be transformed to “FB” by inserting lowercase letters, but the third cannot.

  8. Pattern Longer Than Query (Boundary Case)

    • Input: queries = ["Foo"], pattern = "FooB"
    • Output: [false]
    • Reasoning: The pattern is longer than the query, making it impossible to match.

These cases should provide a robust set of conditions for validating any solution to the problem. They explore edge conditions, case sensitivity, character order, and other constraints that might affect the solution.

Visualizing these cases can be useful for understanding the problem better. One effective way is to use a table or a matrix to represent how each query can or cannot be transformed to match the pattern. This method highlights the interaction between the pattern and the query string.

  1. Empty Queries List (Edge Case)

    • queries = [], pattern = "FB"
    • No queries to visualize.

  2. Single-Character Pattern (Edge Case)

    • queries = ["A", "B", "C"], pattern = "A"
    • Matrix: A | A -> ✔, B -> ✘, C -> ✘

  3. Case Sensitivity (Boundary Case)

    • queries = ["FooBar"], pattern = "fB"
    • Matrix: f | F, B -> ✘

  4. All Lowercase Pattern (Boundary Case)

    • queries = ["foobar", "foobartest"], pattern = "fbt"
    • Matrix: f | f, b, t -> ✘, f, b, t -> ✘

  5. Disorder in Uppercase Letters (Boundary Case)

    • queries = ["FooBar"], pattern = "BF"
    • Matrix: B | F, B -> ✘

  6. Missing Uppercase Letters (Boundary Case)

    • queries = ["Foobar"], pattern = "FB"
    • Matrix: F | F, b -> ✘

  7. Longest Pattern and Query (Boundary Case)

    • queries = ["A"*100], pattern = "A"*100
    • Matrix: A | A, A, ..., A -> ✔

  8. Multiple Matches (Boundary Case)

    • queries = ["FooBar", "FooBat", "FooBasket"], pattern = "FB"
    • Matrix: F | F, B -> ✔, F, B -> ✔, F, B -> ✔

  9. Multiple Queries, Single Pattern (Boundary Case)

    • queries = ["FooBar", "FootBall", "Fumble"], pattern = "FB"
    • Matrix: F | F, B -> ✔, F, B -> ✔, F, u -> ✘

  10. Pattern Longer Than Query (Boundary Case)

    • queries = ["Foo"], pattern = "FooB"
    • Matrix: F | F, o, o -> ✘

In each matrix, the first character represents the first uppercase letter in the pattern, and subsequent characters show whether the query can be transformed to match the pattern (✔ for match, ✘ for no match).

From analyzing the different cases, several key insights emerge:

  1. Case Sensitivity: The pattern matching is case-sensitive. This affects how we compare characters in the pattern and queries.

  2. Pattern Length: If the pattern length is greater than the query length, the query can’t possibly match the pattern.

  3. Uppercase Letters: Only uppercase letters in the pattern need to appear in the same order in the query. Lowercase letters in the pattern don’t have to appear, but if they do, they must appear in the same sequence as in the pattern.

  4. Lowercase Flexibility: You can insert as many lowercase letters in the query as needed to match the pattern.

  5. Single-Character Pattern: When the pattern consists of a single character, the query should have at least that one uppercase character to match.

  6. Multiple Matches: A single pattern can match multiple queries, and vice versa.

  7. Empty Query List: If the list of queries is empty, the result should also be an empty list.

  8. Edge Case of Longest Strings: While it’s less common, the pattern and query can be as long as 100 characters. This might necessitate optimization for long strings.

These insights provide a comprehensive understanding of the problem’s constraints and requirements, paving the way for a more efficient solution.

Identification of Applicable Theoretical Concepts

  1. String Matching: The core operation here is string matching, a well-studied problem in computer science. The KMP algorithm or even basic substring search can be modified to solve this.

  2. Dynamic Programming: To handle variations in the pattern, Dynamic Programming could be useful for storing intermediate results to avoid re-computation.

