for (int i = 0; i < n; i++ ) {
    for (int j = 0; j < n; j++ {
        Simple Statement
    }
}
for (int k = 0; i < n; k++ {
    Simple Statement
    Simple Statement
    Simple Statement
    Simple Statement
    Simple Statement
}
    Simple Statement*25

对于嵌套循环，我发现1时间复杂度（对于int i = 0）+ N + 1（对于i n种）+ N（对于i ++）* [1（对于int J = 0）+ 1 + N（对于J＆n种）+ N（其中j ++）+ N（对于简单语句）。这是（1 + N + 1 + n）个的（1 + 1 + N + N）+ N =（2 + 2n）的的（的2 + 2n）+ N = 4N ^ 2 + 9N +4

For the nested loop, I find a time complexity of 1 (for int i = 0) + n + 1 (for i < n) + n (for i++) * [ 1 (for int j = 0 ) + 1 + n ( for j < n) + n ( for j++) ] + n (for the simple statement). This is (1+n+1+n)(1+1+n+n)+n = (2 + 2n)(2+2n)+n = 4n^2 + 9n + 4.

对于下面的循环，我觉得1（对于int k = 0）+ N + 1的时间复杂度（对于i n种）+ N（对于k ++）+ 5N（为五简单语句）。这是1 + N + 1 + N + 5N = 7N + 2。在接下来的25简单的报表，我发现他们有25时间复杂度。

For the following loop, I find a time complexity of 1 (for int k = 0) + n + 1 (for i < n) + n (for k++) + 5n (for the five simple statements). This is 1+n+1+n+5n = 7n+2. For the next 25 simple statements, I find they have a time complexity of 25.

所以总的时间复杂度为4N ^ 2 + 8N + 4 + 5N + 2 + 25 = 4N ^ 2 + 16N + 31，但是，我的书上说的时间复杂度为n ^ 2 + 5N + 25

So the total time complexity is 4n^2 + 8n + 4 + 5n + 2 + 25 = 4n^2 + 16n + 31, however, my book says the time complexity is n^2 + 5n + 25.

我做了什么错？

编辑：但是现在看来，这本书是讲述的只有的简单语句的时间复杂度。我现在想我的问题是这样的（因为它是在标题）：什么是算法的时间复杂度

It is now apparent that the book is telling the time complexity of only the simple statements. I suppose now my question is this (as it was in the title): What is the time complexity of the algorithm?

推荐答案

您的书是计数的只有的数量 SimpleStatements 执行。

Your book is counting only the number of SimpleStatements executed.