链接：https://ac.nowcoder.com/acm/contest/11166/B 来源：牛客网
时间限制：C/C++ 1秒，其他语言2秒 空间限制：C/C++ 262144K，其他语言524288K Special Judge, 64bit IO Format: %lld
题目描述
A standard sphere ball is falling in the air, and the center of the sphere is exactly on the centerline of an empty isosceles trapezoidal. The trapezoid is hanging horizontally under the sphere.
Please determine whether the ball will get stuck in the trapezoid or drop past the trapezoid.
输入描述:
The input contains four integers r,a,b,h(1≤r,a,b,h≤1000,a>b)r, a, b, h(1 \le r,a,b,h \le 1000, a > b)r,a,b,h(1≤r,a,b,h≤1000,a>b), indicating the radius of the ball, the top base, the bottom base, and the height of the isosceles trapezoid.
It is guaranteed that 2r≠b,2r<a,2r<h2r \ne b, 2r < a, 2r < h2r=b,2r<a,2r<h.输出描述:
Output 'Drop' if the sphere ball will drop past the empty trapezoid, otherwise output 'Stuck'.
If the answer is 'Stuck', please also calculate the stuck position(the height between the center of the sphere and the midpoint of the bottom base). Your answer is considered correct if its absolute or relative error does not exceed 10−610^{-6}10−6.示例1
输入
复制
2 8 2 5输出
复制
Stuck
2.2206345966示例2
输入
复制
1 8 3 5输出
复制
Drop思路与代码
三角形A,B,C相似,忽略证明
大三角形A的三边都知道,小三角形C其中一条边是圆的半径,所以三角形C的上面那个边知道了,然后可以得出三角形B的底边,由三角形A和B的相似可以得出结果
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <string>
#include <iostream>
#include <sstream>
#include <set>
#include <map>
#include <queue>
#include <bitset>
#include <vector>
#include <limits.h>
#include <assert.h>
#include <functional>
#include <numeric>
#include <ctime>
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
#define pb push_back
#define ppb pop_back
#define lbnd lower_bound
#define ubnd upper_bound
#define endl '\n'
#define mll map<ll,ll>
#define msl map<string,ll>
#define mls map<ll, string>
#define rep(i,a,b) for(ll i=a;i<b;i++)
#define repr(i,a,b) for(ll i=b-1;i>=a;i--)
#define trav(a, x) for(auto& a : x)
#define pll pair<ll,ll>
#define vl vector<ll>
#define vll vector<pair<ll, ll>>
#define vs vector<string>
#define all(a) (a).begin(),(a).end()
#define F first
#define S second
#define sz(x) (ll)x.size()
#define hell 1000000007
#define DEBUG cerr<<"/n>>>I'm Here<<</n"<<endl;
#define display(x) trav(a,x) cout<<a<<" ";cout<<endl;
#define what_is(x) cerr << #x << " is " << x << endl;
#define ini(a) memset(a,0,sizeof(a))
#define ini2(a,b) memset(a,b,sizeof(a))
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define sc ll T;cin>>T;for(ll Q=1;Q<=T;Q++)
#define lowbit(x) x&(-x)
#define ordered_set tree<ll, null_type,less<ll>, rb_tree_tag,tree_order_statistics_node_update>
#define FAST ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define DBG(x) \
(void)(cout << "L" << __LINE__ \
<< ": " << #x << " = " << (x) << '\n')
#define TIE \
cin.tie(0);cout.tie(0);\
ios::sync_with_stdio(false);
//using namespace __gnu_pbds;
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const double PI = acos(-1.0);
const double eps = 1e-6;
const int INF = 0x3f3f3f3f;
const int maxn = 2000;
const int N = 10001;
char fa[maxn];
char cb[maxn][maxn];
ll len;
void solve(){
double r,a,b,h,r2;
while(~scanf("%lf %lf %lf %lf",&r,&a,&b,&h)){
r2 = b/2;
if(r2>=r){//r2>=r,r2-r<eps&&r2-r>0
printf("Drop\n");
}else{
printf("Stuck\n");
double p1 = a/2-b/2;
double p2 = sqrt(p1*p1 + h*h);
double x = p2/h*r;
double q = a/2-x;
printf("%.10lf\n",h-(h*(q/(a/2-b/2))));
}
}
}
int main()
{
// #ifndef ONLINE_JUDGE
// freopen ("input.txt","r",stdin);
// #else
// #endif
solve();
// sc{solve();}
// sc{cout<<"Case "<<Q<<":"<<endl;solve();}
}