Print Numbers by Recursion

Print numbers from 1 to the largest number with N digits by recursion.

 Notice

It's pretty easy to do recursion like:

recursion(i) {
    if i > largest number:
        return
    results.add(i)
    recursion(i + 1)
}

however this cost a lot of recursion memory as the recursion depth maybe very large. Can you do it in another way to recursive with at most N depth?

Example

Given N = 1, return [1,2,3,4,5,6,7,8,9].

Given N = 2, return[1,2,3,4,5,6,7,8,9,10,11,12,...,99].

Runtime: 179ms.

class Solution {
public:
    /**
     * @param n: An integer.
     * return : An array storing 1 to the largest number with n digits.
     */
    vector<int> numbersByRecursion(int n) {
        // write your code here
        vector<int> result;
        if (n <= 0) return result;
        
        printNumbers(result, 0, n);
        return result;
    }
    
private:
    void printNumbers(vector<int>& result, int depth, int n) {
        if (depth >= n) return;
        
        int copyNumber = result.size();
        for (int i = 1; i <= 9; i++) {
            int base = i * pow(10, depth);
            result.push_back(base);
            for(int j = 0; j < copyNumber; j++) {
                result.push_back(base + result[j]);
            }
        }
        printNumbers(result, depth + 1, n);
    }
};