Codeforces 514B Han Solo and Lazer Gun【思維】

2019-11-14 10:11:03

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B. Han Solo and Lazer Guntime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output

There are n Imperial stormtroopers on the field. The battle field is a plane with Cartesian coordinate system. Each stormtrooper is associated with his coordinates(x,?y) on this plane.

Han Solo has the newest duplex lazer gun to fight these stormtroopers. It is situated at the point(x₀,?y₀). In one shot it can can destroy all the stormtroopers, situated on some line that crosses point(x₀,?y₀).

Your task is to determine what minimum number of shots Han Solo needs to defeat all the stormtroopers.

The gun is the newest invention, it shoots very quickly and even after a very large number of shots the stormtroopers don't have enough time to realize what's happening and change their location.

Input

The first line contains three integers n,x₀ и y₀ (1?≤?n?≤?1000,?-?10⁴?≤?x₀,?y₀?≤?10⁴) — the number of stormtroopers on the battle field and the coordinates of your gun.

Next n lines contain two integers each x_i, y_i (?-?10⁴?≤?x_i,?y_i?≤?10⁴) — the coordinates of the stormtroopers on the battlefield. It is guaranteed that no stormtrooper stands at the same point with the gun. Multiple stormtroopers can stand at the same point.

Output

PRint a single integer — the minimum number of shots Han Solo needs to destroy all the stormtroopers.

ExamplesInput

4 0 01 12 22 0-1 -1Output2Input2 1 21 11 0Output1NoteExplanation to the first and second samples from the statement, respectively: 
題目大意：
一共有N個目標，給出N個目標點的坐標，并且給出機槍的目標。
這個機槍非常牛X，其開一槍，前后的人都會死。
問最少開多少槍，能夠將所有目標都打到。
思路：
問題尋找共性。
對于一條路徑上的所有目標都有一個唯一的共性，那就是斜率。
那么我們對問題的斜率進行處理即可。任務目標就是統計斜率的個數。
K=（y-y0）/（x-x0）；
注意這個K需要用double類型。
過程用map維護一下第一次出現即可。
Ac代碼：
#include<stdio.h>#include<string.h>#include<map>using namespace std;int main(){    int n;    int x,y;    while(~scanf("%d%d%d",&n,&x,&y))    {        int flag1=0;        int flag2=0;        int output=0;        map<double ,int >s;        for(int i=0;i<n;i++)        {            int xx,yy;            scanf("%d%d",&xx,&yy);            if(xx==x)            {                flag1=1;                continue;            }            if(yy==y)            {                flag2=1;                continue;            }            double  k=(yy-y)*1.0/(xx-x)*1.0;            if(s[k]==0)            {                s[k]=1;                output++;            }        }        printf("%d/n",output+flag1+flag2);    }}