POJ 3069

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

2
4
#include <iostream>#include <vector>#include <algorithm>using namespace std;int main(){int R, n;vector<int> troop;while (cin >> R >> n){if (R == -1 && n == -1)break;troop.clear();int temp, total = 0;for (int ic = 0; ic < n; ic++){cin >> temp;troop.push_back(temp);}sort(troop.begin(), troop.begin() + n);vector<int>::iterator itr = troop.begin();while (itr != troop.end()){int left = *itr++;while (itr != troop.end() && (*itr-left) <= R)itr++;int p = *(--itr);while (itr != troop.end() && (*itr-p) <= R)itr++;total++;}cout << total << endl;}return 0;}