247. Strobogrammatic Number II

Problem:
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.
Example:
Input:  n = 2
Output: ["11","69","88","96"]


Analysis:
找规律： 
n = 0: ""
n = 1: 0, 1, 8
n = 2: 88, 69, 11, 96
n = 3: 808, 609, 101, 906， 818, 619, 111, 916, 888, 689, 181, 986
可以发现n是在n-2的基础上开头和结尾都同时加上strobogrammatic对。如果n是要求的长
度那么还需要排除0.


Solution:


这里第二个parameter的目的就是为了排除leading and tailing zeroes. 








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class Solution {
    public List<String> findStrobogrammatic(int n) {
        return helper(n, n);
    }
    
    private List<String> helper(int n, int m) {
        if (n == 0) return new ArrayList<>(Arrays.asList(""));
        if (n == 1) return new ArrayList<>(Arrays.asList("0", "1", "8"));
        
        List<String> prev = helper(n - 2, m);
        List<String> res = new ArrayList<>();
        for (String num: prev) {
            if (n != m) res.add("0" + num + "0");
            res.add("8" + num + "8");
            res.add("6" + num + "9");
            res.add("1" + num + "1");
            res.add("9" + num + "6");
        }
        return res;
    }
}













































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