c++排列组合刘汝佳紫书

Question

题目：用1,2，3，…，9组成3个数abc,def和ghi，每个数字恰好用一次，要求abc：def:ghi=1:2:3。按照"abc def ghi"的格式输出所有解，每行一个解
下面是我的解答代码，但是遗漏了一个输出 267 534 801

#define _CRT_SECURE_NO_WARNINGS 
#include<cmath>
#include<functional>
#include<cstdio>
using namespace std;
int main() {
    auto i = 0, j = i, k = j;
    for(i=1;i<=9;i++)
        for (j = 1; j <= 9; j++) {
            for (k = 1; k <= 9; k++) {
                auto abc = i * 100 + j * 10 + k, def = 2 * abc, ghi = 3 * abc;
                if (ghi >= 1000)continue;
                bool g[10]{ false };
                g[i] = true; g[j] = true; g[k] = true;
                g[def % 10] = true; g[def % 100 / 10] = true; g[def / 100] = true;
                g[ghi % 10] = true; g[ghi % 100 / 10] = true; g[ghi / 100] = true;
                auto flag = true;
                for (int q = 1; q <= 9; q++) {
                    if (!g[q]) { flag = false;
                    break;
                    }
                    
                }
                if (flag)printf("%d %d %d\n", abc, def, ghi);
            }
        }
}

Answer 1

#include <cstdio>

int main() {
    for (int a = 1; a <= 9; a++) {
        for (int b = 1; b <= 9; b++) {
            if (b == a) continue;
            for (int c = 1; c <= 9; c++) {
                if (c == a || c == b) continue;
                int abc = a * 100 + b * 10 + c;
                int def = abc * 2;
                int ghi = abc * 3;
                if (ghi > 987) break;  // ghi 最大只能是 987
                int d = def / 100, e = def / 10 % 10, f = def % 10;
                int g = ghi / 100, h = ghi / 10 % 10, i = ghi % 10;
                if (d != e && d != f && d != g && d != h && d != i &&
                    e != f && e != g && e != h && e != i &&
                    f != g && f != h && f != i &&
                    g != h && g != i && h != i) {
                        printf("%d %d %d\n", abc, def, ghi);
                }
            }
        }
    }
    return 0;
}