1516 The K Th Lexicographical String Of All Happy Strings Of Length N
1516 The K Th Lexicographical String Of All Happy Strings Of Length N
The k-th Lexicographical String of All Happy Strings of Length n 
A happy string is a string that:
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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:
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**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:
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**Input:** n = 1, k = 4
**Output:** ""
**Explanation:** There are only 3 happy strings of length 1.
Example 3:
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**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:
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1 <= n <= 10
1 <= k <= 100
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class Solution:
def getHappyString(self, n: int, k: int) -> str:
"""
a ab abc abca abcb abcab abcac abcaba abcabc abcaca abcacb
"""
def recurse(s , n):
if n == 0:
return [s]
res = []
a1 , a2, a3 = [] , [], []
if s == "":
a1 = recurse( "a" , n - 1)
a2 = recurse( "b" , n - 1)
a3 = recurse( "c" , n - 1)
if len(s) > 0 and s[-1] == "a":
a1 = recurse( s + "b" , n - 1)
a2 = recurse( s + "c" , n - 1)
if len(s) > 0 and s[-1] == "b":
a1 = recurse( s + "a" , n - 1)
a2 = recurse( s + "c" , n - 1)
if len(s) > 0 and s[-1] == "c":
a1 = recurse( s + "a" , n - 1)
a2 = recurse( s + "b" , n - 1)
for n in a1:
res.append(n)
for n in a2:
res.append(n)
for n in a3:
res.append(n)
return res
x = recurse("", n)
#print(x)
return x[k-1] if k-1 < len(x) else ""
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