November 2017
Beginner to intermediate
344 pages
7h 2m
Chinese
Content preview from 深入理解運算原理｜從簡單的機器到無所不能的程式
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266
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第 8 章
生命的事實
這些都是相當嚴重且重要的問題，所以在試著處理這些問題之前，先讓我們快速的瞭解
運算世界的一些重要事實。其中的部分事實相當顯而易見，其他的就不是那麼明顯，但
它們全都是思考運算機器功能和限制的重要必要條件。
通用系統可以執行演算法
我們通常可以用諸如圖靈機、lambda 演算、部分遞迴函式等通用系統做什麼？如果我
們能正確瞭解這些系統的功能，那麼我們就能鑽研他們的限制。
運算機器的實際目的是執行
演算法
（
algorithm
）；演算法是一成串的指示，這些指示描
述了將輸入值轉換成輸出值的某些過程，而這些指示應該要滿足某些準則：
有限
指令的數量有限。
簡單
每條指令簡單的足以由人以紙、筆執行，而不需動腦筋。
終止
遵循指令的人將根據任何輸入在數量有限的步驟完成。
正確
遵循指令的人將根據任何輸入產生正確的答案。
舉例來說，西元前 300 年左右的歐幾里德演算法是最古老的演算法之一，它需要兩個正
整數，並且會傳回將它們兩個都整除的最大整數，也就是它們的
最大公因數
（
greatest
common divisor
）。以下是它的指令：
1. 將
x
和
y
指定給這兩個數作為名稱。
2. 決定
x
和
y
何者為大數。
3. 以大數減小數（如果
x
是大數，就以
x
減
y
，並以此作為
x
的新值；如果
y
為大
數，就反過來執行）。
4. 重複步驟 2 和 3，一直到
x
等於
y
。
5. 當
x
等於
y
的時候，它們的值就是原來兩個數值的最大公因數。
不可能的程式
|
267
我們很高興將這認定為演算法，因為它似乎符合基本準則。它只包含一些說明，而且它 ...
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I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.