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The idea is to perform a depth-first search (DFS) to generate numbers in lexicographical order. Starting from the number 1, we explore all numbers that can be formed by appending digits from 0 to 9 as long as the generated number is less than or equal to n. If we reach a number greater than n, backtrack and explore the next number at the same level and repeat the process.
Time Complexity: O(n), Space Complexity: O(1) (excluding the output array).
1def dfs(current, n, result):
2 if current > n:
3 return
4 result.append(current)
5 for i in range(10):
6 if current * 10 + i > n:
7 return
8 dfs(current * 10 + i, n, result)
9
10def lexicalOrder(n):
11 result = []
12 for i in range(1, 10):
13 dfs(i, n, result)
14 return result
15
16n = 13
17print(lexicalOrder(n))This Python implementation leverages a result list and recursively calls dfs to append lexicographically ordered numbers until the bounds are met.
This iterative approach attempts to simulate the depth-first search behavior using an iterative procedure. It begins by using a number and incrementally moving to the next lexicographical number by clever digit manipulations. If a number reaches an immediate boundary, it backs off accordingly to stay within valid digits.
Time Complexity: O(n), Space Complexity: O(1) (ignoring return array).
1
This JavaScript code incrementally generates numbers in an iterative method, utilizing logic to manage the progression through potential lexicographical candidates, and adjusts internally to maintain bounds.