CodeForces - 667A Pouring Rain(数学,规律)

xiaoxiao2021-02-27  266

题目:

A. Pouring Rain time limit per test1 second memory limit per test256 megabytes inputstandard input outputstandard output A lot of people in Berland hates rain, but you do not. Rain pacifies, puts your thoughts in order. By these years you have developed a good tradition — when it rains, you go on the street and stay silent for a moment, contemplate all around you, enjoy freshness, think about big deeds you have to do.

Today everything had changed quietly. You went on the street with a cup contained water, your favorite drink. In a moment when you were drinking a water you noticed that the process became quite long: the cup still contained water because of rain. You decided to make a formal model of what was happening and to find if it was possible to drink all water in that situation.

Thus, your cup is a cylinder with diameter equals d centimeters. Initial level of water in cup equals h centimeters from the bottom.

You drink a water with a speed equals v milliliters per second. But rain goes with such speed that if you do not drink a water from the cup, the level of water increases on e centimeters per second. The process of drinking water from the cup and the addition of rain to the cup goes evenly and continuously.

Find the time needed to make the cup empty or find that it will never happen. It is guaranteed that if it is possible to drink all water, it will happen not later than after 104 seconds.

Note one milliliter equals to one cubic centimeter.

Input The only line of the input contains four integer numbers d, h, v, e (1 ≤ d, h, v, e ≤ 104), where:

d — the diameter of your cylindrical cup, h — the initial level of water in the cup, v — the speed of drinking process from the cup in milliliters per second, e — the growth of water because of rain if you do not drink from the cup. Output If it is impossible to make the cup empty, print “NO” (without quotes).

Otherwise print “YES” (without quotes) in the first line. In the second line print a real number — time in seconds needed the cup will be empty. The answer will be considered correct if its relative or absolute error doesn’t exceed 10 - 4. It is guaranteed that if the answer exists, it doesn’t exceed 104.

Examples input 1 2 3 100 output NO input 1 1 1 1 output YES 3.659792366325 Note In the first example the water fills the cup faster than you can drink from it.

In the second example area of the cup’s bottom equals to , thus we can conclude that you decrease the level of water by centimeters per second. At the same time water level increases by 1 centimeter per second due to rain. Thus, cup will be empty in seconds.

思路:

题上给了d,h,v,e,分别代表: d:杯子的直径 h:杯子里的水的当前高度 v:杯子里面的水减少的速度 e:杯子里面水添加的速度 问的是能否在这个状态下经过多少秒使杯子里面的水为空。

我们现先算出杯子里面的水的当前体积,然后在算出水的当前流速,除一下就好

代码:

#include <cstdio> #include <cmath> #include <iostream> using namespace std; const double pi=acos(-1.0); int main() { int d,h,v,e; scanf("%d%d%d%d",&d,&h,&v,&e); double s=(d/2.0)*(d/2.0)*pi;//算出面积 double v1=s*h*1.0;//算出初始体积 if(v-s*e<=1e-5)//确定误差范围 puts("NO"); else printf("YES\n%.10lf\n",v1/(v-s*e)); return 0; }
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