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

# 1088. Confusing Number II

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. 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;
}
}