algoadvance

Given a string s, this is how you encrypt it:

1. Find the middle character of the string.
   • If the string has even length, consider the left middle character.
2. Append the middle character to the encrypted string.
3. Recursively encrypt the left substring and the right substring and append them to the encrypted string.

You need to implement a function that returns the encrypted string for the given input string s.

Example:

Input: s = "abc"
Output: "bac"

Input: s = "abcd"
Output: "bacd"

Clarifying Questions:

1. What should be the output for an empty string?
   • An empty string should return an empty string as output.
2. Can the string contain special characters and spaces?
   • Yes, the string may contain any valid character, including spaces and special characters.
3. Are there constraints on the length of the input string?
   • For the sake of this problem, let’s assume the length of the input string n falls within the reasonable limit to avoid deep recursion problems, for instance, 1 <= n <= 1000.

Strategy:

1. Base Case: If the string s is empty, return an empty string.
2. Recursive Case: Find the middle character.
   • For a string of length n, the middle character index is (n - 1) // 2.
3. Append the middle character to the result.
4. Recursively apply the same process on the left substring (s[:mid]) and the right substring (s[mid+1:]).
5. Concatenate the results appropriately and return.

Code:

def find_encrypted_string(s):
    if not s:
        return ""
    
    def encrypt(s):
        if len(s) == 0:
            return ""
        mid = (len(s) - 1) // 2
        return s[mid] + encrypt(s[:mid]) + encrypt(s[mid+1:])
    
    return encrypt(s)

Time Complexity:

• The time complexity involves breaking down the string recursively:
  • Each step reduces the problem size approximately by half.
  • This will lead to (O(n \log n)) complexity for processing each character in total, where (n) is the length of the input string.

This should efficiently handle the given constraints.

Let’s now consider a few test cases to validate our solution:

Test Cases:

print(find_encrypted_string("abc"))      # Expected Output: "bac"
print(find_encrypted_string("abcd"))     # Expected Output: "bacd"
print(find_encrypted_string("abcdefg"))  # Expected Output: "dbaecfg"
print(find_encrypted_string(""))         # Expected Output: ""
print(find_encrypted_string("a"))        # Expected Output: "a"

By running these tests, you can ensure the function works as expected.

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