欧拉计划28

最新推荐文章于 2022-09-28 21:45:15 发布

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本文介绍了一个解决计算1001x1001螺旋矩阵对角线元素总和的问题的方法，通过两段C++代码实现了高效的计算过程。第一段代码通过迭代减小步长来逼近中心值，第二段代码则通过公式简化了计算步骤。

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Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

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

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

Answer:

669171001

#include<iostream>
using namespace std;

int main()
{
	int n,m;
	int index = 0;
	long long temp = 1002001,ans = temp;
	int de = 1000;
	while((temp-=de) >= 1){
		ans+=temp;
		index++;
		if(index == 4){
			de -= 2;
			index = 0;
		}
		if(de<=0) break;
		
	}
	
	cout<<ans<<endl;
	return 0;
}

更新一下做法：

#include <iostream>
#include <algorithm>
#include <string.h>
using namespace std;

int main() {
    int sum = 1;
    for(int l = 3; l <= 1001; l+= 2) {
        sum += 4 * l * l - 6 * l + 6;
    }
    printf("%d\n", sum);
    return 0;
}