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一些正整数可以由一个或多个连续质数的总和表示。给定一个的正整数n,问满足条件的有多少种情况#xff1f;
题目#xff1a;
Some positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representat…题意
一些正整数可以由一个或多个连续质数的总和表示。给定一个的正整数n,问满足条件的有多少种情况
题目
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 23571113, 111317, 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
分析
1.将 2 至 10000 内的素数存入一个数组 2.对于每一个给定的数从左向右遍历数组根据连续素数的和的大小不断的增减元素直到找到一个个解。
AC模板
#includestdio.h
#includestring.h
#includealgorithm
using namespace std;
const int M1e410;
int n,k,r,l,ans,mi;
int dp[M],book[M];
void init()
{k0;/** for(int i2; iM; i){if(!book[i]){dp[k]i;for(int ji*2; jM; ji)book[j]1;}}*/for(int i2;iM;i){if(!book[i])dp[k]i;for(int j0;jki*dp[j]M;j){book[i*dp[j]]1;if(i%dp[j]0)break;}}}
int solve(int x)
{ans0;for(int i0; ikdp[i]x; i){li,mi0;while(mixlk){midp[l];}if(mix)ans;}return ans;
}
int main()
{init();while(~scanf(%d,n)n){printf(%d\n,solve(n));}return 0;
}备战ccpc分站赛ing 题目分析简略见谅转载请注明出处。。。。。
