Question

Formatted question description: https://leetcode.ca/all/247.html

 247	Strobogrammatic Number II

 A strobogrammatic number is a number that looks the same when rotated 180 degrees (looked at upside down).

 Find all strobogrammatic numbers that are of length = n.

 For example,
 Given n = 2, return ["11","69","88","96"]. // "00" not valid

 Hint:
 Try to use recursion and notice that it should recurse with n - 2 instead of n - 1.

 @tag-string

Algorithm

Let us first enumerate the cases where n is 0,1,2,3,4:

n = 0: none

n = 1: 0, 1, 8

n = 2: 11, 69, 88, 96

n = 3: 101, 609, 808, 906, 111, 619, 818, 916, 181, 689, 888, 986

n = 4: 1001, 6009, 8008, 9006, 1111, 6119, 8118, 9116, 1691, 6699, 8698, 9696, 1881, 6889, 8888, 9886, 1961, 6969, 8968, 9966

Pay attention to the observation of n=0 and n=2, you can find that the latter is based on the former, and the left and right sides of each number are increased by [1 1], [6 9], [8 8], [9 6]

Look at n=1 and n=3, it’s more obvious, increase [1 1] around 0, become 101, increase around 0 [6 9], become 609, increase around 0 [8 8] , Becomes 808, increases [9 6] to the left and right of 0, becomes 906, and then adds the four sets of numbers to the left and right sides of 1 and 8 respectively

In fact, it starts from the m=0 layer and adds layer by layer. It should be noted that when the n layer is added.

[0 0] cannot be added to the left and right sides, because 0 cannot appear at the beginning of two or more digits. In the process of recursive in the middle, it is necessary to add 0 to the left and right sides of the number.

Code

Java

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

public class Strobogrammatic_Number_II {

    public static void main(String[] args) {
        Strobogrammatic_Number_II out = new Strobogrammatic_Number_II();
        Solution s = out.new Solution();

        System.out.println(s.findStrobogrammatic(2));
    }

    class Solution {

        List<String> singleDigitList = new ArrayList<>(Arrays.asList("0", "1", "8")); // not char[], because List can direct return as result
        char[][] digitPair = { {'1', '1'}, {'8', '8'}, {'6', '9'}, {'9', '6'} }; // except '0', a special case

        public List<String> findStrobogrammatic(int n) {
            return dfs(n, n);
        }

        public List<String> dfs(int k, int n) {
            if (k <= 0) {
                return new ArrayList<String>(Arrays.asList(""));
            }
            if (k == 1) {
                return singleDigitList;
            }

            List<String> subList = dfs(k - 2, n);
            List<String> result = new ArrayList<>();

            for (String str : subList) {
                if (k != n) { // @note: cannot start with 0
                    result.add("0" + str + "0");
                }
                for (char[] aDigitPair : digitPair) {
                    result.add(aDigitPair[0] + str + aDigitPair[1]);
                }
            }

            return result;
        }
    }

}

All Problems

All Solutions