2739 -- Sum of Consecutive Prime Numbers

Keywords:Collecting prime numbers algorithm

筛选法求素数

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

1不算

遍历一遍，删掉2的倍数：得2 3 5 7 9 11 13 15 17 19 21 23 25

遍历一遍，删掉3的倍数：得2 3 5 7 11 13 17 19 23 25

遍历一遍，删掉5的倍数：得2 3 5 7 11 13 17 19 23

The key thinking is that when we delete all the non-prime numbers, we get prime numbers.

/*****************************************

* Problem No. 2739

* Algorithm: Prime Numbers Collecting

* Date: Oct 18,2008

* Author: Jessie Zhang

******************************************/

#include <iostream>

using namespace std;

const int SIZE = 10000;

const int minPrime = 2;

int primesCnt = 0;

//prime numbers table

int prePrimes[SIZE + 1];

bool isPrime[SIZE + 1];

int main(void)

{

//initialize isPrime table

for(int i = 2;i <= SIZE;i++)

{

isPrime[i] = true;

prePrimes[i] = 0;

}

//get all primes

int maxDivider = 100;

for(int divider = 2;divider <= maxDivider;divider++)

{

if(!isPrime[divider])

continue;

int maxMultiplier = SIZE / divider;

for(int multiplier = 2;multiplier <= maxMultiplier;multiplier++)

{

isPrime[divider * multiplier] = false;

}

}

for(int i = SIZE;i >= 3;)

{

int j = i;

while(j >= 2)

{

j--;

if(isPrime[j])

break;

}

for(int k = i;k > j;k--)

{

prePrimes[k] = j;

}

i = j;

}

int inputNum;

int counter;

int numOfAdders;

int sum;

while(true)

{

cin>>inputNum;

if(inputNum == 0)

break;

if(inputNum == 1)

{

cout<<0<<endl;

continue;

}

if(inputNum == 2)

{

cout<<1<<endl;

continue;

}

counter = 0;

if(isPrime[inputNum])

counter++;

numOfAdders = 2;

int index = prePrimes[inputNum];

while(true)

{

bool flag = false;

sum = 0;

int oldIndex = index;

for(int i = 0;i < numOfAdders;i++)

{

if(index == 0)

{

flag = true;

break;

}

sum += index;

index = prePrimes[index];

}

if(flag)

break;

if(sum == inputNum)

{

numOfAdders++;

index = prePrimes[oldIndex];

counter++;

}

else if(sum < inputNum)

{

numOfAdders++;

index = oldIndex;

}

else

{

index = prePrimes[oldIndex];

}

}

cout<<counter<<endl;

}

return 0;

}