  3. Hashing: If the pattern and queries are constant and we have multiple test cases, a hash table could be used to memoize results for specific queries to accelerate subsequent matching operations.

  4. Graph Theory: You could conceptualize the problem as a graph traversal problem, where each node represents a position in the pattern and the query. This may make certain complex matching tasks more intuitive to reason about.

  5. Boolean Algebra: The result is a Boolean array. Boolean algebra could potentially simplify the evaluation of whether a query matches a pattern or not, especially when multiple conditions need to be checked.

  6. Queue or Stack: To keep track of the matching characters’ order, you could use a queue or stack data structure.

  7. Big O Notation: Given constraints about the maximum length of patterns and queries, consider time complexity to ensure your solution scales.

These concepts can make the problem more manageable and potentially lead to more efficient solutions.

Simple Explanation

Imagine you have a bunch of letter magnets. Some of these magnets are big and bold, and others are small. You also have a special word made up of big and bold letters only, like “FB”.

Now, your task is to take other words, which can have both big and small letters, and see if you can recreate them using the special word’s big letters. You’re allowed to add as many small letters as you want in between the big letters, but you can’t change the order of the big letters.

For example, if your special word is “FB” (only big letters allowed), you can make the word “FooBar” by adding small letters ‘o’, ‘o’, ‘a’, and ‘r’. But you can’t make the word “BarFoo” because that changes the order of the big letters “F” and “B”.

So, the problem is to figure out which words you can and cannot make using the big letters of your special word, while following these rules.

Problem Breakdown and Solution Methodology

To solve this problem, we can follow these steps:

Step 1: Prepare

  • Have two pointers ready: one for the query string and one for the special word, let’s call them queryPtr and patternPtr.

Step 2: Loop Through Each Query

  • For each query word in the list, reset both pointers to the start of their respective strings.

Step 3: Loop Through Each Character

  • Inside each query, loop through its characters one at a time using queryPtr.

Step 4: Check Conditions

  • As you loop, compare the character at queryPtr with the character at patternPtr. Three scenarios can happen:
    1. If they match and are both uppercase, move both pointers forward.
    2. If they match but are not both uppercase, only move queryPtr forward.
    3. If they don’t match, but the character at queryPtr is lowercase, move queryPtr forward.

Step 5: Check Validity

  • At the end of each query, if patternPtr has moved through all characters of the pattern, the query is valid. Otherwise, it’s not.

Step 6: Store Result

  • Record the result (true or false) for each query in a list.

Metaphor

Think of this like a conveyor belt of mixed items—fruits and boxes. Your job is to pick out boxes in the order they appear on your checklist. You can skip as many fruits as you want, but you can’t change the order of the boxes you pick. The pattern string is your checklist, and the query string is the conveyor belt.

Effect of Changes in Parameters

  • Increasing the length of either the query or pattern string would affect the time it takes to solve the problem, but the steps remain the same.

Example Case

  • Let’s say your pattern is “FB” and your query is “FooBar”.
    1. Both pointers start at ‘F’.
    2. They match and are both uppercase, so both pointers move one step.
    3. Now, queryPtr is at ‘o’ and patternPtr is at ‘B’. They don’t match, but ‘o’ is lowercase, so only queryPtr moves.
    4. Repeat until patternPtr has gone through all characters in “FB”.
    5. The query is valid because we reached the end of the pattern.

This way, you can determine if each query string is a valid match for the given pattern.

Inference of Problem-Solving Approach from the Problem Statement

Here are the key terms or concepts and their implications for the solution:

1. Array of Strings (queries)

  • This indicates that we’ll need to loop through each query one by one, applying the same logic for pattern matching.

2. String (pattern)

  • This is what we are trying to locate within each query. It helps set the rules for how to move through each query string.

3. Boolean Array (answer)

  • The goal is to produce a Boolean array of the same length as queries. This tells us that our function needs to return an array and informs the data type for our result.

