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Language: Default Physics Experiment
Description Simon is doing a physics experiment with N identical balls with the same radius of R centimeters. Before the experiment, all N balls are fastened within a vertical tube one by one and the lowest point of the lowest ball is H meters
Simon wants to know where are the N balls after T seconds. Can you help him? In this problem, you can assume that the gravity is constant: g = 10 m/s2. Input The first line of the input contains one integer C (C ≤ 20) indicating the number of test cases. Each of the following lines contains four integers N, H, R, T. 1≤ N ≤ 100. 1≤ H ≤ 10000 1≤ R ≤ 100 1≤ T ≤ 10000 Output For each test case, your program should output N real numbers indicating the height in meters of the lowest point of each ball separated by a single space in a single line. Each number should be rounded to 2 digit after the decimal point. Sample Input 2 1 10 10 100 2 10 10 100 Sample Output 4.95 4.95 10.20 Source |
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题意：将N个半径为R的球放入一个圆桶（圆桶口径刚好放入一个球），将圆桶竖直放着，最下端距离地面H高度，让球每隔一秒自由下落，求T时刻各个球距离地面的高度。
思路：所有的球都一样可以忽视它们的碰撞，视为互相穿过继续运动。这样就可以分别单独求出每个球T时刻的高度后排序就是答案了。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <string>
#include <map>
#include <stack>
#include <vector>
#include <set>
#include <queue>
#pragma comment (linker,"/STACK:102400000,102400000")
#define maxn 105
#define MAXN 2005
#define mod 1000000009
#define INF 0x3f3f3f3f
#define pi acos(-1.0)
#define eps 1e-6
#define lson rt<<1,l,mid
#define rson rt<<1|1,mid+1,r
typedef long long ll;
using namespace std;
int N,T;
double H,R;
double ans[maxn];
double solve(int T)
{
if (T<0) return H;
double t=sqrt((2*H)/10.0);
int k=(int)T/t;
if (k%2)
return H-5.0*(k*t+t-T)*(k*t+t-T);
else
return H-5.0*(T-k*t)*(T-k*t);
}
int main()
{
int c;
scanf("%d",&c);
while (c--)
{
scanf("%d%lf%lf%d",&N,&H,&R,&T);
for (int i=0;i<N;i++)
ans[i]=solve(T-i);
sort(ans,ans+N);
printf("%.2f",ans[0]);
for (int i=1;i<N;i++)
printf(" %.2f",ans[i]+2*R*i/100.0);
printf("\n");
}
return 0;
}
/*
2
1 10 10 100
2 10 10 100
*/
代码：