扩展欧几里得
来源:互联网 发布:卡扎菲怎么死的 知乎 编辑:程序博客网 时间:2024/06/05 12:50
The Balance
5000ms
5000ms
65536KB
64-bit integer IO format: %lld Java class name: Main
Font Size:
Ms. Iyo Kiffa-Australis has a balance and only two kinds of weights to measure a dose of medicine. For example, to measure 200mg of aspirin using 300mg weights and 700mg weights, she can put one 700mg weight on the side of the medicine and three 300mg weights on the opposite side (Figure 1). Although she could put four 300mg weights on the medicine side and two 700mg weights on the other (Figure 2), she would not choose this solution because it is less convenient to use more weights.
You are asked to help her by calculating how many weights are required.
You are asked to help her by calculating how many weights are required.
Input
The input is a sequence of datasets. A dataset is a line containing three positive integers a, b, and d separated by a space. The following relations hold: a != b, a <= 10000, b <= 10000, and d <= 50000. You may assume that it is possible to measure d mg using a combination of a mg and b mg weights. In other words, you need not consider "no solution" cases.
The end of the input is indicated by a line containing three zeros separated by a space. It is not a dataset.
The end of the input is indicated by a line containing three zeros separated by a space. It is not a dataset.
Output
The output should be composed of lines, each corresponding to an input dataset (a, b, d). An output line should contain two nonnegative integers x and y separated by a space. They should satisfy the following three conditions.
No extra characters (e.g. extra spaces) should appear in the output.
- You can measure dmg using x many amg weights and y many bmg weights.
- The total number of weights (x + y) is the smallest among those pairs of nonnegative integers satisfying the previous condition.
- The total mass of weights (ax + by) is the smallest among those pairs of nonnegative integers satisfying the previous two conditions.
No extra characters (e.g. extra spaces) should appear in the output.
Sample Input
700 300 200500 200 300500 200 500275 110 330275 110 385648 375 40023 1 100000 0 0
Sample Output
1 31 11 00 31 149 743333 1
#include <cstdio>using namespace std;typedef long long LL;LL gcd(LL a, LL b){ return b == 0 ? a : gcd(b, a%b);}void Euler_extends(LL a, LL b, LL& x, LL& y){ if(!b) { x = 1; y = 0; } else { Euler_extends(b, a%b, y, x); //白书加强版的写法,个人觉得,妙极! y -= a / b * x; }}int main(){ LL a, b, d, x, y; while(~scanf("%I64d%I64d%I64d", &a, &b, &d)) { if(!a && !b && !d) return 0; LL gcd_ab = gcd(a, b); a /= gcd_ab; b /= gcd_ab; d /= gcd_ab; Euler_extends(a, b, x, y); LL y1 = (y * d % a + a) % a; LL x1 = (d - b * y1) / a; if(x1 < 0) x1 = -x1; LL x2 = (x * d % b + b) % b; LL y2 = (d - a * x2) / b; if(y2 < 0) y2 = -y2; if(x1+y1 < x2+y2) printf("%I64d %I64d\n", x1, y1); else printf("%I64d %I64d\n", x2, y2); } return 0;}
0 0
- 【欧几里得&扩展欧几里得】
- 欧几里得和扩展欧几里得
- 欧几里得 与 扩展欧几里得
- 欧几里得&扩展欧几里得
- 欧几里得和扩展欧几里得
- 欧几里得与扩展欧几里得
- 欧几里得和扩展欧几里得
- 欧几里得 与 扩展欧几里得
- 欧几里得 扩展欧几里得
- 欧几里得与扩展欧几里得
- 欧几里得 & 扩展欧几里得
- 欧几里得 与 扩展欧几里得
- 欧几里得和扩展欧几里得
- 欧几里得与扩展欧几里得
- 扩展欧几里得
- 扩展欧几里得
- 扩展欧几里得
- 扩展欧几里得
- Maven 2 for Eclipse配置全攻略(Windows篇)
- 自定义dialog的布局样式
- stdcall详解
- 关于当前搭建Spring Mvc和hibernate框架接口的总结
- PE文件结构详解
- 扩展欧几里得
- adt20以上代码混淆
- 求两个正整数的最大公约数
- 在iis中发布自己asp.net网站
- java.lang.IllegalStateException: commit already called
- 转载--数论总结
- Java NIO框架Netty教程(一) – Hello Netty
- Chrome的无痕浏览实现初探
- Sep 15 FullCalendar日历插件说明文档