4. Insert Lowercase English Letters

  • This implies that we can ignore lowercase letters in the query when they don’t match the pattern, but they can be present. This is crucial when deciding when to move the pointer within each query string.

5. You may not insert any characters

  • This condition informs us that we cannot add any new characters; we can only work with what is already in the query and pattern strings.

6. Constraints on String Lengths

  • The constraint that 1 <= pattern.length, queries.length <= 100 informs us that we don’t have to worry too much about the computational complexity, but it’s still good to aim for an efficient solution.

Understanding each of these terms guides us to use a two-pointer technique to iterate through the query and pattern strings, allowing us to find a match or mismatch in an efficient way.

Visualizing properties through tables or diagrams can be highly beneficial for understanding the problem better. Here are ways to represent some of the key concepts:

1. Array of Strings (queries)

  • You can use a simple table where each row represents one query string.
  • Columns could be for each character in the query string.

2. String (pattern)

  • Place the pattern string on a single line or row, possibly above or below your table for queries, so you can easily compare it against each query.
QueryPattern
F o o B a rF B
F o o t B a l lF B

3. Boolean Array (answer)

  • Add another column to your table called “Match”, where you mark whether the query matches the pattern (True or False).
QueryPatternMatch
F o o B a rF BTrue
F o o t B a l lF BTrue

4. Insert Lowercase English Letters

  • Use color-coding or another form of annotation to distinguish between letters that must match (upper-case from pattern) and those that are optional (lowercase in queries).

5. You may not insert any characters

  • For this, ensure that no extra characters are in your pattern row compared to the query row. The integrity of this rule can be visually checked.

6. Constraints

  • Constraints are hard to visualize but understanding the limitations (e.g., max length 100) helps you mentally validate that your approach will be computationally feasible.

By laying out these tables and visual elements, you can manually walk through your approach step-by-step, ensuring it handles all the complexities of the problem. This aids both in problem understanding and in verifying that your approach is sound.

How did you infer from the problem statement that this problem can be solved using ?

Simple Explanation of the Proof

I’m having trouble understanding the proof of this algorithm. Could you explain it in a way that’s easy to understand?

Stepwise Refinement

High-Level Approach

At a high level, the problem asks us to check if a given pattern can be formed from each query string. We will walk through each query and pattern, character by character, to see if a query conforms to the given pattern.

Granular Steps

  1. Initialize Results Array: Create an empty boolean array, answer, to hold the results for each query.

  2. Iterate Through Queries: Loop through each string in the queries array.

    • Reset any temporary variables needed for this specific query.

  3. Pattern Matching:

    • Initialize pointers for the query and pattern.
    • Walk through the characters of the query and pattern.
    • If a character in the pattern matches a character in the query, move both pointers.
    • If the pattern character doesn’t match, move the query pointer if it’s a lowercase letter.

  4. Check Completion: At the end of each query, check if you’ve gone through the entire pattern. If so, the query is a match. Update the answer array accordingly.

  5. Return Result: After checking all queries, return the answer array.

Independent Parts

  • Each query is independent of the others. You could, in theory, run these checks in parallel.

Repeatable Patterns

  • The pattern-matching logic is a repeatable pattern, consistently applied to each query.

Here’s how you could code these steps:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35

def camelMatch(queries, pattern):
    answer = []
    
    # Step 2
    for query in queries:
        i, j = 0, 0  # Pointers for query and pattern
        
        match = True  # Temporary variable
        
        # Step 3
        while i < len(query) and j < len(pattern):
            if query[i] == pattern[j]:
                i += 1
                j += 1
            elif query[i].islower():
                i += 1
            else:
                match = False
                break
        
        # Complete the remaining lowercase letters in query
        while i < len(query):
            if query[i].isupper():
                match = False
                break
            i += 1
        
        # Step 4
        if j != len(pattern):
            match = False
        
        answer.append(match)
        
    # Step 5
    return answer

PENDING TEST

By breaking down our approach into these granular steps, we make the problem more manageable and set the stage for potential optimizations or parallelizations.

