[Project Euler] Problem 58

Problem Description

Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.

3736 35 34 33 3231

381716 15 141330

39 1854312 29

40 19 6 1 2 11 28

41 2078 9 10 27

42 21 22 23 24 25 26

4344 45 46 47 48 49

It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 = 62%.

If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?

C++

This problem is similar with problem 28, not too hard, just brute force.

const double THRESHOLD = 0.1;

void Problem_58()
{

    int firstNum = 0;
    int lastNum = 1;
    int layer = 0;

    double ratio = 1;
    int whole = 1;
    int prime = 0;
    while(ratio >= THRESHOLD)
    {
        layer++;
        int increment = layer * 2;
        int firstNum = lastNum + increment;
        lastNum = firstNum;
        if(IsPrime(lastNum))
        {
            prime++;
        }
        for(int i=0; i<3; i++)
        {
            lastNum += increment;
            if(IsPrime(lastNum))
            {
                prime++;
            }
        }
        whole += 4;
        ratio = ((double)prime) / whole;
        printf("%d/%d, %f,%d\n", prime, whole, ratio, increment + 1);
    }
        printf("%f,%d\n", ratio, 2 * layer + 1);

}

原文链接: https://www.cnblogs.com/quark/archive/2012/08/15/2639550.html

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