POJ-3069 Saruman's Army （贪心）

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字数统计: 596 | 阅读时长 ≈ 3

描述

传送门：POJ-3069 Saruman's Army

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.

输入描述

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.

输出描述

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

示例

输入

1
2
3
4
5
0 3
10 20 20
10 7
70 30 1 7 15 20 50
-1 -1

输出

1
2
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.

题解

题目大意

从n个点中选择若干个进行标记，对于每一个点，其距离为R的区域以内必须有带标记的点，问最少有多少点被标记。

思路

标记从最左边的点开始，距离为R以内的最远的点。对于添加了符号的点右侧，相距超过R的下一个点，采用同样的方法找到其右侧R距离以内最远的点添加标记。

代码

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#include <vector>
#include <map>
#include <set>
#include <algorithm>
#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <string>
#include <cstring>
#include <queue>
const int MAXN = 1e3 +5;
using namespace std;
int a[MAXN];

int main(){
    int r, n;
    while(cin >> r >> n){
        if(r == -1 && n == -1) break;
        for(int i = 0; i < n; i++){
            cin >> a[i];
        }
        sort(a, a+n);
        int i = 0, ans = 0;
        while(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++;
        }
        cout << ans << endl;
    }
}