3069:Saruman's Army

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本文介绍了一个关于萨鲁曼军队布局的算法问题，旨在通过合理分布“看见石”来覆盖整个军队，确保每个士兵都在特定范围内。文章提供了一种贪心策略实现方案，并附带了完整的代码示例。

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Saruman's Army

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 12700		Accepted: 6390

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 3
10 20 20
10 7
70 30 1 7 15 20 50
-1 -1

Sample Output

2
4

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

贪心策略，从最左边的点开始，距离为R以内的最远的点进行标记，重复以上过程。

#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn = 1005;
int r,n,x[maxn];
int main(){
    scanf("%d %d",&r,&n);
    while(r != -1 && n != -1){
        for(int i=0;i<n;i++) scanf("%d",&x[i]);
        sort(x,x + n);
        int cnt = 0,i= 0;
        while(i < n){
            int s = x[i++];
            while(i < n && x[i] <= s + r) i++;
            int p = x[i-1];
            while(i < n && x[i] <= p + r) i++;
            cnt++;
        }
        printf("%d\n",cnt);
        scanf("%d %d",&r,&n);
    }
    return 0;
}