Fold and Find

We’re interested in determining whether a given string consists of repeated substrings. This problem can be approached in different ways, but one unique approach is to “fold” the string by concatenating it to itself (excluding the last character), and then search for the original string within this new string. If the original string appears more than once, it means that the string consists of repeated substrings.

Description

The concept of finding a repeated substring pattern can be visualized by the following steps:

1. Fold: Concatenate the original string with itself, excluding the first and last characters.
2. Find: Look for the original string within this new “folded” string.
3. If the original string is found, then it consists of repeated substrings.

Tabular Representation

Here’s a table to represent the “fold” operation for the given string “abab”:

1. Original String: The original string is “abab”.
2. Remove the First Character: This step involves taking the original string, excluding the first character, which results in “bab”.
3. Remove the Last Character: This step involves taking the original string, excluding the last character, which results in “aba”.
4. Concatenate the Above Two (excluding first&last): Finally, the strings from steps 2 and 3 are concatenated together to form “bababa”.

The purpose of this “fold” operation is to create a new string in which we will look for the original string. If the original string appears within this new string, it confirms that the original string consists of repeated substrings.

Solution

Below are the code implementations for this “fold and find” approach in Java, C++, and Python.

Java:

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public class FoldAndFind {
    public static boolean repeatedSubstringPattern(String s) {
        String folded = s.substring(1) + s.substring(0, s.length() - 1);
        return folded.contains(s);
    }

    public static void main(String[] args) {
        String str = "abab";
        System.out.println(repeatedSubstringPattern(str)); // Output: true
    }
}

C++

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#include <iostream>
#include <string>

bool repeatedSubstringPattern(const std::string &s) {
    std::string folded = s.substr(1) + s.substr(0, s.size() - 1);
    return folded.find(s) != std::string::npos;
}

int main() {
    std::string str = "abab";
    std::cout << std::boolalpha << repeatedSubstringPattern(str); // Output: true
    return 0;
}

Python

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def repeated_substring_pattern(s):
    folded = s[1:] + s[:-1]
    return s in folded

str = "abab"
print(repeated_substring_pattern(str))  # Output: True

Key Takeaways

• The “fold and find” approach is a unique method to determine if a string consists of repeated substrings.
• By concatenating the string to itself (excluding the first and last characters) and searching for the original string within this new string, one can quickly determine if the original string is made of repeated substrings.
• This approach is efficiently implemented using built-in string manipulation methods in different programming languages.

Here is the content on Fold and Find following the requested structure:

Fold and Find

Description

Fold and find refers to a technique of iteratively combining elements of a data structure with a function to locate a desired element.

For example, to find the maximum value in an array, we can compare and fold elements two at a time to narrow down on the max element.

On each fold, we apply a function like max() on pairs of elements to find the local max, thereby folding the search space in half.

After repeated folds, we eventually isolate the global maximum element. This divide and conquer approach improves efficiency.

Solution

Here is an implementation to find the maximum value in an array:

Java

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int foldFindMax(int[] arr) {
  int n = arr.length;
  int max = 0;

  for(int i=0; i<n/2; i++) {
    max = Math.max(max, Math.max(arr[2*i], arr[2*i+1])); 
  }

  if (n % 2 != 0) {
    max = Math.max(max, arr[n-1]);
  }

  return max;
}

C++

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int foldFindMax(vector<int> arr) {
  int n = arr.size();
  int max = 0;

  for(int i=0; i<n/2; i++) {
    max = std::max(max, std::max(arr[2*i], arr[2*i+1]));
  }

  if (n % 2 != 0) {
    max = std::max(max, arr[n-1]); 
  }

  return max;
}

Python

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def fold_find_max(arr):
  
  n = len(arr)
  max_elem = 0

  for i in range(n//2):
    max_elem = max(max_elem, max(arr[2*i], arr[2*i+1]))

  if n % 2 != 0:
    max_elem = max(max_elem, arr[n-1])

  return max_elem

This iteratively folds the array by applying max() function to reduce search space in half at each step.

Fold and find can apply to various functions beyond finding max element.