zoukankan      html  css  js  c++  java
  • [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);
    }
    
  • 相关阅读:
    利用python做矩阵的简单运算(行列式、特征值、特征向量等的求解)
    numpy.linalg.svd函数
    梯度裁剪(Clipping Gradient):torch.nn.utils.clip_grad_norm
    tf.matmul()报错expected scalar type Float but found Double
    1283 最小周长
    1182 完美字符串
    1091 线段的重叠
    1090 3个数和为0
    1087 1 10 100 1000
    1083 矩阵取数问题
  • 原文地址:https://www.cnblogs.com/quark/p/2555946.html
Copyright © 2011-2022 走看看