Saruman’s Army
Time Limit: 1000MS Memory Limit: 65536K
题目链接
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, …, xn of each troop (where 0 ≤ xi ≤ 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
Solution
题意：一条路上有n个路灯，每个路灯都能照亮左右的一段距离，问最少需要多少路灯才能使街道都亮着
greedy
从最左开始向右延伸r，在r的范围内将最右的路灯点亮，此时这盏路灯将照亮左边和右边，从暗处的最左路灯开始，已知重复下去。
时间复杂度 O(n)
!!!需要将路灯位置排序
#include<iostream>
#include<algorithm>
using namespace std;
int r,n;
int x[1006];
int main()
{//freopen("input.txt","r",stdin);while(scanf("%d%d",&r,&n)==2 && r!=-1){for(int i=0;i<n;i++)scanf("%d",&x[i]);sort(x,x+n); // ！！！记得排序int j=0,ans=0;while(j<n){int s=x[j++];while(j<n && x[j]<=s+r) j++;int p=x[j-1];while(j<n && p+r>=x[j]) j++;ans++;} printf("%d\n",ans);}return 0;
}