Programming abstractions in C阅读笔记：p166-p175

《Programming Abstractions In C》学习第58天，p166-p175总结。

一、技术总结

1.斐波那契数列(Fibonacci Sequenc)

(1)斐波那契数列来源

斐波那契数列来自于《Liber Abaci》一书里兔子繁殖问题，相关资料很多，这里不赘述。

(2)关于《Liber Abaci》一书

《Liber Abaci》——Liber：a book(意思是“书”)；Abaci：abacus的复数形式(意思是“算盘”)。

根据Laurence Sigler《Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation》一书第9页内容“One should here again make the point, that while derived from the word abacus the word abaci refers in the thirteenth century paradoxically to calculation without the abacus. Thus Liber abaci should not be translated as The Book of the Abacus......”在13世纪， abaci是指直接使用印度数字(Hindu numerals)，而不用“算盘”进行计算。所以，这本书恰当的中文译名应该是《计算之书》(The Book of Calculation，注：纪志刚翻译的中文版用的就是这个名字)。

(3)关于“斐波那契”这个名字

既然称为斐波那契数列，那么作者的名字是否叫斐波那契？根据百科说法是：Liber Abaci is a historic 1202 Latin manuscript on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci。Fibonacci是“filius Bonacci”，即“son of Bonacci”(波那契之子)。参考Keith Devlin所著《The Man of Numbers: Fibonacci's Arithmetic Revolution》一书)。

2.递推关系(recurrence realtion)

p173：

t_n = t_n-1 + t_n-2

An expression of this type, in which each element of a sequence is defined in terms of earlier elements, is called a recurrence relation。

3.斐波那契序列的C语言实现

/*
 * File: fib.c
 * -----------
 * This program lists the terms in the Fibonacci sequence with
 * indices ranging from MinIndex to MaxIndex
 */

#include <stdio.h>
#include "genlib.h"

/* Constants */
#define MinIndex 0
#define MaxIndex 12

/* private function prototype */
int Fib(int n);

/* Main program */

int main() {
    int i;

    printf("This program lists the Fibonacci sequence.\n");
    for (i = MinIndex; i < MaxIndex; i++) {
        printf("Fib(%d)", i);
        if (i < 10) { // 打印对齐
            printf(" ");
        }
        printf(" = %4d\n", Fib(i));
    }
    return 0;
}

/*
 * Function: Fib
 * Usage: t = Fib(n)
 * -----------------
 * This function returns the nth term in the Fibonacci sequence
 * using a recursive implementation of the recurrence relation
 *
 * Fib(n) = Fib(n - 1) + Fib(n - 2)
 */

int Fib(int n) {
    if (n < 2) {
        return n;
    } else {
        return (Fib(n - 1) + Fib(n - 2));
    }
}

二、英语总结

1.suspcious什么意思？

答：

(1)suspicious < suspicion：adj. feel doubt or not trust(可疑的)。 语法结构：be suspicious of。

(2)suspicion < suspect：c/u.

(3)suspect: vt. sub-("up to") + *spek-("to observe")，The notion behind the word is "look at secretly," hence, "look at distrustfully"(怀疑)。

2.supersede是什么意思？

答：p168，The frame for Fact temporarily supersedes the frame for Main。vt. super-(above) + *sed-(to sit)，即“displace, replace”之意。

3.essence是什么意思？

答：u. the basic or most import quality of sth(本质、核心)。示例：p174, The essence of recursion is to break problems down into simpler ones that can be solved by calls to exactly the same function。形容词格式：essential。之前老是不记得essential是什么意思，这里对比着来记。

三、参考资料

1. 编程

(1)Eric S.Roberts，《Programming Abstractions in C》：https://book.douban.com/subject/2003414

2. 英语

(1)Etymology Dictionary：https://www.etymonline.com

(2) Cambridage Dictionary：https://dictionary.cambridge.org

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