POJ3069——Saruman's Army

Saruman's Army

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 9418 Accepted: 4747

Description

Saruman the White must lead his army along a straight path from Isengard to Helm’s Deep. To keep track of his forces, Saruman distributes seeing stones, known as palantirs, among the troops. Each palantir has a maximum effective range of R units, and must be carried by some troop in the army (i.e., palantirs are not allowed to “free float” in mid-air). Help Saruman take control of Middle Earth by determining the minimum number of palantirs needed for Saruman to ensure that each of his minions is within R units of some palantir.

Input

The input test file will contain multiple cases. Each test case begins with a single line containing an integer R, the maximum effective range of all palantirs (where 0 ≤ R ≤ 1000), and an integer n, the number of troops in Saruman’s army (where 1 ≤ n ≤ 1000). The next line contains n integers, indicating the positions x₁, …, x_n of each troop (where 0 ≤ x_i ≤ 1000). The end-of-file is marked by a test case with R = n = −1.

Output

For each test case, print a single integer indicating the minimum number of palantirs needed.

Sample Input

0 310 20 2010 770 30 1 7 15 20 50-1 -1

Sample Output

24

Hint

In the first test case, Saruman may place a palantir at positions 10 and 20. Here, note that a single palantir with range 0 can cover both of the troops at position 20.

In the second test case, Saruman can place palantirs at position 7 (covering troops at 1, 7, and 15), position 20 (covering positions 20 and 30), position 50, and position 70. Here, note that palantirs must be distributed among troops and are not allowed to “free float.” Thus, Saruman cannot place a palantir at position 60 to cover the troops at positions 50 and 70.

Source

Stanford Local 2006

题意：

一条直线上有n个点，坐标为x[i]，从这n个点中选择若干个加上标记，使得每个点距离为r的区域里必须有带有标记的点，问最少需要标记几个点。

解：

贪心解决。从最左边开始扫描，标记的点为 a[index]+r范围内最远的那个，标记点为news，下一个标记点为距离news为r的点的下一个点，依次遍历，直到遍历完成整个数组所有点。

#include <stdio.h>#include <string.h>#include <algorithm>using namespace std;int a[1005];int main(){int n,r;while(~scanf("%d %d",&r,&n) && n>=0 && r>=0){for(int i=0;i<n;i++){scanf("%d",&a[i]);}sort(a,a+n);int index=0;int count=0;while(index<n){int s=a[index++];while(index<n && a[index]<=s+r) index++;int news=a[index-1];while(index<n && news+r>=a[index]) index++;count++;}printf("%d\n",count);}return 0;}