Loops 计算迭代次数

对于任意给定的N（>=1），我如何计算这些循环将进行多少次迭代

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for（1在不更改内部循环执行次数的情况下（尽管您将更改顺序），您可以将循环更改为：（这可以完成，因为
i
和
j
彼此独立）

也就是说，
1+2+3+…+N=N（N+1）/2
执行（对于这些类型的计算，这是值得了解的）

添加
i
只需将其增加6倍，因此我们有
3*N（N+1）
而不更改内部循环的执行次数（尽管您会更改顺序），您可以将循环更改为：（这可以实现，因为
i
和
j
彼此独立）

也就是说，
1+2+3+…+N=N（N+1）/2
执行（对于这些类型的计算，这是值得了解的）

添加
i
只需将其增加6倍，因此我们有
3*N（N+1）
？
应该是（N+1）/2，正整数的和等于N。为了确保我编写了一个powershell脚本来检查该理论：

for($N=1; $N -le 10; $N++)
{
  $totalCount = 0

  for ($k=1; $k -le $N; $k++)
  {
    for ($i=0; $i -lt 6; $i++)
    {
      for ($j=0; $j -lt $k; $j++)
      {    
        $totalCount++
      }
    }
  }

  Write-Host("Total Count for N={0} is {1}" -f $N, $totalCount)
  $calcTotal = ($N*($N+1)/2)*6
  Write-Host("Calulated total ={0}" -f $calcTotal)
}

这将产生：

Total Count for N=1 is 6
Calulated total =6
Total Count for N=2 is 18
Calulated total =18
Total Count for N=3 is 36
Calulated total =36
Total Count for N=4 is 60
Calulated total =60
Total Count for N=5 is 90
Calulated total =90
Total Count for N=6 is 126
Calulated total =126
Total Count for N=7 is 168
Calulated total =168
Total Count for N=8 is 216
Calulated total =216
Total Count for N=9 is 270
Calulated total =270
Total Count for N=10 is 330
Calulated total =330

？？？
应该是（N+1）/2，正整数的和等于N。为了确保我编写了一个powershell脚本来检查该理论：

for($N=1; $N -le 10; $N++)
{
  $totalCount = 0

  for ($k=1; $k -le $N; $k++)
  {
    for ($i=0; $i -lt 6; $i++)
    {
      for ($j=0; $j -lt $k; $j++)
      {    
        $totalCount++
      }
    }
  }

  Write-Host("Total Count for N={0} is {1}" -f $N, $totalCount)
  $calcTotal = ($N*($N+1)/2)*6
  Write-Host("Calulated total ={0}" -f $calcTotal)
}

这将产生：

Total Count for N=1 is 6
Calulated total =6
Total Count for N=2 is 18
Calulated total =18
Total Count for N=3 is 36
Calulated total =36
Total Count for N=4 is 60
Calulated total =60
Total Count for N=5 is 90
Calulated total =90
Total Count for N=6 is 126
Calulated total =126
Total Count for N=7 is 168
Calulated total =168
Total Count for N=8 is 216
Calulated total =216
Total Count for N=9 is 270
Calulated total =270
Total Count for N=10 is 330
Calulated total =330

似乎是正确的，但N=1将导致0次迭代遵循您的公式，当它实际循环6次时（易于遵循）似乎是正确的，但N=1将导致0次迭代遵循您的公式，当它实际循环6次时（易于遵循）
Total Count for N=1 is 6
Calulated total =6
Total Count for N=2 is 18
Calulated total =18
Total Count for N=3 is 36
Calulated total =36
Total Count for N=4 is 60
Calulated total =60
Total Count for N=5 is 90
Calulated total =90
Total Count for N=6 is 126
Calulated total =126
Total Count for N=7 is 168
Calulated total =168
Total Count for N=8 is 216
Calulated total =216
Total Count for N=9 is 270
Calulated total =270
Total Count for N=10 is 330
Calulated total =330