1415. The k-th Lexicographical String of All Happy Strings of Length n

Description

A happy string is a string that:

• consists only of letters of the set ['a', 'b', 'c'].
• s[i] != s[i + 1] for all values of i from 1 to s.length - 1 (string is 1-indexed).

For example, strings "abc", "ac", "b" and "abcbabcbcb" are all happy strings and strings "aa", "baa" and "ababbc" are not happy strings.

Given two integers n and k, consider a list of all happy strings of length n sorted in lexicographical order.

Return the kth string of this list or return an empty string if there are less than k happy strings of length n.

 

Example 1:

Input: n = 1, k = 3
Output: "c"
Explanation: The list ["a", "b", "c"] contains all happy strings of length 1. The third string is "c".

Example 2:

Input: n = 1, k = 4
Output: ""
Explanation: There are only 3 happy strings of length 1.

Example 3:

Input: n = 3, k = 9
Output: "cab"
Explanation: There are 12 different happy string of length 3 ["aba", "abc", "aca", "acb", "bab", "bac", "bca", "bcb", "cab", "cac", "cba", "cbc"]. You will find the 9th string = "cab"

 

Constraints:

• 1 <= n <= 10
• 1 <= k <= 100

 

Solutions

Solution: Backtracking

• Time complexity: O(2ⁿ)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number} n
 * @param {number} k
 * @return {string}
 */
const getHappyString = function (n, k) {
  const perCounts = Math.pow(2, n - 1);
  const totalCounts = 3 * perCounts;

  if (k > totalCounts) return '';
  const letters = ['a', 'b', 'c'];
  const happyStr = Array.from({ length: n }, () => '');

  const kthHappyString = index => {
    if (index >= n) {
      k -= 1;
      return k ? '' : happyStr.join('');
    }

    for (const letter of letters) {
      if (happyStr[index - 1] === letter) continue;

      happyStr[index] = letter;
      const result = kthHappyString(index + 1);

      if (result) return result;
    }

    return '';
  };

  return kthHappyString(0);
};