The HackerRank Caesar's Cipher problem tells us that Julius Caesar encrypted his confidential information using a cipher. Caesar's cipher shifts each letter by a number of letters. The cipher only encrypts letters, not symbols.

Example

Original alphabet

abcdefghijklmnopqrstuvwxyz;

Alphabet rotated by 3 letters

defghijklmnopqrstuvwxyzabc;

If the shifting of the letters goes past the end of the alphabet, we are told to just rotate back to the front of the alphabet. In the case of a rotation by 3, w, x, y and z would map to z, a, b and c.

We are asked to define a caesarCipher function that receives a string of characters and an integer that represents the alphabet rotation factor. This function should return the encrypted string.

Pseudo code solution

1. Define a string containing all lowercase alphabet characters.
2. Define a string containing all uppercase alphabet characters.
3. Map over the characters in the input string.
   • If the current character is in the string of lowercase characters, find its position in the string and add 3 to it. Use the remainder operator to ensure that this addition does not exceed the 26 positions in the string.
   • If the current character is in the string of uppercase characters, find its position in the string and add 3 to it. Use the remainder operator to ensure that this addition does not exceed the 26 positions in the string.
   • If it's not an alphabetical character, return it as-is.
4. Return a string representation of the array of characters returned by mapping over the input string.

Code solution

function caesarCipher(s, k) {
  const lowerA = 'abcdefghijklmnopqrstuvwxyz';
  const upperA = lowerA.toUpperCase();

  const res = s.split('').map((c) => {
    if (lowerA.includes(c)) {
      return lowerA[(lowerA.indexOf(c) + k) % 26];
    } else if (upperA.includes(c)) {
      return upperA[(upperA.indexOf(c) + k) % 26];
    } else {
      // any other characters
      return c;
    }
  });

  return res.join('');
}

If indexOf(c) is 25 and k is 2, adding them gives us 27, which exceeds the 26-character alphabet. Therefore, we applied the remainder operator to clamp the addition operation to 26 (27 % 26 = 1).

Test cases

Let's test the caesarCipher function above with the following test case.

console.log(caesarCipher('middle-Outz', 2)); // okffng-Qwvb;

The result is what we expect. The special hyphen character in the string is left as-is. The capital O in the string becomes Q after adding a k of 2 to it. Lastly, manually moving each lowercase character ahead by a k of 2 helps us confirm that the cipher is correct.

Time and space complexity

The Big O time complexity of the solution is linear, or O(n), where n is the length of the input string. The solution used one loop that iterated over all the characters in the input string.

The Big O space complexity of the solution is linear, or O(26 * 2). The length of the lowerA string and the upperA string that we defined for our solution carries a space complexity of 2 times the length of the alphabet.