HDU 5826-physics

physics

                                                                     Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
                                                                                               Total Submission(s): 866    Accepted Submission(s): 477

Problem Description

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

 

题意：给你n个小球，这些小球有起始的位置和方向，然后还有一个常数C，小球的瞬时速度和加速度满足av=C，有q次查询，问你在t秒后速度第k小的小球的速度。小球碰撞的时候是完全弹性碰撞。

解题思路：两个小球完全弹性碰撞之后，可以想象为两个球穿过去了。根据题意可以列出方程a=dv/dt=C/v,得v*v-v0*v0=2Ct，v0为小球初始速度，v为t秒后小球的速度，这样就可以解出来了，要求第k个，因为小球的速度是不断增加，那么我们将小球按照初始速度排序，那么最后直接求v[k]在t秒后的速度即可

#include <iostream>#include <cstdio>#include <cstring>#include <string>#include <algorithm>#include <map>#include <cmath>#include <set>#include <stack>#include <queue>#include <vector>#include <bitset>#include <functional>using namespace std;#define LL long longconst int INF = 0x3f3f3f3f;int n,q,x,d,y;double v[100009],c;int main(){    int t;    scanf("%d",&t);    while(t--)    {        scanf("%d%lf",&n,&c);        for(int i=1;i<=n;i++)            scanf("%lf%d%d",&v[i],&x,&d);        sort(v+1,v+1+n);        scanf("%d",&q);        while(q--)        {            scanf("%d%d",&x,&y);            double vv=v[y];            printf("%.3lf\n",1.0*sqrt(2*c*x+vv*vv));        }    }    return 0;}