What is the space complexity of LeetCode 1415. The k-th Lexicographical String of All Happy Strings of Length n?

The Python solution on this page uses O(n) auxiliary space.

The k-th Lexicographical String of All Happy Strings of Length n — LeetCode 1415 Python Solution

MediumStringBacktracking

Problem: #1415
Pattern: Backtracking
Reading time: 3 min
Source: leetcode.com

The problem

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).

Example

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".

Python solution

Python

class Solution:
    def getHappyString(self, n: int, k: int) -> str:
        def dfs():
            if len(s) == n:
                ans.append("".join(s))
                return
            if len(ans) >= k:
                return
            for c in "abc":
                if not s or s[-1] != c:
                    s.append(c)
                    dfs()
                    s.pop()

        ans = []
        s = []
        dfs()
        return "" if len(ans) < k else ans[k - 1]

Complexity

Measure	Complexity
Time	O(n \times 2^n)
Space	O(n) auxiliary

Pattern: Backtracking

Build candidates one choice at a time and abandon a branch the moment it cannot work. LeetCode 1415. The k-th Lexicographical String of All Happy Strings of Length n is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Backtracking.

The backtracking guide has the Python template for the pattern and the 105 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1415. The k-th Lexicographical String of All Happy Strings of Length n?: LeetCode 1415. The k-th Lexicographical String of All Happy Strings of Length n is rated Medium on LeetCode.
What is the time complexity of LeetCode 1415. The k-th Lexicographical String of All Happy Strings of Length n?: The Python solution on this page runs in O(n \times 2^n).
What is the space complexity of LeetCode 1415. The k-th Lexicographical String of All Happy Strings of Length n?: The Python solution on this page uses O(n) auxiliary space.
What topics does LeetCode 1415. The k-th Lexicographical String of All Happy Strings of Length n cover?: LeetCode 1415. The k-th Lexicographical String of All Happy Strings of Length n is tagged String and Backtracking on LeetCode.