Solution Approach and Analysis

Breakdown into Smaller Steps

  1. Initialization: First, we prepare an empty list to store the boolean answers for each query string.

  2. Iterate Over Queries: For each query string in the list of queries, we’ll follow a set of steps to determine if it matches the pattern.

  3. Pattern Matching:

    • Start with two pointers, one at the beginning of the query string and another at the beginning of the pattern string.
    • Move through each string comparing the characters at the pointer positions.

  4. Character Matching and Skipping:

    • If the characters match, move both pointers ahead.
    • If they don’t match and the character in the query string is lowercase, move the query pointer ahead.
    • If they don’t match and the character in the query is uppercase, the pattern does not match.

  5. Completion Check: At the end of the query, verify that you’ve gone through the entire pattern string. If so, this query is a match.

  6. Result Compilation: Store the match result in the answers list.

  7. Final Answer: Return the list of boolean answers.

Analogy

Think of each query string as a train and the pattern as a sequence of key stations. A train can have many stations (characters), but we are looking for trains that go through all the key stations (pattern characters) in the same order. Some trains might have extra stops (lowercase characters), and that’s okay.

Parameters and Their Effects

  • Query Length: The longer the query string, the more time it’ll take to process it.
  • Pattern Length: A longer pattern will also require more comparisons, affecting the time complexity.

Code Demonstration

Here’s a quick demonstration using Python:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28

def camelMatch(queries, pattern):
    answer = []
    for query in queries:
        i, j = 0, 0  # Initialize pointers
        is_match = True
        while i < len(query) and j < len(pattern):
            if query[i] == pattern[j]:
                i += 1
                j += 1
            elif query[i].islower():
                i += 1
            else:
                is_match = False
                break
        while i < len(query):
            if query[i].isupper():
                is_match = False
                break
            i += 1
        if j != len(pattern):
            is_match = False
        answer.append(is_match)
    return answer

# Example case
queries = ["FooBar", "FooBarTest", "FootBall", "FrameBuffer", "ForceFeedBack"]
pattern = "FB"
print(camelMatch(queries, pattern))  # Output should be [True, False, True, True, False]

In this example, we used the pattern “FB”. The output is [True, False, True, True, False], which is consistent with the example given in the problem statement.

Identify Invariant

The invariant in this problem is the sequence of uppercase letters in the pattern and the query. During the entire process of matching, the uppercase letters must appear in the same order in both the query and the pattern for a match to be considered valid. The sequence of uppercase letters serves as a “skeleton” that both the query and the pattern must adhere to. This invariant helps guide the comparison and allows us to ignore lowercase letters when they don’t match, focusing only on the sequence of uppercase letters.

Identify Loop Invariant

The loop invariant in this problem would be that, at the start of each iteration, the indices for the query and pattern up to that point must represent a partial match. In other words, the uppercase letters in the pattern must occur in the same sequence up to that point in the query. The loop invariant ensures that as long as the loop continues, we have a “candidate” for a full match, making it valid to continue checking the subsequent letters.

So, if you loop through each query string and each pattern string, the loop invariant ensures that you can stop the loop early if at any point the invariant is violated. Otherwise, it guarantees that the sequence is still a potential match.

In this problem, the term “invariant” and “loop invariant” can be considered the same. Both refer to the condition that the uppercase letters in the pattern must appear in the same sequence in the query up to the point being considered. This condition must hold true at the start of each iteration for the loop to continue, serving as both a loop invariant and the general invariant for this problem’s logic.

Thought Process

  1. Pattern Matching: The problem involves finding if the sequence of uppercase letters in pattern can be found in the same sequence within the queries.

  2. String Manipulation: To verify the sequence, we need to traverse the string and match characters.

  3. Case Sensitivity: Uppercase letters are the cues. Lowercase letters can be ignored or considered as gaps between the uppercase letters.

