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package g0301_0400.s0386_lexicographical_numbers;

// #Medium #Depth_First_Search #Trie #2022_07_13_Time_4_ms_(93.65%)_Space_57.2_MB_(30.81%)

import java.util.ArrayList;
import java.util.List;

/**
 * 386 - Lexicographical Numbers\.
 *
 * Medium
 *
 * 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 * 104
**/
public class Solution {
    public List lexicalOrder(int n) {
        List lst = new ArrayList<>();
        dfs(lst, n, 0);
        return lst;
    }

    private void dfs(List 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);
        }
    }
}




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