HDU 5826 physics (数学推导)（规律）

There are n balls on a smooth horizontal straight track. The track can be considered to be a number line. The balls can be considered to be particles with the same mass.

At the beginning, ball i is at position Xi. It has an initial velocity of Vi and is moving in direction Di.(Di∈−1,1)
Given a constant C. At any moment, ball its acceleration Ai and velocity Vi have the same direction, and magically satisfy the equation that Ai * Vi = C.
As there are multiple balls, they may collide with each other during the moving. We suppose all collisions are perfectly elastic collisions.

There are multiple queries. Each query consists of two integers t and k. our task is to find out the k-small velocity of all the balls t seconds after the beginning.

* Perfectly elastic collision : A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision.

 

Input

The first line contains an integer T, denoting the number of testcases.

For each testcase, the first line contains two integers n <= 10^5 and C <= 10^9.
n lines follow. The i-th of them contains three integers Vi, Xi, Di. Vi denotes the initial velocity of ball i. Xi denotes the initial position of ball i. Di denotes the direction ball i moves in.  

The next line contains an integer q <= 10^5, denoting the number of queries.
q lines follow. Each line contains two integers t <= 10^9 and 1<=k<=n.
1<=Vi<=10^5,1<=Xi<=10^9

 

Output

For each query, print a single line containing the answer with accuracy of 3 decimal digits.

 

Sample Input

13 73 3 13 10 -12 7 132 31 23 3

 

Sample Output

6.0834.7967.141

 

Author

学军中学

 

Source

2016 Multi-University Training Contest 8 

 

Recommend

wange2014

总结

看到这道题并不难想到蚂蚁爬杆的那道题，思路很清晰，中间的求定积分一开始没有推出来真是不应该，va=c  , a=dv/dt ,v*dv/dt=c ,v*dv=dt*c,然后两边同时积分就可以解出来了

////  main.cpp//  physics////  Created by 张嘉韬 on 16/8/11.//  Copyright © 2016年 张嘉韬. All rights reserved.//#include <iostream>#include <cstring>#include <cstdio>#include <cmath>#include <algorithm>using namespace std;typedef long long ll;const int maxn=100000+10;ll v[maxn];int main(int argc, const char * argv[]) {    //freopen("/Users/zhangjiatao/Documents/暑期训练/input.txt","r",stdin);    int T;    scanf("%d",&T);    while(T--)    {        ll n,c;        int q;        scanf("%lld%lld",&n,&c);        for(int i=0;i<n;i++)        {            int x,d;            scanf("%lld%d%d",&v[i],&x,&d);        }        sort(v+0,v+n);        scanf("%d",&q);        for(int i=1;i<=q;i++)        {            ll t,k;            scanf("%lld%lld",&t,&k);            double r=sqrt((double)(2*t*c+v[k-1]*v[k-1]));            printf("%.3f\n",r);        }    }    return 0;}