  4. Iterate Over Array: Since we have multiple queries, we’ll need a loop to iterate over each.

  5. Result Array: We have to return a boolean array, meaning we’ll create an empty array to store True or False values for each query.

Code:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11

def camelMatch(queries, pattern):
    def isMatch(query, pattern):
        i = 0
        for char in query:
            if i < len(pattern) and char == pattern[i]:
                i += 1
            elif char.isupper():
                return False
        return i == len(pattern)

    return [isMatch(query, pattern) for query in queries]

Explanation:

  1. Helper Function isMatch: Checks whether a single query string matches the pattern.

    • i Variable: Keeps track of the position in pattern that we’re trying to match.

    • Inner Loop: Goes through each character (char) in the query.

      • If char matches the current pattern character (pattern[i]), we move to the next character in pattern (increment i).

      • If char is an uppercase letter that does not match the current pattern character, the query doesn’t match the pattern.

  2. Main Function camelMatch: Returns a list comprehension that runs isMatch for each query in queries.

Cues and Insights:

  • Uppercase Letters: They act as anchors or checkpoints in the pattern.

  • Lowercase Letters: They are flexible and can appear anywhere between the uppercase letters.

  • Boolean Array: The problem requires a True or False for each query, making it suitable for list comprehension.

By iterating through each query and pattern in this way, the algorithm effectively solves the problem with time complexity (O(n \times m)), where (n) is the number of queries and (m) is the length of each query.

Establishing Preconditions and Postconditions

1. Parameters:

  • Inputs: The inputs to the camelMatch method are queries and pattern.
  • Types:
    • queries is a list of strings.
    • pattern is a string.
  • Context:
    • queries represents the array of strings we need to match against pattern.
    • pattern is the string whose uppercase characters should appear in the same order in each query.

2. Preconditions:

  • State of Program: No specific state is required.
  • Constraints:
    • 1 <= pattern.length, queries.length <= 100
    • 1 <= queries[i].length <= 100
    • Both queries[i] and pattern consist of English letters.

3. Method Functionality:

  • Expected to Do: The method is expected to return a boolean array where each element is True if the corresponding query matches the pattern, and False otherwise.
  • Interaction: The method processes the queries and pattern to produce a boolean array that fulfills the problem constraints.

4. Postconditions:

  • State of Program: The program state is unchanged (the function is pure).
  • Return Value: The return value is a boolean array, where each element indicates whether the corresponding query in queries matches pattern.
  • Side Effects: None, the function doesn’t modify any external state.

5. Error Handling:

  • Preconditions Not Met: The constraints are assumed to be upheld based on the problem description. The function doesn’t include explicit error handling for these.
  • Response: If the constraints were not to be met, Python would naturally throw an exception (e.g., IndexError), but this is not expected given the constraints.

Problem Decomposition

1. Problem Understanding:

  • In My Own Words: The problem is about checking if a list of queries matches a given pattern. A query matches the pattern if we can insert lowercase characters in the pattern so that it equals the query. The output is a boolean list where each entry signifies if the corresponding query matches the pattern.
  • Key Components: Queries list, pattern string, and the rules for matching.

2. Initial Breakdown:

  • Major Parts:
    1. Input Parsing: Read the queries and pattern.
    2. Initialization: Prepare a list to store boolean results.
    3. Pattern Matching: Process each query to check if it matches the pattern.

3. Subproblem Refinement:

  • Pattern Matching:
    1. Iterate through each query and pattern character.
    2. Compare and track uppercase characters.
    3. Confirm lowercase characters can be inserted to make the pattern equal to the query.

4. Task Identification:

  • Reusable Tasks:
    • Character comparison and tracking can be generalized.

5. Task Abstraction:

  • Abstracted Enough: Yes, tasks like ‘Character Comparison’ are abstract enough to be understood in the problem’s context but are also reusable.

