Physics Experiment
Simon wants to know where are the N balls after T seconds. Can you help him?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 above the ground. At beginning of the experiment, (at second 0), the first ball is released and falls down due to the gravity. After that, the balls are released one by one in every second until all balls have been released. When a ball hits the ground, it will bounce back with the same speed as it hits the ground. When two balls hit each other, they with exchange their velocities (both speed and direction).
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
POJ Founder Monthly Contest – 2008.08.31, Simon
题目类型：简单数学
算法分析：可以先考虑将每个球的起点设置在高度H处，然后小球之间的碰撞可以看做是互不影响地相交而过。其实就是计算T时刻每个小球的位置，由于这里小球是有半径的，每个小球(从下到上的第i个球)的最终位置都要加上2Ri，注意若小球的最终时刻小于0，则表示还没有出发，位置为H！！！
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#pragma comment(linker, "/STACK:102400000,102400000") #include <set> #include <bitset> #include <list> #include <map> #include <stack> #include <queue> #include <deque> #include <string> #include <vector> #include <ios> #include <iostream> #include <fstream> #include <sstream> #include <iomanip> #include <algorithm> #include <utility> #include <complex> #include <numeric> #include <functional> #include <cmath> #include <ctime> #include <climits> #include <cstdarg> #include <cstdio> #include <cstdlib> #include <cstring> #include <cctype> #include <cassert> using namespace std; #define CFF freopen ("aaa.txt", "r", stdin) #define CPPFF ifstream cin ("aaa.txt") #define DB(ccc) cout << #ccc << " = " << ccc << endl #define PB push_back #define MP(A, B) make_pair(A, B) typedef long long LL; typedef unsigned long long ULL; typedef double DB; typedef pair <int, int> PII; typedef pair <int, bool> PIB; const int INF = 0x7FFFFFFF; const int MOD = 1e9 + 7; const double EPS = 1e-10; const double PI = 2 * acos (0.0); const int maxn = 1e6 + 6666; double aa[maxn]; int N, H, R, T; double PP (int t) { double tt = sqrt (2 * H / 10.0); if (t < 0) return H; int k = t / tt; if (k & 1) tt = k * tt + tt - t; else tt = t - k * tt; return H - 10.0 / 2 * (tt * tt); } void SS () { for (int i = 0; i < N; i++) aa[i] = PP (T - i); sort (aa, aa + N); } int main() { // CFF; int t; scanf ("%d", &t); while(t--) { scanf ("%d%d%d%d", &N, &H, &R, &T); SS (); for (int i = 0; i < N; i++) { if (i == 0) printf("%.2lf", aa[i] + 2 * R * i / 100.0); else printf (" %.2lf", aa[i] + 2 * R * i / 100.0); } puts (""); } return 0; } |