Finding Lines(随机暴力)

Finding Lines

Time Limit: 20000ms, Special Time Limit:50000ms, Memory Limit:65536KB

Total submit users: 25, Accepted users: 11

Problem 13348 : No special judgement

Problem description

Annabel and Richard like to invent new games and play against each other. One day Annabel has a new game for Richard. In this game there is a game master and a player. The game master draws n points on a piece of paper. The task for the player is to find a straight line, such that at least p percent of the points lie exactly on that line. Richard and Annabel have very good tools for measurement and drawing. Therefore they can check whether a point lies exactly on a line or not. If the player can find such a line then the player wins. Otherwise the game master wins the game.

There is just one problem. The game master can draw the points in a way such that it is not possible at all to draw a suitable line. They need an independent mechanism to check whether there even exists a line containing at least p percent of the points, i.e., dn · p/100e points. Now it is up to you to help them and write a program to solve this task.

Input

The input consists of:

• one line with one integer n (1 ≤ n ≤ 10^5), the number of points the game master has drawn;

• one line with one integer p (20 ≤ p ≤ 100), the percentage of points which need to lie on the line;

• n lines each with two integers x and y (0 ≤ x,y ≤ 10^9), the coordinates of a point. No two points will coincide.

Output

Output one line containing either “possible” if it is possible to find a suitable line or “impossible” otherwise.

Sample Input

5
55
0 0
10 10
10 0
0 10
3 3
5
45
0 0
10 10
10 0
0 10
3 4

Sample Output

possible
impossible

题意：平面上个你n个点，问你一条直线能穿过最多点的比例是否大于p

思路：随机函数随机两个点，随机200次，暴力找

#include<algorithm>
#include<iostream>
#include<limits.h>
#include<stdlib.h>
#include<string.h>
#include<complex>
#include<cstring>
#include<iomanip>
#include<stdio.h>
#include<bitset>
#include<cctype>
#include<math.h>
#include<string>
#include<time.h>
#include<vector>
#include<cmath>
#include<queue>
#include<stack>
#include<list>
#include<map>
#include<set>

#define LL long long

using namespace std;
const LL mod = 1e9 + 7;
const double PI = acos(-1.0);
const double E = exp(1.0);
const int M = 1e5 + 5;

int x[M];
int y[M];

double calc(int i, int j)
{
    return (y[i] - y[j]) / (double)(x[i] - x[j]);
}

int main()
{
    int n, p;
    while( cin >> n >> p ){
        for(int i = 0; i < n; ++i)
            scanf("%d%d", &x[i], &y[i]);
        if(n == 1){
            puts("possible");
            continue;
        }
        bool flag = 1;
        for(int j = 0; j < 200; ++j){
            int s = rand() % n;
            int e = rand() % n;
            while(e == s)
                e = rand() % n;
            double slope;
            bool ok = 0;
            if(x[s] == x[e])
                ok = 1;
            else
                slope = (y[s] - y[e]) / (double)(x[s] - x[e]);
            int sum = 2;
            for(int i = 0; i < n; ++i){
                if(i == s || i == e)
                    continue;
                if(ok){
                    if(x[i] == x[s])
                        sum++;
                }
                else{
                    if(calc(s, i) == slope)
                        sum++;
                }
            }
            if(sum * 100 / n >= p){
                puts("possible");
                flag = 0;
                break;
            }
        }
        if(flag)
            puts("impossible");
    }
    return 0;
}