POJ 3069

Saruman's Army

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 887		Accepted: 487

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

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难度： 1    代码：  1    分类： 贪心

分析：

将所有的点排序，从初始点的坐标+r作为预期最好的中心点，然后查找后面的点，如果正好是坐标点，否则就取最接近初始点+r的略小的那个点作为中心点，把所有坐标<=中心点+r的点都滤掉，以第一个>初始点+2r的点作为初始点继续贪心。

代码：

#include  < stdio.h >

int  pt[ 1000 ];

int  cmp( const   void   *  a, const   void   *  b)
... {
    return *((int *)a)-*((int *)b);
}

int  main()
... {
    int r,n,i,count;
    int s,tag;
    while(1)
    ...{
        scanf("%d%d",&r,&n);
        if(r==-1&&n==-1) break;        
        for(i=0;i<n;i++)
        ...{
            scanf("%d",pt+i);
        }
        
        qsort(pt,n,sizeof(int),cmp);
        s=pt[0]+r;count=1;
        tag=0;
        for(i=0;i<n;)
        ...{    
            while(i<n&&pt[i]<s) i++;
            if(i==n) break;
            if(pt[i]==s)
            ...{
                s+=r;                                
            }
            else
            ...{
                s=pt[i-1]+r;                                    
            }
            while(i<n&&pt[i]<=s) i++;
                if(i==n) break;                
                s=pt[i]+r;
                count++;
        }
        printf("%d ",count);
    }
}