1684: [Usaco2005 Oct]Close Encounter
1684: [Usaco2005 Oct]Close Encounter
Time Limit: 5 Sec Memory Limit: 64 MBSubmit: 387 Solved: 181
[Submit][Status][Discuss]
Description
Lacking even a fifth grade education, the cows are having trouble with a fraction problem from their textbook. Please help them. The problem is simple: Given a properly reduced fraction (i.e., the greatest common divisor of the numerator and denominator is 1, so the fraction cannot be further reduced) find the smallest properly reduced fraction with numerator and denominator in the range 1..32,767 that is closest (but not equal) to the given fraction. 找一个分数它最接近给出一个分数. 你要找的分数的值的范围在1..32767
Input
* Line 1: Two positive space-separated integers N and D (1 <= N < D <= 32,767), respectively the numerator and denominator of the given fraction
Output
* Line 1: Two space-separated integers, respectively the numerator and denominator of the smallest, closest fraction different from the input fraction.
Sample Input
Sample Output
OUTPUT DETAILS:
21845/32767 = .666676839503.... ~ 0.666666.... = 2/3.
HINT
Source
题解:感觉很像是NOIP2014普及组的那道题,貌似当时干掉了好多人= =(HansBug:呵呵哒我会说我第一想法是二分答案么,但是显然二分是没有办法控制分母的大小的)
于是继续脑洞,于是我想到既然分母范围那么小,那么为何不枚举分母呢?然后直接根据原来分数的大致值来估测分子,然后不断打擂台
(PS:值得注意的是要特判和原分数相同的情况,否则你会输入什么就输出什么的= =,不过敢直接这么枚举还是需要一定脑洞哒)
1 /************************************************************** 2 Problem: 1684 3 User: HansBug 4 Language: Pascal 5 Result: Accepted 6 Time:44 ms 7 Memory:224 kb 8 ****************************************************************/ 9 10 var 11 i,j,k,l,m,n,a,b:longint; 12 ans:double; 13 procedure check(x,y:longint); 14 var t:double; 15 begin 16 if (x*m)=(y*n) then exit; 17 t:=abs((x/y)-(n/m)); 18 if t<ans then 19 begin 20 ans:=t; 21 a:=x; 22 b:=y; 23 end; 24 end; 25 begin 26 readln(n,m);ans:=maxint;; 27 for j:=1 to 32767 do 28 begin 29 i:=trunc((n/m)*j); 30 check(i,j); 31 check(i+1,j); 32 end; 33 writeln(a,' ',b); 34 readln; 35 end.
【推荐】编程新体验,更懂你的AI,立即体验豆包MarsCode编程助手
【推荐】凌霞软件回馈社区,博客园 & 1Panel & Halo 联合会员上线
【推荐】抖音旗下AI助手豆包,你的智能百科全书,全免费不限次数
【推荐】博客园社区专享云产品让利特惠,阿里云新客6.5折上折
【推荐】轻量又高性能的 SSH 工具 IShell:AI 加持,快人一步
· 浏览器原生「磁吸」效果!Anchor Positioning 锚点定位神器解析
· 没有源码,如何修改代码逻辑?
· 一个奇形怪状的面试题:Bean中的CHM要不要加volatile?
· [.NET]调用本地 Deepseek 模型
· 一个费力不讨好的项目,让我损失了近一半的绩效!
· PowerShell开发游戏 · 打蜜蜂
· 在鹅厂做java开发是什么体验
· 百万级群聊的设计实践
· WPF到Web的无缝过渡:英雄联盟客户端的OpenSilver迁移实战
· 永远不要相信用户的输入:从 SQL 注入攻防看输入验证的重要性