6. Method Naming:

  • Names:
    • parseInput for Input Parsing.
    • initializeResultList for Initialization.
    • matchPattern for Pattern Matching.
    • compareCharacters for Character Comparison.

7. Subproblem Interactions:

  • Interaction:
    • Input Parsing comes first, followed by Initialization.
    • Each query is then processed by matchPattern.
  • Order:
    • Input Parsing -> Initialization -> Pattern Matching.
  • Dependencies:
    • matchPattern depends on the Initialization step to prepare the result list.

By understanding each of these aspects, we can gain a comprehensive view of the problem and strategize our approach to solving it.

From Brute Force to Optimal Solution

Brute Force Solution

In a brute-force approach, for each query, we could:

  1. Initialize an index i for the query and an index j for the pattern.
  2. Loop through each character in the query:
  • If query[i] matches pattern[j], increment j.
  • Else if query[i] is lowercase and j < len(pattern), continue.
  • Else, mark this query as not matching the pattern.

Here’s some Python code to illustrate this approach:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16

def camelMatch(queries, pattern):
    results = []
    for query in queries:
        i, j = 0, 0
        match = True
        while i < len(query):
            if j < len(pattern) and query[i] == pattern[j]:
                j += 1
            elif query[i].islower():
                pass
            else:
                match = False
                break
            i += 1
        results.append(match and j == len(pattern))
    return results

Inefficiencies:

  1. Time Complexity: For each query, we go through each character, making it O(N * M) where N is the total number of queries and M is the average length of a query.
  2. Space Complexity: We are using a constant amount of extra space, so it is O(1).

Optimizing the Solution

Step 1: Removing Unnecessary Checks

In the brute-force solution, there’s an elif query[i].islower() that does nothing. We can remove it.

Step 2: Use a Single Loop for Both Strings

Instead of one loop to iterate through the query, we could create one loop that iterates through both the query and the pattern. This may make the code cleaner and easier to understand.

Here’s the optimized code:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13

def camelMatch(queries, pattern):
    results = []
    for query in queries:
        j = 0
        match = True
        for char in query:
            if j < len(pattern) and char == pattern[j]:
                j += 1
            elif char.isupper():
                match = False
                break
        results.append(match and j == len(pattern))
    return results

Complexity Analysis

  1. Time Complexity: Still O(N * M) but with fewer unnecessary checks, making it slightly faster.
  2. Space Complexity: Still O(1).

As you can see, the optimizations did not dramatically change the time or space complexity, but they made the code cleaner and more straightforward. Sometimes, clarity and ease of understanding are valuable optimizations as well.

Code Explanation and Design Decisions

1. Initial Parameters

  • queries: A list of strings that represent the queries we need to check.
  • pattern: A string that contains the pattern we are looking for in the queries.

The parameters encapsulate the core of the problem—checking each query to see if it matches the given pattern.

2. Primary Loop

The primary loop iterates through each query in the queries list. Each iteration is focused on checking if a single query matches the pattern.

3. Conditions within the Loop

  • if j < len(pattern) and char == pattern[j]: Checks if the current character in the query matches the current character in the pattern.
  • elif char.isupper(): Checks if the current character is an uppercase letter but doesn’t match the pattern.

These conditions follow the constraints of the problem—matching the pattern while allowing for lowercase characters in between.

4. Updates to Parameters

  • j += 1: We increment j when we find a match in the pattern, so the next iteration focuses on the next character in the pattern.

These updates signify progression through the pattern and reflect a partial match between the pattern and the query so far.

5. Invariant

The invariant here is the index j. It maintains the position in the pattern that we are trying to match. This helps in ensuring that we are always checking the next character in the pattern, keeping the algorithm on track.

6. Final Output

The final output is a list of Boolean values corresponding to each query. True means the query matches the pattern, and False means it doesn’t. This list satisfies the problem’s requirements by indicating which queries match the pattern.

