386. Lexicographical Numbers

Problem

Given an integer n, return all the numbers in the range [1, n] sorted in lexicographical order.

You must write an algorithm that runs in O(n) time and uses O(1) extra space. 

  Example 1:

Input: n = 13
Output: [1,10,11,12,13,2,3,4,5,6,7,8,9]

Example 2:

Input: n = 2
Output: [1,2]

  Constraints:

• 1 <= n <= 5 * 10^4

Solution

class Solution {
    public List<Integer> lexicalOrder(int n) {
        List<Integer> lst = new ArrayList<>();
        dfs(lst, n, 0);
        return lst;
    }

    private void dfs(List<Integer> lst, int n, int num) {
        for (int i = 0; i <= 9; i++) {
            int cur = 10 * num + i;
            // get rid of 0
            if (cur == 0) {
                continue;
            }
            // when larger than n, return to the previous level
            if (cur > n) {
                return;
            }
            lst.add(cur);
            dfs(lst, n, cur);
        }
    }
}

Explain:

nope.

Complexity:

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