Project Euler：Problem 77 Prime summations

Posted 2020-09-25 jhcelue

It is possible to write ten as the sum of primes in exactly five different ways:

7 + 3
5 + 5
5 + 3 + 2
3 + 3 + 2 + 2
2 + 2 + 2 + 2 + 2

What is the first value which can be written as the sum of primes in over five thousand different ways?

#include <iostream>
#include <string>
using namespace std;

int prime[1000];  //存储前1000个质数
bool vis[10000];

void getPrime()
{
	int count = 0;
	memset(vis, 0, sizeof(vis));
	for (int i = 2; i < 10000; i++)
	{
		if (!vis[i])
		{
			if (count >= 1000)
				break;
			prime[count++] = i;
			for (int j = i*i; j < 10000; j += i)
				vis[j] = 1;
		}
	}
}
int main()
{
	getPrime();
	int *ways;
	int num = 2;
	while (true)
	{
		
		ways = new int[num+1];
		for (int i = 0; i < num + 1; i++)
			ways[i] = 0;
		ways[0] = 1;
		for (int i = 0; i < 1000; i++)
		{
			for (int j = prime[i]; j <= num; j++)
			{
				ways[j] += ways[j - prime[i]];
			}
		}
		//cout << num <<" " << ways[num]<< endl;
		if (ways[num]>5000)
			break;
		else
			num++;
	}
	cout << num << endl;
	
	system("pause");
	return 0;
}