如何计算三重嵌套循环中的频率计数

Question

我正在尝试确定三重嵌套循环的频率计数。

for i = 1 to n do
    for j = 1 to i do
        for k = i to j do
            x =  x + 1

我知道语句x = x + 1在获得n

的值之前不会被执行

有关如何入门的任何提示/建议？

Answer 1

让我们以4和5为例。当i = 4时，

...
    for j = 1 to 4 do
        for k = 4 to j do
            x =  x + 1

...j = 1
   for k = 4 to 1 do  // 4 times
       x =  x + 1
...j = 2
   for k = 4 to 2 do  // 3 times
       x =  x + 1
...j = 3
   for k = 4 to 3 do   // twice
       x =  x + 1
...j = 4
   for k = 4 to 4 do   // once
       x =  x + 1

当i = 5时，

...
    for j = 1 to 5 do
        for k = 5 to j do
            x =  x + 1

...j = 1
   for k = 5 to 1 do  // 5 times
       x =  x + 1
...j = 2
   for k = 5 to 2 do  // 4 times
       x =  x + 1
...j = 3
   for k = 5 to 3 do   // 3 times
       x =  x + 1
...j = 4
   for k = 5 to 4 do   // twice
       x =  x + 1
...j = 5
   for k = 5 to 5 do   // once
       x =  x + 1

图案？