hdu 2739(尺取法)

Sum of Consecutive Prime Numbers

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 22876		Accepted: 12509

Description

Some positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representations does a given positive integer have? For example, the integer 53 has two representations 5 + 7 + 11 + 13 + 17 and 53. The integer 41 has three representations 2+3+5+7+11+13, 11+13+17, and 41. The integer 3 has only one representation, which is 3. The integer 20 has no such representations. Note that summands must be consecutive prime
numbers, so neither 7 + 13 nor 3 + 5 + 5 + 7 is a valid representation for the integer 20.
Your mission is to write a program that reports the number of representations for the given positive integer.

Input

The input is a sequence of positive integers each in a separate line. The integers are between 2 and 10 000, inclusive. The end of the input is indicated by a zero.

Output

The output should be composed of lines each corresponding to an input line except the last zero. An output line includes the number of representations for the input integer as the sum of one or more consecutive prime numbers. No other characters should be inserted in the output.

Sample Input

Sample Output

1
1
2
3
0
0
1
2

题意:给你一个数，询问有多少个连续质数序列和等于该数例如53=5 + 7 + 11 + 13 + 17 
题解:筛选出所有质数，然后利用尺取法在O(n)的时间复杂度里面找到所有满足条件的子序列。

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <stdlib.h>
#include <map>
using namespace std;
typedef long long LL;
const int N = 10005;
bool p[N];
int a[2000];
void init(){
    int id = 1;
    for(int i=2;i<N;i++){
        if(!p[i]){
            a[id++] = i;
            for(int j=i*i;j<N;j+=i){
                p[j] = true;
            }
        }
    }
}
int bin(int x){
    int l = 1,r=1300;
    while(l<=r){
        int mid = (l+r)>>1;
        if(a[mid]==x) return mid;
        else if(a[mid]>x) r = mid-1;
        else l = mid+1;
    }
    return l;
}
int main()
{
    init();
    int n;
    while(scanf("%d",&n),n){
        int l=1,r=1,sum=0,cnt=0;
        int len = bin(n);
        while(l<=len){
            while(r<=len&&sum<n){
                sum+=a[r++];
            }
            if(sum<n) break;
            if(sum==n) cnt++;
            sum-=a[l];
            l++;
        }
        printf("%d
",cnt);
    }
    return 0;
}