Coding Constructs

1. High-Level Strategies

The code uses a two-level iteration strategy: one loop to iterate through each query, and another loop within to iterate through each character in the current query. It uses conditional checks to determine if each query matches the given pattern.

2. Purpose to a Non-Programmer

This code checks if a series of text strings (“queries”) fit a particular pattern. It returns a list of yes/no answers, indicating whether each string matches the pattern or not.

3. Logical Elements

  • Iteration: Loops through the list of queries and through each character in the individual query.
  • Conditionals: Checks if characters match specific criteria.
  • Variables: Temporary storage to keep track of the position in the pattern.
  • Output List: Accumulates the results of each query check.

4. Algorithmic Approach in Plain English

For each query, we start at the beginning of the pattern. We go through every character in the query. If it matches the next character in the pattern, we proceed to the next character in both the query and the pattern. If it’s a lowercase letter that doesn’t match the pattern, we just move to the next character in the query. If it’s an uppercase letter that doesn’t match, the query fails to match the pattern. We repeat this for each query and save the results.

5. Key Steps on Input Data

  • Iterate over each query.
  • Within each query, iterate over each character.
  • Use conditionals to check if the query matches the pattern.
  • Record the match or non-match in the output list.

These steps are essential for checking each query against the pattern, following the rules of the problem statement.

6. Algorithmic Patterns

  • Nested Loop Iteration: For multiple levels of data (list of queries, characters in each query).
  • Conditionals: For logical decision-making.
  • Pointer/Index: To track position in the pattern string.
  • Accumulator Pattern: For collecting results in an output list.

Language Agnostic Coding Drills

1. Distinct Coding Concepts

  1. Variable Initialization: Setting up variables to store temporary values.
  2. Basic Looping: Iterating over a list or a string.
  3. Conditional Statements: Basic if, else statements.
  4. List Operations: Appending to a list.
  5. String Operations: Accessing individual characters from a string.
  6. Nested Looping: Placing one loop inside another.
  7. Index Tracking: Managing a separate index for two different loops.
  8. Boolean Operations: Handling boolean variables for conditional flags.
  9. Logical AND, OR Operations: Combining multiple conditions.
  10. Pattern Matching: Complex logic for string pattern matching.

2. Difficulty Classification

  1. Variable Initialization: Easy. Basic requirement for any code.
  2. Basic Looping: Easy. Core concept in almost all programming tasks.
  3. Conditional Statements: Easy. Vital for logical decision-making.
  4. List Operations: Easy. Extends variable usage to collections.
  5. String Operations: Moderate. Requires understanding strings as sequence types.
  6. Nested Looping: Moderate. Adds complexity due to multiple levels of iteration.
  7. Index Tracking: Moderate. Balancing two separate indices adds a layer of complexity.
  8. Boolean Operations: Moderate. Understanding True and False in logical flow.
  9. Logical AND, OR Operations: Hard. Requires precise logical thinking.
  10. Pattern Matching: Hard. Complex logic involving multiple conditions and loops.

3. Problem-Solving Approach

  1. Variable Initialization: Begin by initializing variables to keep track of the pattern index and result list.

  2. Basic Looping: Iterate over the list of queries to apply the pattern matching logic to each one.

  3. Conditional Statements: Within the loop, make basic checks to determine the type of the current character in the query (uppercase or lowercase).

  4. List Operations: Create an empty list to store results.

  5. String Operations: Within each iteration, you’ll need to extract individual characters from both the query and the pattern strings.

  6. Nested Looping: Inside the loop iterating through queries, introduce another loop to go through the characters in the current query.

  7. Index Tracking: Maintain a separate index for the pattern. Update this index only when a character from the query matches the corresponding character in the pattern.

  8. Boolean Operations: Introduce a boolean flag that indicates whether the current query matches the pattern. Update this flag based on the conditions met.

  9. Logical AND, OR Operations: Use these to combine multiple conditions when checking if a character in the query matches the character in the pattern.

