POJ1328解题报告
2017-06-05 16:23
316 查看
Radar Installation
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
Sample Output
题意:假设海岸线是一条无限延伸的直线。陆地在海岸线的一侧,而海洋在另一侧。每一个小的岛屿是海洋上的一个点。雷达坐落于海岸线上,只能覆盖d距离,所以如果小岛能够被覆盖到的话,它们之间的距离最多为d。
题目要求计算出能够覆盖给出的所有岛屿的最少雷达数目。
我们假设岛屿i它的x坐标为island[i][0],而y坐标为island[i][1],那么有以下几种情况是invalide的,即输出-1的情况:
1.island[i][1]<0
2.abs(island[i][1])<d
3.d<0
其他的情况,应该就是正常情况,进入计算最小雷达数目。
如上图,红色的点为岛屿,那么能够覆盖到此岛屿的雷达所在的区间,应该就是以该岛屿为圆心的圆与x轴交点所在的区间。
这样,我们就可以计算出所有岛屿的雷达所在的区间,得到一个区间数组。
我们将这个数组按照区间左部分进行排序,那么重叠部分就表明这些岛屿的雷达可以共用一个。从而计算出最终解。
#include<stdio.h>
#include<limits.h>
#include<math.h>
#define MAXNUM 12701
//以岛屿为圆心,以d为半径做圆;得到各个圆与x轴相交的区间;去掉重复区间,即得到雷达数目
int calMin(int **island,int n,int d);
int main() {
int num = 0;
char s[10];
while(1){
num++;
int n,d,i;
scanf("%d%d",&n,&d);
if(n==0&&d==0){
break;
}
int **island = (int**)malloc(sizeof(int*)*n);
for(i=0;i<n;i++){
island[i] = (int*)malloc(sizeof(int)*2);
scanf("%d%d",&island[i][0],&island[i][1]);
}
//计算最少雷达个数
int min = calMin(island,n,d);
printf("Case %d: %d\n",num,min);
//读取空白行
gets(s);
free(island);
}
system("pause");
return 0;
}
int calMin(int **island,int n,int d){
double *arr = (double*)malloc(sizeof(double)*n*2);
int i,j;
for(i=0;i<n;i++){
if(island[i][1]<0||island[i][1]>d||d<0){
return -1;
}
//计算左右区间
if(abs(island[i][1]-d)<1e-6){
arr[2*i] = island[i][0];
arr[2*i+1] = island[i][0];
}else{
//计算
double x = sqrt(pow(d,2)-pow(island[i][1],2));
arr[2*i] = (double)island[i][0] - x;
arr[2*i+1] = (double)island[i][0] + x;
}
}
//排序
for(i=0;i<n-1;i++){
for(j=0;j<n-i-1;j++){
if(arr[2*j]>arr[2*(j+1)]){
double temp = arr[2*(j+1)];
arr[2*(j+1)] = arr[2*j];
arr[2*j] = temp;
temp = arr[2*(j+1)+1];
arr[2*(j+1)+1] = arr[2*j+1];
arr[2*j+1] = temp;
}
}
}
//去掉重合区间,得到雷达个数
int num = 0;
double right = -1;
for(i=0;i<n;i++){
if(i==0){
num++;
right = arr[2*i+1];
}else{
if(arr[2*i]<=right){
if(arr[2*i+1]<right){
right = arr[2*i+1];
}
continue;
}else{
num++;
right = arr[2*i+1];
}
}
}
return num;
}
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 40799 | Accepted: 9034 |
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:假设海岸线是一条无限延伸的直线。陆地在海岸线的一侧,而海洋在另一侧。每一个小的岛屿是海洋上的一个点。雷达坐落于海岸线上,只能覆盖d距离,所以如果小岛能够被覆盖到的话,它们之间的距离最多为d。
题目要求计算出能够覆盖给出的所有岛屿的最少雷达数目。
