[Project Euler] Problem 50

Problem Description

The prime 41, can be written as the sum of six consecutive primes:

41 = 2 + 3 + 5 + 7 + 11 + 13

This is the longest sum of consecutive primes that adds to a prime below one-hundred.

The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and is equal to 953.

Which prime, below one-million, can be written as the sum of the most consecutive primes?

 

C++

Here is the way:

Firstly, we fill a integer array with primes which ranges from 1 to one million, we use the prime array to calculate later;

Secondly, We set two pointers, one points to the first element of the array above, the other points to the position behind the last element, we assume that the longest consecutive primes are these from the start pointer to the end pointer. If not, we move the end pointer to its previous position, then check again.

Thirdly, If we find a valid list, we record it, and add the start pointer by one and reset the end pointer which means move the end pointer to the (last element + 1) place. Repeat step 2.

 

Codes:

int* g_primeArray = NULL;
int g_primeCount = 0;

const int MAX_NUM = 1000000;

void Initialize()
{
	g_primeCount = MAX_NUM / 5;
	g_primeArray = new int[g_primeCount];
	MakePrimes(g_primeArray, g_primeCount, MAX_NUM);

}

int CalculateSum(int* start, int* end, int& length, bool& isMax)
{
	isMax = false;
	int* low = start;
	int* high = end;
	int sum = 0;
	while(low < high)
	{
		sum += *low;
		if(sum > MAX_NUM)
		{
			isMax = true;
			sum -= *low;
			break;
		}
		else
		{
			low++;
		}
	}
	length = low - start; 
	return sum;
}

void Problem_50()
{
	Initialize();
	int maxLength = 1;
	int maxPrime = 0;
	int* start = g_primeArray;
	int* end = g_primeArray + g_primeCount;

	while(start < end)
	{
		int length = 0;
		bool isMax = false;
		int sum = CalculateSum(start, end, length, isMax);
		if(length < maxLength)
		{
			if(isMax)
				break;
			start++;
			end = g_primeArray + g_primeCount;
			continue;
		}
		if(IsPrime(sum))
		{
			maxLength = length;
			maxPrime = sum;
			// printf("max length = %d, max prime = %d\n", maxLength, maxPrime);

			start++;
			end = g_primeArray + g_primeCount;
		}
		else
		{
			end = start + length - 1;
		}
	}
	printf("max length = %d, max prime = %d\n", maxLength, maxPrime);
}