Repeated Substring Pattern

In this problem, you need to find out whether the input string can be created by repeating a substring. One of the simplest ways to approach this problem is by iterating through all possible substring lengths. For each length, you check whether the string can be constructed by repeating the substring of that length. If it can, you return True. If no such substring is found after checking all lengths, you return False.

Python solution:

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class Solution:
    def repeatedSubstringPattern(self, s: str) -> bool:
        n = len(s)

        for i in range(1, n//2 + 1):
            if n % i == 0:
                if s[:i] * (n // i) == s:
                    return True

        return False

In this code, the for loop iterates over possible lengths for the substring. The if n % i == 0: condition checks whether the length of the string is divisible by the current substring length. If it is, it checks whether the string is equal to the substring repeated n // i times. If these conditions are met, it means the string can be constructed by repeating the substring and the function returns True. If no such substring is found after the loop, the function returns False. This approach leverages the fact that if a string is composed of multiple repetitions of a substring, the length of the entire string will be a multiple of the length of the substring.

Fold and Find

If s = ‘abcd’, then s[1:] is ‘bcd’ and s[:-1] is ‘abc’. When you concatenate these two strings, you get ‘bcdabc’, not ‘bcdbc’.

To solve this problem using Fold and Find methods, we can use a Pythonic approach.

The idea is to duplicate the string, and then search for the original string starting from the second character till the end of the duplicated string minus 1. This is because if the original string is a repeated substring pattern, it will always appear at least twice in the new string. The extra characters in the new string (1st and last) make sure that we don’t consider the original string itself.

Here is how we can implement it:

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def repeatedSubstringPattern(s):
    return s in (s + s)[1:-1]

Let’s understand the rationale behind this approach.

If the input string s consists of a repeated pattern, when we append s to itself, s should be found somewhere within the new string. However, s at the start and the end of the new string are the original s we appended. To exclude these two instances, we slice the new string from index 1 to -1 (excluding the first and last character) and then search for s within this sliced string. If s is found, it means s consists of a repeated substring pattern.

This algorithm works under the concept of “Fold” (where we fold the string into two halves) and “Find” (where we find if the original string exists in the folded string).

In Ruby, we can achieve the “Fold and Find” methodology using string concatenation and the include? method, which checks if a particular substring is present in a given string.

Here is the equivalent Ruby code:

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def repeatedSubstringPattern(s)
    ((s + s)[1..-2]).include? s
end

This Ruby code concatenates the string s with itself, then removes the first and last characters of the resulting string by using the [1..-2] range. This new string is checked for the inclusion of the original string s using the include? method.

If s is found, the include? method will return true, meaning s is a repeated substring pattern. Otherwise, it will return false.

Drills

Exercise 1: String slicing in Python

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def slice_string(s, start, end):
    return s[start:end]

# test the function
print(slice_string("Hello, world!", 0, 5))  # expected output: "Hello"

Exercise 2: Understanding the modulus operation

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def is_divisible(n, m):
    return n % m == 0

# test the function
print(is_divisible(10, 5))  # expected output: True
print(is_divisible(10, 3))  # expected output: False

Exercise 3: String repetition in Python

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def repeat_string(s, n):
    return s * n

# test the function
print(repeat_string("abc", 4))  # expected output: "abcabcabcabc"

Remember to test these exercises with different inputs to make sure you understand how they work. After that, you can integrate these concepts to create the final solution for the problem.

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class Solution:
    def repeatedSubstringPattern(self, s: str) -> bool:
        size = len(s)

        postfix = s[1:size]
        prefix = s[0:size-1]

        s_fold = postfix + prefix

        return s in s_fold

In this Python code, we use Python’s built-in string slicing to get the prefix and postfix of the string. The in keyword in Python checks if a substring exists within another string. If it does, it returns True; otherwise, it returns False.

Problem Classification

Problem Classification:

This problem can be classified under String Manipulation and Pattern Recognition.

What and How:
- What: Determine if a given string can be formed by repeating a substring.
- How: This is typically done by looking for patterns in the string or through the use of string manipulation techniques.
What-centric Classification:

If we only focus on the “what” (needs to be done) from the problem statement, we could classify this problem as a Pattern Recognition problem. This is because the core task is to recognize a pattern (the repeating substring) within the string.

Language Agnostic Coding Drills

Understanding Basic Data Types (String): Before jumping into any operation, it’s important to understand the data type that we are dealing with. In this case, we are dealing with strings which are a sequence of characters.
Understanding Length of Strings: The len() function in Python returns the length of a given string. This is a basic operation to perform on strings.
Understanding String Slicing: Slicing in Python is a feature that enables accessing parts of sequences like strings. In Python, indexing syntax can be used as a substitute for the slice object. This is an easy and convenient way to slice a string both syntax wise and execution wise.
String Concatenation: Combining of two or more strings. Python allows for string concatenation using the ‘+’ operator.
Understanding String Membership Test: We can test if a substring exists within a string or not, using the keyword in.

The problem solving approach for this problem is:

First, calculate the length of the string s using the len() function.
Next, create two substrings - postfix and prefix. The postfix is created by slicing s from the second character to the end. The prefix is created by slicing s from the start up to the second last character.
Create a new string s_fold by concatenating postfix and prefix.
Finally, check if the original string s is present in the new string s_fold. If it is, return True; else return False. This will tell us if the string s can be constructed by repeating a substring of itself.

Targeted Drills in Python

Understanding Basic Data Types (String): The first step is to understand how to create and manipulate strings.
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s = "Hello, world!" print(s)
Understanding Length of Strings: Learn to use the len() function to measure the length of a string.
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s = "Hello, world!" print(len(s))
Understanding String Slicing: Learn to slice strings, which is essentially when you take a subset of the string and create a new string.
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s = "Hello, world!" print(s[1:5]) # This will print "ello"

String Concatenation: Learn to combine two strings into one.

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s1 = "Hello"
s2 = ", world!"
s3 = s1 + s2
print(s3)  # This will print "Hello, world!"

Understanding String Membership Test: Learn to check whether a string is a substring of another string.
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s1 = "world" s2 = "Hello, world!" print(s1 in s2) # This will print "True"

For the specific problem, you can practice creating substrings, combining them, and checking for membership:

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s = "abcabcabc"
postfix = s[1:]
prefix = s[:-1]
s_fold = postfix + prefix
print(s in s_fold)  # This will print "True"

These drills will help to develop the necessary skills to solve the problem at hand. The final solution then combines these drills to implement the given problem.