我们假设岛屿i它的x坐标为island[i][0],而y坐标为island[i][1],那么有以下几种情况是invalide的,即输出-1的情况:
1.island[i][1]<0
2.abs(island[i][1])<d
3.d<0
其他的情况,应该就是正常情况,进入计算最小雷达数目。
如上图,红色的点为岛屿,那么能够覆盖到此岛屿的雷达所在的区间,应该就是以该岛屿为圆心的圆与x轴交点所在的区间。
这样,我们就可以计算出所有岛屿的雷达所在的区间,得到一个区间数组。
我们将这个数组按照区间左部分进行排序,那么重叠部分就表明这些岛屿的雷达可以共用一个。从而计算出最终解。
#include<stdio.h>
#include<limits.h>
#include<math.h>
#define MAXNUM 12701
//以岛屿为圆心,以d为半径做圆;得到各个圆与x轴相交的区间;去掉重复区间,即得到雷达数目
int calMin(int **island,int n,int d);
int main() {
int num = 0;
char s[10];
while(1){
num++;
int n,d,i;
scanf("%d%d",&n,&d);
if(n==0&&d==0){
break;
}
int **island = (int**)malloc(sizeof(int*)*n);
for(i=0;i<n;i++){
island[i] = (int*)malloc(sizeof(int)*2);
scanf("%d%d",&island[i][0],&island[i][1]);
}
//计算最少雷达个数
int min = calMin(island,n,d);
printf("Case %d: %d\n",num,min);
//读取空白行
gets(s);
free(island);
}
system("pause");
return 0;
}
int calMin(int **island,int n,int d){
double *arr = (double*)malloc(sizeof(double)*n*2);
int i,j;
for(i=0;i<n;i++){
if(island[i][1]<0||island[i][1]>d||d<0){
return -1;
}
//计算左右区间
if(abs(island[i][1]-d)<1e-6){
arr[2*i] = island[i][0];
arr[2*i+1] = island[i][0];
}else{
//计算
double x = sqrt(pow(d,2)-pow(island[i][1],2));
arr[2*i] = (double)island[i][0] - x;
arr[2*i+1] = (double)island[i][0] + x;
}
}
//排序
for(i=0;i<n-1;i++){
for(j=0;j<n-i-1;j++){
if(arr[2*j]>arr[2*(j+1)]){
double temp = arr[2*(j+1)];
arr[2*(j+1)] = arr[2*j];
arr[2*j] = temp;
temp = arr[2*(j+1)+1];
arr[2*(j+1)+1] = arr[2*j+1];
arr[2*j+1] = temp;
}
}
}
//去掉重合区间,得到雷达个数
int num = 0;
double right = -1;
for(i=0;i<n;i++){
if(i==0){
num++;
right = arr[2*i+1];
}else{
if(arr[2*i]<=right){
if(arr[2*i+1]<right){
right = arr[2*i+1];
}
continue;
}else{
num++;
right = arr[2*i+1];
}
}
}
return num;
}
相关文章推荐
- poj1328解题报告.
- poj1328解题报告(贪心、线段交集)
- 2018.1.21【POJ - 1328】小岛与雷达解题报告(二维转一维,贪心)
- POJ 1328 解题报告
- poj解题报告——1328
- poj-1657解题报告
- POJ1321 棋盘问题 解题报告
- poj解题报告——1061
- poj 1003 Hangover 解题报告
- 【原】 POJ 1308 Is It A Tree? 并查集树结构 解题报告
- poj 1417 True Liars 解题报告 并查集 DP
- 【原】 POJ 3414 Pots 状态BFS 解题报告
- POJ 2485 Highways 解题报告
- poj2236解题报告
- poj2996解题报告
- Poj 1953 World Cup Noise之解题报告
- poj解题报告——1250
- POJ - 2406 Power Strings解题报告(KMP,字符串划分成若干连续相同子串)
- POJ 2247 解题报告
- POJ 1004 Financial Management 解题报告