大量求和 [英] Summing Large Numbers

问题描述

我在欧拉计划网站上遇到了一些问题，遇到了问题。问题问：算出以下一百五十位数的总和的前十位数。我猜想有某种数学方法可以解决这个问题，但我只是想知道这么大的数字是如何相加的？我将数字存储为字符串，并将每个数字转换为长整数，但是数字太大，以至于总和不起作用。

I have being doing some problems on the Project Euler website and have come across a problem. The Question asks,"Work out the first ten digits of the sum of the following one-hundred 50-digit numbers." I am guessing there is some mathematical way to solve this but I was just wondering how numbers this big are summed? I store the number as a string and convert each digit to a long but the number is so large that the sum does not work.

有没有一种方法可以保存很大的数字数字作为变量（不是字符串）？我不需要代码解决问题，因为我想自己解决问题。

Is there a way to hold very large numbers as a variable (that is not a string)? I do not want the code to the problem as I want to solve that for myself.

推荐答案

我只是想知道这么大的数字是如何相加的？

I was just wondering how numbers this big are summed?

您可以使用数组：

long LargeNumber[5] = { < first_10_digits>, < next_10_digits>....< last_10_digits> };

现在您可以计算2个大数的总和：

Now you can calculate the sum of 2 large numbers:

  long tempSum = 0;
  int carry = 0;
  long sum[5] = {0,0,0,0,0};

  for(int i = 4; i >= 0; i--)
  {
    tempSum = largeNum1[i] + largeNum2[i] + carry; //sum of 10 digits

    if( i == 0)
      sum[i] = tempSum; //No carry in case of most significant digit
    else
      sum[i] = tempSum % 1000000000; //Extra digits to be 'carried over'

    carry = tempSum/1000000000;
  }

  for( int i = 0; i < 5; i++ )
    cout<<setw(10)<<setfill('0')<<sum[i]<<"\n"; //Pad with '0' on the left if needed

一种将非常大的数字作为变量保存的方法（不是
字符串）？

Is there a way to hold very large numbers as a variable (that is not a string)?

对此没有原始方法，您可以使用任何数据结构（数组/队列/链表）并适当地处理它

There's no primitive for this, you can use any data structure (arrays/queues/linkedlist) and handle it suitably

我想有一些数学方法可以解决这

I am guessing there is some mathematical way to solve this

当然！但是，

我不想让代码出现问题，因为我想自己解决这个问题。

I do not want the code to the problem as I want to solve that for myself.

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