HDU 6373 Pinball

Pinball

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 131    Accepted Submission(s): 55

Problem Description

There is a slope on the 2D plane. The lowest point of the slope is at the origin. There is a small ball falling down above the slope. Your task is to find how many times the ball has been bounced on the slope.

It's guarantee that the ball will not reach the slope or ground or Y-axis with a distance of less than 1 from the origin. And the ball is elastic collision without energy loss. Gravity acceleration $g = 9.8 m/s^2$.

 

Input

There are multiple test cases. The first line of input contains an integer T (1 $le$ T $le$ 100), indicating the number of test cases.

The first line of each test case contains four integers a, b, x, y (1 $le$ a, b, -x, y $le$ 100), indicate that the slope will pass through the point(-a, b), the initial position of the ball is (x, y).

 

Output

Output the answer.

It's guarantee that the answer will not exceed 50.

 

Sample Input

1 5 1 -5 3

 

Sample Output

2

 

Source

2018 Multi-University Training Contest 6

 

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chendu

 

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分析：高中物理题可还行，直接正交分解推个公式就好了。

#include <iostream>
#include <string>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
#include <deque>
#include <map>
#define range(i,a,b) for(auto i=a;i<=b;++i)
#define LL long long
#define ULL unsigned long long
#define elif else if
#define itrange(i,a,b) for(auto i=a;i!=b;++i)
#define rerange(i,a,b) for(auto i=a;i>=b;--i)
#define fill(arr,tmp) memset(arr,tmp,sizeof(arr))
#define IOS ios::sync_with_stdio(false);cin.tie(0)
using namespace std;
int t,a,b,x,y;
const double g=9.8;
void init(){
    scanf("%d",&t);
}
void solve(){
    while(t--){
        scanf("%d%d%d%d",&a,&b,&x,&y);
        double SIN=b*1.0/sqrt(a*a+b*b);
        double h=y+b*x*1.0/a,l=h*SIN+sqrt(x*x*(1+b*b*1.0/(a*a)));
        double TR=sqrt(2*l/(g*SIN)),T=sqrt(2*h/g);
        int cnt=int(TR/T),ans=(cnt+1)>>1;
        cout<<ans<<endl;
    }
}
int main() {
    init();
    solve();
    return 0;
}