• poj1328Radar Installation


    Radar Installation
    Time Limit: 1000MS   Memory Limit: 10000K
    Total Submissions: 76972   Accepted: 17240

    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

    题意:在笔直的航线附近有许多岛屿,给定岛屿的坐标,雷达的半径,求至少多少雷达才可以覆盖所有的岛屿,若无法覆盖,输出-1,若行,输出雷达数量(x轴当做航向)
    思路:先以每一个点为中心画弧,与x轴相交两点成一块区域,则在区域内任意一点为圆心画圆都可以覆盖那个点,将所有的区间按照每个区间最左端从小到大排序
    从起始区间开始,1:若上一个区间的最右端小于当前区间最左端,上一个雷达将无法覆盖当前区间,则需要换一个新雷达来覆盖当前的区间
    2:若1条件不成立,即上一个区间最右端大于当前区间最左端,雷达能覆盖当前区间,就需要取两个区间的公共部分,即比较两个区间最右端大小;那个小取哪个
    AC代码:
    #define _CRT_SECURE_NO_DEPRECATE
    #include<iostream>
    #include<algorithm>
    #include<vector>
    #include<math.h>
    
    using namespace std;
    struct section {
        double left;
        double right;
        //bool operator < (const section& b) const
        //{
         //   return left < b.left;
        //}
    };
    bool cmp(const struct section&a, const struct section&b) {
        return a.left < b.left;
    }
    int main() {
        int n, d,j=1;
        while (scanf("%d%d", &n,&d) && n) {
            int what = 0;
            vector<section>s(n);
            for (int i = 0;i < n;i++) {
                double x, y;
                //cin >> x >> y;
                scanf("%lf%lf",&x,&y);
                if (y > d) { what = 1; continue; }
                if (what)continue;
                double r = sqrt(d * d - y * y);
                s[i].left = x - r;
                s[i].right= x + r;
            }
            if (what) { cout << "Case "<< j++ << ": " << -1 << endl; continue; }
            sort(s.begin(), s.end(),cmp);
            double end = -INT_MAX;
            int radar = 0;
            for (vector<section>::iterator it = s.begin();it != s.end(); it++) {
                if (end < it->left) {//如果上一个区间范围的最右端小于当前区间最左端,则需第二个雷达
                    radar++;
                    end = it->right;
                }
                else if (end>it->right) {
                    end = it->right;
                }
            }
            cout<< "Case " << j++ << ": " << radar << endl;
        }
        return 0;
    }


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  • 原文地址:https://www.cnblogs.com/ZefengYao/p/5819559.html
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