"Problem solution" with score

（ Math teacher ： Is this the simplest score for you ！）

Link to the original title ：link

   This is a deep search , The average time $3000\mathrm{ms}$; Personal practice is violence enumeration , when $139\mathrm{ms}$.
   But I don't know this classmate （ metamorphosis ）$130\mathrm{ms}$ How to do it ……

「 My question making process 」：

step1： Observation surface .

  「 With points , Numbers $1\sim 9$ Appears separately and only once （ It doesn't contain $0$）, Output the number $N$ Use digital $1\sim 9$ No repetition, no omission To form with fractions All species 」, The first thing that pops up is deep search , But because I can't figure out how to search , Turn to violence .（ Question type ：DFS or Violence enumeration ）

step2： Think about the solution .

   Grasp With the characteristics of fractional composition ： Integers + False score , namely $x=a+\frac{b}{c}(a,b,c\ne 0)$（ False fractions can be reduced to integers , namely The numerator can divide the denominator $(b=kc,c\mid b)$ ）.
   So I thought of enumerating the previous integers first $a$, Then we get the result of pseudo fractional reduction $k$, By enumeration $c$ To get $b$. To determine $a,b,c$ Whether it meets the meaning of the question .
   You can't enumerate indefinitely , Come on Estimated range . The smallest molecule is $1$, Then the integer part is at least $2$, The maximum denominator is $9876543$, You can also get the equivalent number $N$ Greater than $9876545$ There is no solution to time （ However $N\le 10^6$ , This $N$ The scope of is useless ）.

step3： Completion code .

Code （ Resist academic misconduct , Refuse Ctrl + C）：

#include <bits/stdc++.h>
using namespace std;
const int N = 1e6 + 5;
int n, sum;
bool vis[11]; //  Used to judge whether the number is repeated 、 missing 
inline bool nosame(int x) {
     //  Judge whether the number of a number is repeated 
    memset(vis, 0, sizeof vis);
    while (x != 0) {
    
        if (vis[x % 10] || x % 10 == 0) {
    
            return false;
        }
        vis[x % 10] = true;
        x /= 10;
    }
    return true;
}
inline int len(int x) {
     //  Get the number of digits （ length ）
    int l = 0;
    while (x != 0) {
    
        l++;
        x /= 10;
    }
    return l;
}
inline bool nopublic(int a, int b, int c) {
     //  Judge whether there is a duplicate number in the band score 
    memset(vis, 0, sizeof vis);
    while (a != 0) {
    
        vis[a % 10] = true;
        if (a % 10 == 0) {
    
            return false;
        }
        a /= 10;
    }
    while (b != 0) {
    
        if (vis[b % 10] || b % 10 == 0) {
    
            return false;
        }
        vis[b % 10] = true;
        b /= 10;
    }
    while (c != 0) {
    
        if (vis[c % 10] || c % 10 == 0) {
    
            return false;
        }
        vis[c % 10] = true;
        c /= 10;
    }
    return true;
}
inline void get(int x) {
    
    int l = len(n - x);
    //  Enumerating multiples 
    for (int i = 1; i <= 9876543; i++) {
     //  The molecule is at least one , The integer part can only be two , The maximum denominator is  9876543
        if (nosame(x * i) && nosame(i) && nopublic(x * i, i, n - x) && len(x * i) + len(i) + l == 9) {
    
            printf("%d=%d+%d/%d\n", n, n - x, x * i, i);
            sum++;
        }
        if (len(x * i) + len(i) + l > 9) {
     //  If the number is greater than  9  You don't have to count any more 
            break;
        }
    }
    return;
}
int main() {
    
    freopen("fraction.in", "r", stdin);
    freopen("fraction.out", "w", stdout);
    while (~scanf("%d", &n)) {
    
        sum = 0;
        for (int i = 1; i < n; i++) {
    
            if (nosame(i)) {
    
                get(n - i);
            }
        }
        printf("%d\n", sum);
    }
    return 0;
}

data Hack What about it ~ Yours Accepted By Hack Did you drop it ~(￣y▽,￣)╭

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Let's solve it 『 With fractions 』 beep ~

Bye bye!!1