  10. Pattern Matching: The ultimate goal is to assemble all these drills to complete the pattern-matching logic. Combine loops, conditionals, and index tracking to match each query against the pattern.

Each of these steps builds upon the previous, culminating in a comprehensive solution that addresses the problem statement.

Targeted Drills in Python

1. General Coding Drills in Python

  1. Variable Initialization

    1
2

    a = 10
b = "Hello"

  2. Basic Looping

    1
2

    for i in range(5):
    print(i)

  3. Conditional Statements

    1
2
3
4

    if a > 5:
    print("Greater")
else:
    print("Smaller")

  4. List Operations

    1
2
3

    my_list = []
my_list.append(1)
my_list.append(2)

  5. String Operations

    1
2

    my_string = "Hello"
first_char = my_string[0]

  6. Nested Looping

    1
2
3

    for i in range(3):
    for j in range(2):
        print(i, j)

  7. Index Tracking

    1
2
3
4

    i, j = 0, 0
while i < 5 and j < 3:
    i += 1
    j += 1

  8. Boolean Operations

    1
2
3

    flag = True
if flag:
    print("Flag is True")

  9. Logical AND, OR Operations

    1
2

    if a > 5 and b == "Hello":
    print("Both conditions met")

  10. Pattern Matching

    1
2
3
4

    string = "abc"
pattern = "a*c"
if string[0] == pattern[0] and string[-1] == pattern[-1]:
    print("Pattern matched")

2. Problem-Specific Drills

  • String Comparison with Index
    1
2
3
4

    pattern = "Aa"
query = "aA"
if pattern[0].lower() == query[0].lower():
    print("First letter matches")
    This is essential for our problem to compare characters in a case-insensitive way.

3. Assembling the Drills

  1. Initialize variables to store your pattern index and result list (Drill 1).
  2. Iterate over the list of queries (Drill 2).
  3. In each iteration, compare the current character’s type in the query and pattern (Drills 3, 5).
  4. Create an empty list to store intermediate results (Drill 4).
  5. Extract individual characters from the query and pattern strings for comparison (Drill 5).
  6. Use a nested loop to go through the characters in the current query (Drill 6).
  7. Maintain a separate index for the pattern (Drill 7).
  8. Use a boolean flag to indicate match status (Drill 8).
  9. Use logical AND, OR to combine multiple conditions (Drill 9).
  10. Assemble all these drills to complete the pattern-matching logic (Drills 5, 10, and the problem-specific drill).

By putting these drills together in the specified sequence and adding proper conditional checks, you can build a complete solution for the initial problem.

Q&A

Similar Problems

Here are 10 problems that involve similar underlying concepts to the problem we’ve discussed:

  1. Two Sum: This problem involves iterating through an array and using a data structure to store intermediate results, similar to our use of a list to store intermediate matching characters.

  2. Valid Parentheses: Like our pattern matching, this problem involves checking for patterns (open and close parentheses) in a sequence.

  3. Longest Substring Without Repeating Characters: This problem requires keeping track of indices and involves string manipulation, much like our original problem.

  4. Reverse Integer: Involves number manipulation and keeping track of individual digits, somewhat akin to how we kept track of individual characters in the strings.

  5. Palindrome Number: This problem requires you to extract individual digits and compare them, similar to our requirement to extract individual characters for comparison.

  6. Roman to Integer: Involves pattern matching and conversion, like our problem where we matched string patterns.

  7. Longest Common Prefix: Requires character-by-character comparison across multiple strings, similar to how we compared characters in individual strings.

  8. Valid Anagram: Involves character count and comparison, which is somewhat similar to our pattern matching and character comparison.

  9. Contains Duplicate: This problem involves iterating over a list and keeping track of elements using a data structure, similar to how we kept track of matched characters.

  10. First Unique Character in a String: This problem also involves iterating over a string and maintaining a record of characters, similar to what was required in our problem.

These involve similar concepts like iteration, index tracking, pattern matching, and character/string manipulation.