【贪心】「poj1328」Radar Installation

建模：二维转一维；贪心

Description

Assume the coasting is an infinite straight line. Land is in one side of coasting, sea in the other. Each small island is a point locating in the sea side. And any radar installation, locating on the coasting, can only cover d distance, so an island in the sea can be covered by a radius installation, if the distance between them is at most d. 

We use Cartesian coordinate system, defining the coasting is the x-axis. The sea side is above x-axis, and the land side below. Given the position of each island in the sea, and given the distance of the coverage of the radar installation, your task is to write a program to find the minimal number of radar installations to cover all the islands. Note that the position of an island is represented by its x-y coordinates. 
 
Figure A Sample Input of Radar Installations

Input

The input consists of several test cases. The first line of each case contains two integers n (1<=n<=1000) and d, where n is the number of islands in the sea and d is the distance of coverage of the radar installation. This is followed by n lines each containing two integers representing the coordinate of the position of each island. Then a blank line follows to separate the cases. 

The input is terminated by a line containing pair of zeros 

Output

For each test case output one line consisting of the test case number followed by the minimal number of radar installations needed. "-1" installation means no solution for that case.

Sample Input

3 2
1 2
-3 1
2 1

1 2
0 2

0 0

Sample Output

Case 1: 2
Case 2: 1

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鄙人仍然码力不够……建模虽然很快就建出来了，但是写了老半天交了近十发才磕磕碰碰A掉此题。

先来分析一下吧

题意

有n个在一二象限上的整点，要求在x轴上选取ans个点，满足以每个点为圆的图形并集包含n个整点且ans最小。

分析

因为这里每个监测站的有效范围为圆形，我们可以反过来以n个整点为圆心，d为半径作圆。每个圆在x轴上有两个交点，即映射后的线段，那么在这条线段上至少要有一个监测站。想到这里我马上就想起以前做过的一道叫做“监测站”的题目，于是很快开写了。

CE第一发

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
struct seg{int l,r;}f[1003];
bool cmp(seg a, seg b){return a.r<b.r;}
int n,d,ans;
inline void mapping(int x, int y, int i)
{
    int ss = (int)sqrt(d*d-y*y);
    f[i].l = x-ss;
    f[i].r = x+ss;
    return;
}
inline void work()
{
    memset(f, 0, sizeof(f));
    ans = -1;
    for (int i=1; i<=n; i++)
    {
        int x,y;
        scanf("%d%d",&x,&y);
        if (y > d)return;
        mapping(x, y, i);
    }
    ans = 0;
    sort(f+1, f+n+1, cmp);
    int i = 1;int j = 1;
    while (j<=n)
    {
        ans++;
        while(f[j].l<=f[i].r&&j<=n)j++;
        i = j;
    } 
    return;
}
int main()
{
    scanf("%d%d",&n,&d);
    while (n!=0&&d!=0)
    {
        work();
        printf("%d
",ans);
        scanf("%d%d",&n,&d);
    }
    return 0;
}

然后，愉快快快快快快快地CE了：）

woc在poj上面sqrt(int)会爆我的天哪。

解决方法：

　　1.$sqrt(int * 1.0)$

　　2.$sqrt((double) int)$

　　3.$sqrtf(int)$

WA第一发

　　隐隐发觉：似乎监测点可以不在整点上？把segment的l,r改成double

　　然而不只有这个错

WA第二发

　　手算一组数据发现线段要按左端点排序

　　然而不只有这个错

WA第三发

　　逐条check时候更新不对

　　第三发的

WA第四发

　　第四发交的

　　好的吧显而易见第四发也是错的

WA第五发

　　已经心态爆炸

　　找了一组讨论区里的数据跑了跑，发现！

　　我在判不可能情况时候就在子过程里return了

　　但这是多组数据啊！没读完的被当成下组数据读进去了……

　　还有，我一直把输出里的"Case"当成看看的……（毕竟有些USACO的题不就这样么）

　　没想到它居然是要输出的：）

AC这一发

　　

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
struct seg{double l,r;}f[1003];//WA-1
bool cmp(seg a, seg b){return a.l-b.l<1E-5;}//WA-2
int n,d,ans;
inline void mapping(int x,int y, int i)
{
    double ss = sqrt(d*d*1.0-y*y*1.0);
    f[i].l = x*1.0-ss;
    f[i].r = x*1.0+ss;
    return;
}
inline void work()
{
    memset(f, 0, sizeof(f));
    ans = -1;
    bool fl = 0;
    for (int i=1; i<=n; i++)
    {
        int x,y;
        scanf("%d%d",&x,&y);
        if (y > d)fl = 1;
        mapping(x, y, i);
    }if (fl)return;
    ans = 0;
    sort(f+1, f+n+1, cmp);
    int i = 1;int j = 1;
    while (j<=n)
    {
        ans++;
        while((f[j].l-f[i].r<=1E-5)&&j<=n)
        {
            j++;
            if (f[j].r-f[i].r < 1E-5)i = j;　　　　//WA-3 WA-4
        }
        i = j;
    } 
    return;
}
int main()
{
    scanf("%d%d",&n,&d);
    int t = 0;
    while (n!=0||d!=0)
    {
        t++;
        work();
        printf("Case %d: %d
",t,ans);　　//WA-5
        scanf("%d%d",&n,&d);
    }
    return 0;
}

　　代码能力差还得多写题啊~