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247. Strobogrammatic Number II πŸ”’

Description

Given an integer n, return all the strobogrammatic numbers that are of length n. You may return the answer in any order.

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

 

Example 1:

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

Example 2:

Input: n = 1
Output: ["0","1","8"]

 

Constraints:

  • 1 <= n <= 14

Solutions

Solution 1: Recursion

If the length is $1$, then the strobogrammatic numbers are only $0, 1, 8$; if the length is $2$, then the strobogrammatic numbers are only $11, 69, 88, 96$.

We design a recursive function $dfs(u)$, which returns the strobogrammatic numbers of length $u$. The answer is $dfs(n)$.

If $u$ is $0$, return a list containing an empty string, i.e., [""]; if $u$ is $1$, return the list ["0", "1", "8"].

If $u$ is greater than $1$, we traverse all the strobogrammatic numbers of length $u - 2$. For each strobogrammatic number $v$, we add $1, 8, 6, 9$ to both sides of it, and we can get the strobogrammatic numbers of length u.

Note that if $u \neq n$, we can also add $0$ to both sides of the strobogrammatic number.

Finally, we return all the strobogrammatic numbers of length $n$.

The time complexity is $O(2^{n+2})$.

Similar problems:

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class Solution:
    def findStrobogrammatic(self, n: int) -> List[str]:
        def dfs(u):
            if u == 0:
                return ['']
            if u == 1:
                return ['0', '1', '8']
            ans = []
            for v in dfs(u - 2):
                for l, r in ('11', '88', '69', '96'):
                    ans.append(l + v + r)
                if u != n:
                    ans.append('0' + v + '0')
            return ans

        return dfs(n)

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class Solution {
    private static final int[][] PAIRS = {{1, 1}, {8, 8}, {6, 9}, {9, 6}};
    private int n;

    public List<String> findStrobogrammatic(int n) {
        this.n = n;
        return dfs(n);
    }

    private List<String> dfs(int u) {
        if (u == 0) {
            return Collections.singletonList("");
        }
        if (u == 1) {
            return Arrays.asList("0", "1", "8");
        }
        List<String> ans = new ArrayList<>();
        for (String v : dfs(u - 2)) {
            for (var p : PAIRS) {
                ans.add(p[0] + v + p[1]);
            }
            if (u != n) {
                ans.add(0 + v + 0);
            }
        }
        return ans;
    }
}

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class Solution {
public:
    const vector<pair<char, char>> pairs = {{'1', '1'}, {'8', '8'}, {'6', '9'}, {'9', '6'}};

    vector<string> findStrobogrammatic(int n) {
        function<vector<string>(int)> dfs = [&](int u) {
            if (u == 0) return vector<string>{""};
            if (u == 1) return vector<string>{"0", "1", "8"};
            vector<string> ans;
            for (auto& v : dfs(u - 2)) {
                for (auto& [l, r] : pairs) ans.push_back(l + v + r);
                if (u != n) ans.push_back('0' + v + '0');
            }
            return ans;
        };
        return dfs(n);
    }
};

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func findStrobogrammatic(n int) []string {
    var dfs func(int) []string
    dfs = func(u