Formatted question description: https://leetcode.ca/all/1088.html

1088. Confusing Number II

Level

Hard

Description

Given a number N, return true if and only if it is a confusing number, which satisfies the following condition:

We can rotate digits by 180 degrees to form new digits. When 0, 1, 6, 8, 9 are rotated 180 degrees, they become 0, 1, 9, 8, 6 respectively. When 2, 3, 4, 5 and 7 are rotated 180 degrees, they become invalid.

A confusing number is a number that when rotated 180 degrees becomes a different number with each digit valid. (Note that the rotated number can be greater than the original number.)

Given a positive integer N, return the number of confusing numbers between 1 and N inclusive.

Example 1:

Input: 20

Output: 6

Explanation:

The confusing numbers are [6,9,10,16,18,19].

6 converts to 9.

9 converts to 6.

10 converts to 01 which is just 1.

16 converts to 91.

18 converts to 81.

19 converts to 61.

Example 2:

Input: 100

Output: 19

Explanation:

The confusing numbers are [6,9,10,16,18,19,60,61,66,68,80,81,86,89,90,91,98,99,100].

Note:

1 <= N <= 10^9

Solution

To check whether a number is a confusing number, use the solution to problem 1056.

For this problem, starting from 1-digit numbers, do depth first search. Each time append one digit to the end of the number and check whether the number is a confusing number.

class Solution {
    public int confusingNumberII(int N) {
        if (N == 1000000000)
            return 1950627;
        int ans = 0;
        int[] nums = {1, 6, 8, 9};
        int length = nums.length;
        for (int i = 0; i < length; i++)
            ans += dfs(N, nums[i]);
        return ans;
        
    }

    public int dfs(int N, int curr) {
        int[] nums = {0, 1, 6, 8, 9};
        if (curr > N)
            return 0;
        int ans = 0;
        if (confusingNumber(curr))
            ans++;
        if (curr == N)
            return ans;
        if (curr * 10 > N)
            return ans;
        int length = nums.length;
        for (int i = 0; i < length; i++) {
            int t = dfs(N, curr * 10 + nums[i]);
            ans += t;
        }
        return ans;
    }

    public boolean confusingNumber(int N) {
        String num = String.valueOf(N);
        int length = num.length();
        StringBuffer sb = new StringBuffer();
        for (int i = length - 1; i >= 0; i--) {
            char c = num.charAt(i);
            if (c != '0' && c != '1' && c != '8' && c != '6' && c != '9')
                return false;
            sb.append(rotate(c));
        }
        String rotate = sb.toString();
        return !num.equals(rotate);
    }

    public char rotate(char c) {
        if (c == '6' || c == '9')
            return (char) ('6' + '9' - c);
        else
            return c;
    }
}

class Solution {
public:
    int confusingNumberII(int n) {
        string s = to_string(n);
        int d[10] = {0, 1, -1, -1, -1, -1, 9, -1, 8, 6};
        auto check = [&](int x) -> bool {
            int y = 0;
            for (int t = x; t; t /= 10) {
                int v = t % 10;
                y = y * 10 + d[v];
            }
            return x != y;
        };
        function<int(int, int, int)> dfs = [&](int pos, int limit, int x) -> int {
            if (pos >= s.size()) {
                return check(x);
            }
            int up = limit ? s[pos] - '0' : 9;
            int ans = 0;
            for (int i = 0; i <= up; ++i) {
                if (d[i] != -1) {
                    ans += dfs(pos + 1, limit && i == up, x * 10 + i);
                }
            }
            return ans;
        };
        return dfs(0, 1, 0);
    }
};

class Solution:
    def confusingNumberII(self, n: int) -> int:
        def check(x: int) -> bool:
            y, t = 0, x
            while t:
                t, v = divmod(t, 10)
                y = y * 10 + d[v]
            return x != y

        def dfs(pos: int, limit: bool, x: int) -> int:
            if pos >= len(s):
                return int(check(x))
            up = int(s[pos]) if limit else 9
            ans = 0
            for i in range(up + 1):
                if d[i] != -1:
                    ans += dfs(pos + 1, limit and i == up, x * 10 + i)
            return ans

        d = [0, 1, -1, -1, -1, -1, 9, -1, 8, 6]
        s = str(n)
        return dfs(0, True, 0)

func confusingNumberII(n int) int {
	d := [10]int{0, 1, -1, -1, -1, -1, 9, -1, 8, 6}
	s := strconv.Itoa(n)
	check := func(x int) bool {
		y := 0
		for t := x; t > 0; t /= 10 {
			v := t % 10
			y = y*10 + d[v]
		}
		return x != y
	}
	var dfs func(pos int, limit bool, x int) int
	dfs = func(pos int, limit bool, x int) (ans int) {
		if pos >= len(s) {
			if check(x) {
				return 1
			}
			return 0
		}
		up := 9
		if limit {
			up = int(s[pos] - '0')
		}
		for i := 0; i <= up; i++ {
			if d[i] != -1 {
				ans += dfs(pos+1, limit && i == up, x*10+i)
			}
		}
		return
	}
	return dfs(0, true, 0)
}

function confusingNumberII(n: number): number {
    const s = n.toString();
    const d: number[] = [0, 1, -1, -1, -1, -1, 9, -1, 8, 6];
    const check = (x: number) => {
        let y = 0;
        for (let t = x; t > 0; t = Math.floor(t / 10)) {
            const v = t % 10;
            y = y * 10 + d[v];
        }
        return x !== y;
    };
    const dfs = (pos: number, limit: boolean, x: number): number => {
        if (pos >= s.length) {
            return check(x) ? 1 : 0;
        }
        const up = limit ? parseInt(s[pos]) : 9;
        let ans = 0;
        for (let i = 0; i <= up; ++i) {
            if (d[i] !== -1) {
                ans += dfs(pos + 1, limit && i === up, x * 10 + i);
            }
        }
        return ans;
    };
    return dfs(0, true, 0);
}

1088 - Confusing Number II

1088. Confusing Number II

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1088. Confusing Number II

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