我不明白sigma表示法和for循环 [英] I don't understand the sigma notation and for loop

问题描述

我有一本书说

，并说这等同于

  for（i = 1; i< = N; i ++）
 Sum + = i; 
  

它进一步说，利用这个简单的公式，

最大值-最小值+ 1）

，并说将其更改为C代码将是

  for（k = j; k< = 1; k ++）
 Sum + = k; 
  

但是，我真的无法理解！有人可以向我解释吗？？???

非常感谢

解决方案

关于第二个总和，起始于 k = j ，终止于 i 。该总和不等于（j-i-1），而是等于（i-j + 1）。让我们举个例子：

如果 j = 3 和 i = 6 ，则 k = 3 和 sum = 1 + 1 + 1 + 1 = 4 。通过应用公式： sum =（i-j + 1）= 6-3 +1 = 4 。

现在，第一个示例的C代码说：

for（i = 1; i <= N; i ++）
Sum + = i;

这是错误的。相反，它应该是：

  for（i = 1; i< = N; i ++）
 Sum + = 1; 
  

在第二个中，他们说：

< blockquote>

for（k = j; k< = 1; k ++）
Sum + = k;

它应该是：

  for（k = j; k< = i; k ++）
总和== 1; //其中i> = j 
  

I have the book saying that

and says that this is equivalent to saying

for(i = 1; i <= N; i++)
    Sum += i;

and it further says utilising this simple formula,

since (maximum value - minimum value + 1 )

and it says changing this to C code would be

for(k = j; k <= 1; k++)
    Sum += k;

However, I seriously cannot understand this! can anyone explain this to me?????

Thank you very much

解决方案

About the second sum, it starts at k=j and ends at i. That sum is not equal to (j - i - 1), instead, it's equal to (i - j + 1). Let's do an example :

If j = 3 and i = 6, then k = 3 and sum = 1+1+1+1 = 4. By applying the formula : sum = (i - j + 1) = 6 - 3 + 1 = 4.

Now, the C code for the first example, they said :

for(i = 1; i <= N; i++) Sum += i;

This is wrong. Instead, it should be :

for(i = 1; i <= N; i++)
    Sum += 1;

In the second one, they said :

for(k = j; k <= 1; k++) Sum += k;

Instead, it should be :

for(k = j; k <= i; k++)
    Sum += 1;     // Where i >= j

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