Sum of Consecutive Prime Numbers(poj2739)

Posted 2020-06-11

Sum of Consecutive Prime Numbers

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 22019		Accepted: 12051

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

2
3
17
41
20
666
12
53
0

Sample Output

1
1
2
3
0
0
1
2

Source

Japan 2005

思路：先筛选出0到10000的素数，再尺取法跑一遍就可以了

 1 import java.util.*;
 2 import java.lang.*;
 3 import java.io.*;
 4 
 5 public class Main {
 6     public static void main(final String[] args) {
 7         Scanner in = new Scanner(System.in);
 8         int n, i, j, k, p, q;
 9         int aa[] = new int[20000];
10         int bb[] = new int[20000];
11         Arrays.fill(aa, 0);
12         aa[1] = 1;
13         aa[0] = 1;
14         int cnt = 0;
15         for (i = 2; i <= 100; i++) {
16             if (aa[i] == 0) {
17                 for (j = i; i * j <= 10000; j++) {
18                     aa[i * j] = 1;
19                 }
20             }
21 
22         }
23         for (i = 0; i <= 10000; i++) {
24             if (aa[i] == 0) {
25                 bb[cnt++] = i;
26             }
27         }
28         int ss = 1;
29         while (ss == 1) {
30             k = in.nextInt();
31             int ans = 0;
32             if (k == 0) {
33                 break;
34             } else {
35                 int sum = 0;
36                 int ll = 0;
37                 int rr = 0;
38                 while (ss == 1) {
39                     if (rr > cnt) {
40                         break;
41                     }
42                     if (bb[rr] > k) {
43                         break;
44                     }
45                     if (ll > rr) {
46                         break;
47                     }
48                     while (ss == 1) {
49                         sum += bb[rr];
50                         if (sum >= k) {
51                             break;
52                         } else {
53                             rr++;
54                         }
55                         if (rr > cnt) {
56                             break;
57                         }
58                     }
59                     if (sum == k) {
60                         ans++;
61                     }
62                     sum -= bb[ll];
63                     sum -= bb[rr];
64                     ll++;
65                 }
66             }
67             System.out.println(ans);
68         }
69         return;
70     }
71 }

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