POJ 3069 Saruman's Army

Saruman's Army

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 11388 Accepted: 5758

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 positionsx₁, …, 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

解析：题意为在街道上有n个点，在这些点上放置路灯，告诉你路灯的照射范围为R，求最少放置多少路灯能照亮所有的点。运用贪心即可：从最左边的点开始，找到这个点向右范围R以内的最远能到达的点，在这里设置路灯，然后前进到大于R的点（跳过右边路灯能覆盖到的范围），剩下的部分也照此处理。
 

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