如何計算三重嵌套循環中的頻率計數

Question

我正在嘗試確定三重嵌套循環的頻率計數。

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

我知道聲明x = x + 1將不會執行，直到我實現n

關於如何開始任何提示/建議的價值？

Answer 1

我們以4和5爲例。當i = 4，

... 
    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 

當i = 5，

... 
    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 

圖案？