Shortest Palindrome

To solve the problem of converting the given string s into the shortest palindrome by adding characters in front of it, we need to find the longest palindrome that starts from the first character of s. Once we find it, we can simply reverse the remaining characters and add them to the beginning of s.

Here are the steps to solve the problem:

  1. Finding the Longest Palindrome Starting from the Beginning: We need to find the longest prefix of the string that is also a palindrome.

  2. Reverse the Remaining Part: Whatever part is remaining, reverse it and add it to the beginning of the string.

  3. Concatenation: The concatenation of the reversed remaining part and the original string s is the shortest palindrome we can get.

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class Solution:
    def shortestPalindrome(self, s: str) -> str:
        # Find the length of the longest palindrome starting at the beginning of s
        i = 0
        for j in range(len(s) - 1, -1, -1):
            if s[i] == s[j]:
                i += 1

        # If the whole string is a palindrome, simply return it
        if i == len(s):
            return s

        # Take the remaining part, reverse it, and concatenate it with the original string
        remaining = s[i:]
        return remaining[::-1] + self.shortestPalindrome(s[:i]) + s[i:]

Key Takeaways:

  • The key to solving this problem is to find the longest prefix that is also a palindrome.
  • Recursive approach here ensures that we are considering all the characters in the correct order.
  • The reversed remaining part is added to the beginning of the original string to form the shortest palindrome.

Identifying Problem Isomorphism

“Shortest Palindrome” can be mapped to “Longest Palindromic Substring”.

Reasoning:

Both problems are about palindromes and string manipulation. “Shortest Palindrome” requires us to find the shortest possible palindrome by adding characters in front of the original string. In contrast, “Longest Palindromic Substring” is about finding the longest palindromic substring within a given string.

“Shortest Palindrome” is more complex due to the requirement of adding characters to create the shortest palindrome. “Longest Palindromic Substring” simply requires finding a palindrome within the given string. Both problems, however, need a similar approach to identify palindromes within a string.

10 Prerequisite LeetCode Problems

“Shortest Palindrome” requires understanding of string manipulation, prefix function computation, and potentially even knowledge of algorithms like KMP (Knuth–Morris–Pratt). Here are some simpler problems to prepare for it:

  1. 125. Valid Palindrome: Basic problem for checking if a string is a palindrome or not.

  2. 680. Valid Palindrome II: An extension of the previous problem, allows deletion of a character.

  3. 5. Longest Palindromic Substring: A problem that introduces the concept of expanding around center for palindrome problems.

  4. 647. Palindromic Substrings: Another problem to reinforce the concept of expanding around center.

  5. 409. Longest Palindrome: Problem to understand how to build a palindrome from given characters.

  6. 132. Palindrome Partitioning II: Problem on finding minimum cuts for palindromes, introduction to dynamic programming with palindromes.

  7. 516. Longest Palindromic Subsequence: Problem on palindromic subsequences, shows how dynamic programming can be used with palindromes.

  8. 214. Shortest Palindrome: A harder problem related to palindromes and prefix computation.

  9. 1392. Longest Happy Prefix: A hard problem that introduces the concept of prefix function computation, a necessary step for the efficient solution of “Shortest Palindrome”.

  10. 28. Implement strStr(): A classic problem that is usually solved using the KMP algorithm, can serve as an introduction to KMP.

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def shortestPalindrome(self, s: str) -> str:
    if s=="": return ""
    if s==s[::-1]: return s

    for i in range(len(s)-1, -1, -1):
        if(s[:i]==s[:i][::-1]):
            to_add = s[i:][::-1]
            break
    return to_add+s

Problem Classification

You are given a string s. You can convert s to a palindrome by adding characters in front of it.

Return the shortest palindrome you can find by performing this transformation.

Example 1:

Input: s = “aacecaaa” Output: “aaacecaaa” Example 2:

Input: s = “abcd” Output: “dcbabcd”

Constraints:

0 <= s.length <= 5 * 104 s consists of lowercase English letters only.

Language Agnostic Coding Drills

  1. Understanding the problem and data structures used: The problem requires us to identify the shortest palindrome by adding characters at the start of the given string. A palindrome is a word that is the same forward and backward. The basic data structure used here is a string.

  2. String slicing and manipulation: Strings in Python can be sliced in various ways to obtain the desired parts. In this problem, we are using slicing to get parts of the string and reverse them. This includes understanding how to use slice notation in Python to create substrings.

  3. Understanding of iteration and loops: A loop is used to iterate through the string in reverse order. Understanding how to use the range function to create a reverse sequence is important.

  4. Understanding of conditional statements: If statements are used to check whether a string is a palindrome and to break out of the loop once the shortest palindrome has been found.

  5. Problem-solving approach:

    a. Check if the string is empty or is already a palindrome. If so, return the string. b. Iterate through the string in reverse order starting from the last character. c. In each iteration, check if the current substring (from the start to the current index) is a palindrome. d. If it is, record the characters from the current index to the end of the string, reverse them, and break out of the loop. e. Finally, append the reversed characters to the original string and return the result. This will be the shortest palindrome that can be created by adding characters to the start of the string.

Targeted Drills in Python

  1. Understanding the problem and data structures used:

    In Python, a string is a sequence of Unicode characters. You can create a string in Python using single, double, or triple quotes. Let’s create a string and print it:

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    s = "Hello, world!"
print(s)

  2. String slicing and manipulation:

    In Python, strings are arrays of bytes representing Unicode characters. We can use square brackets to access elements of the string.

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    s = "Hello, world!"
print(s[2:5])  # Prints "llo"
print(s[::-1])  # Prints "!dlrow ,olleH"

  3. Understanding of iteration and loops:

    Python has two primitive loop commands - for loops and while loops. A for loop is used for iterating over a sequence. A range function generates a sequence of numbers, which can be used to iterate over with for loop.

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    for i in range(5, -1, -1):
    print(i)

    This will print numbers from 5 to 0.

  4. Understanding of conditional statements:

    Python supports the usual logical conditions from mathematics. If statements are written by using the if keyword.

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    a = 50
b = 100
if b > a:
    print("b is greater than a")

  5. Problem-solving approach:

    Here’s the code that creates the shortest palindrome by adding characters at the start of the given string. The steps are the same as described in the previous response.

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    def shortest_palindrome(s):
    if s == "" or s == s[::-1]: 
        return s

    for i in range(len(s) - 1, -1, -1):
        if s[:i] == s[:i][::-1]:
            to_add = s[i:][::-1]
            break
    return to_add + s

print(shortest_palindrome("abcd"))  # Output: "dcbabcd"