桥本分数c语言,桥本分数式问题的C++算法

用枚举法，得到结果10个解，各位读者 可查看结果帮忙审核

之所以使用枚举法，是因为实现简单

分析：如果采用回溯法，是否有利于实现算法的并行计算(如果需要的话？)；而采用枚举，则有利于实现并行

/*用枚举法求解桥本分数式问题

问题：寻找p1(1位数)/p2(2位数)+p3(1位数)/p4(2位数)=p5(1位数)/p6(2位数),每位数取值[1..9]

特点：实现比回溯法简单

*/

#include

#include

#include

#include

using namespace std;

//取得最大公约数

int getGCD(int a, int b)

{

int c, r;

/*

//确保a>b

if (a < b)

{

c = a;

a = b;

b = c;

}

*/

r = a % b;

while( r != 0 )

{

a = b;

b = r;

r = a % b;

}

return b;

}

bool check(int p1, int p2, int p3, int p4, int *cnt, int& p5, int &p6)

{

int pa1, pa2, pbX, gcd, k;

bool find;

pa1 = p1 * p4; //同分母后的分子1

pa2 = p2 * p3; //同分母后的分子2

//要求：第1个分数的分子小于第2个分数的分子

if (p1 > p3) return false;

p5 = pa1 + pa2;

p6 = p2 * p4; //同分母后的分母

//计算真分数

if (p6 < p5) return false;

gcd = getGCD(p6, p5);

p5 /= gcd;

p6 /= gcd;

//由真分数依次派生假分数，检验是否符合需要

find = false;

k = 1;

while(true) //p6尾数也不能为0

{

//如果不满足条件，则搜索假分数

if (p5 > 9 || p6 > 99) break;

if (p5 == p6 % 10 || p5 == p6 / 10 || p6 % 10 == p6 / 10 || cnt[p5] > 0 || p6 % 10 == 0 || cnt[p6 % 10] > 0 || cnt[p6 / 10] > 0)

{

p5 = p5 / k * (k + 1);

p6 = p6 / k * (k + 1);

k++;

}

else

{

find = p6 > 9;

break;

}

}

return find;

}

void Qiaoben()

{

int val = 123456, tmp, part, p1, p2, p3, p4, p5, p6;

int cnts[10] = {0};

int cnt = 0;

while( true )

{

next:

if (val > 999999) break; //结束条件

//不允许数字重复

memset(cnts, 0, sizeof(int) * 10); //设置10个元素值的计数为0

tmp = val;

for(int i = 1; i <= 6; i++)

{

part = tmp % 10;

tmp /= 10;

cnts[part]++;

if (cnts[part] > 1 || part == 0)

{

val++;

goto next;

}

}

//从val中检验等式是否符合条件

tmp = val;

p4 = tmp % 100;

tmp /= 100;

p3 = tmp % 10;

tmp /= 10;

p2 = tmp % 100;

tmp /= 100;

p1 = tmp;

if (check(p1, p2, p3, p4, cnts, p5, p6))

{

cnt++;

printf("%2d: ", cnt);

cout << val << p5 << p6 << " ==> " << p1 << "/" << p2 << " + " << p3 << "/" << p4 << " = " << p5 << "/" << p6 << endl;

}

val++;

}

}

int main()

{

Qiaoben();

return 0;

}

1: 126578439 ==> 1/26 + 5/78 = 4/39

2: 132596784 ==> 1/32 + 5/96 = 7/84

3: 132796548 ==> 1/32 + 7/96 = 5/48

4: 178439652 ==> 1/78 + 4/39 = 6/52

5: 196748532 ==> 1/96 + 7/48 = 5/32

6: 268934517 ==> 2/68 + 9/34 = 5/17

7: 268951734 ==> 2/68 + 9/51 = 7/34

8: 456798321 ==> 4/56 + 7/98 = 3/21

9: 526978413 ==> 5/26 + 9/78 = 4/13

10: 634851927 ==> 6/34 + 8/51 = 9/27