# ---
# title: 1415. The k-th Lexicographical String of All Happy Strings of Length n
# id: problem1415
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Backtracking
# link: <https://leetcode.com/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/description/>
# hidden: true
# ---
# 
# 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"
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: n = 2, k = 7
#     Output: ""
#     
# 
# **Example 5:**
# 
#     
#     
#     Input: n = 10, k = 100
#     Output: "abacbabacb"
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= n <= 10`
#   * `1 <= k <= 100`
# 
# 
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
