So, in Studio Zero, you created some empirical estimates of performance.

所以，在 Studio Zero 中，你對性能進行了一些經驗估算。

So, you used ticks, which are a useful way to measure operations empirically, as in an actual experiment.

所以，你使用了 "刻度線"，這是一種根據經驗測量操作的有用方法，就像在實際實驗中一樣。

So, the ticks represented the constant time operations if you place them correctly.

是以，如果放置得當，刻度線就代表了恆定的時間運算。

So, if you place them correctly, they're proportional to time.

是以，如果放置得當，它們就會與時間成正比。

So, there's some limits to these empirical approaches.

是以，這些實證方法有一定的侷限性。

So, the empirical approaches requires a lot of work.

是以，實證方法需要大量的工作。

You have to create the code.

您必須創建代碼。

You have to set up some experiments.

你必須做一些實驗。

You have to choose the right data for your experiments.

您必須為實驗選擇正確的數據。

So, in some of the examples we'll look at later with sorting, the code performs differently on different orders of data.

是以，在我們稍後要看的一些排序示例中，代碼對不同順序的數據執行不同的操作。

And you want to be sure to examine the ones that would be of interest to you or where the worst case would occur.

你要確保檢查那些你感興趣的或最壞情況會發生的地方。

Then, you actually have to run the experiments.

然後，你就必須進行實驗。

And as you experienced in the studio, running experiments takes time.

正如你在工作室所經歷的那樣，進行實驗需要時間。

Then, you have to analyze the results.

然後，你必須對結果進行分析。

And it's possible that you messed something up in this process and have to repeat it all in order to get valid data, okay?

有可能你在這個過程中弄錯了什麼，為了得到有效的數據，你必須重複這一切，好嗎？

Not only that, remember that often we're trying to figure out which of multiple algorithms is better.

不僅如此，請記住，我們經常試圖找出多種算法中哪一種更好。

So, if you're trying to decide between two alternatives, you have to go through all of this for both alternatives.

是以，如果您要在兩個備選方案中做出決定，您必須對兩個備選方案都進行上述操作。

Create two sets of code.

創建兩套代碼。

Run multiple sets of experiments.

進行多組實驗。

Analyze all of the results of both experiments to compare them to one another.

分析兩個實驗的所有結果，將它們進行比較。

So, today we're going to focus on an alternative, an analytical approach.

是以，今天我們將重點討論另一種分析方法。

So, as compared to the empirical approach, no code is needed.

是以，與經驗方法相比，無需編寫代碼。

So, you can use this approach to decide which version of code is worth creating before you actually create it.

是以，在實際創建代碼之前，您可以使用這種方法來決定哪個版本的代碼值得創建。

Now, you do need to have a plan.

現在，你確實需要有一個計劃。

You need to know what your code is going to be doing.

你需要知道你的代碼要做什麼。

And you have to be pretty precise about it.

而且你必須非常精確。

But still, you can use this in advance of actual implementation.

不過，您還是可以在實際實施前使用它。

Another huge advantage of this is that it's easier to focus on the worst case.

這樣做的另一個巨大優勢是，更容易將注意力集中在最壞的情況上。

You can estimate operations needed in the worst case even without a really precise idea of what causes the worst case or when the worst case occurs.

即使不知道造成最壞情況的原因或最壞情況何時發生，也可以估算出最壞情況下所需的操作。