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248. Strobogrammatic Number III πŸ”’

Description

Given two strings low and high that represent two integers low and high where low <= high, return the number of strobogrammatic numbers in the range [low, high].

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

 

Example 1:

Input: low = "50", high = "100"
Output: 3

Example 2:

Input: low = "0", high = "0"
Output: 1

 

Constraints:

  • 1 <= low.length, high.length <= 15
  • low and high consist of only digits.
  • low <= high
  • low and high do not contain any leading zeros except for zero itself.

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 $u$.

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.

Let the lengths of $low$ and $high$ be $a$ and $b$ respectively.

Next, we traverse all lengths in the range $[a,..b]$. For each length $n$, we get all strobogrammatic numbers $dfs(n)$, and then check whether they are in the range $[low, high]$. If they are, we increment the answer.

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

Similar problems:

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class Solution:
    def strobogrammaticInRange(self, low: str, high: str) -> int:
        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

        a, b = len(low), len(high)
        low, high = int(low), int(high)
        ans = 0
        for n in range(a, b + 1):
            for s in dfs(n):
                if low <= int(s) <= high:
                    ans += 1
        return ans

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

    public int strobogrammaticInRange(String low, String high) {
        int a = low.length(), b = high.length();
        long l = Long.parseLong(low), r = Long.parseLong(high);
        int ans = 0;
        for (n = a; n <= b; ++n) {
            for (String s : dfs(n)) {
                long v = Long.parseLong(s);
                if (l <= v && v <= r) {
                    ++ans;
                }
            }
        }
        return ans;
    }

    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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using ll = long long;

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

    int strobogrammaticInRange(string low, string high) {
        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;
        };

        int a = low.size(), b = high.size();
        int ans = 0;
        ll l = stoll(low), r = stoll(high);
        for (n = a; n <= b; ++n) {
            for (auto& s : dfs(n)) {
                ll v = stoll(s);
                if (l <= v && v <= r) {
                    ++ans;
                }
            }
        }
        return ans;
    }
};

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func strobogrammaticInRange(low string, high string) int {
    n := 0
    var dfs func(int) []string
    dfs = func(u int) []string {
        if u == 0 {
            return []string{""}
        }
        if u == 1 {
            return []string{"0", "1", "8"}
        }
        var ans []string
        pairs := [][]string{{"1", "1"}, {"8", "8"}, {"6", "9"}, {"9", "6"}}
        for _, v := range dfs(u - 2) {
            for _, p := range pairs {
                ans = append(ans, p[0]+v+p[1])
            }
            if u != n {
                ans = append(ans, "0"+v+"0")
            }
        }
        return ans
    }
    a, b := len(low), len(high)
    l, _ := strconv.Atoi(low)
    r, _ := strconv.Atoi(high)
    ans := 0
    for n = a; n <= b; n++ {
        for _, s := range dfs(n) {
            v, _ := strconv.Atoi(s)
            if l <= v && v <= r {
                ans++
            }
        }
    }
    return ans
}

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