Python程序设计（第三版）约翰·策勒 编程练习课后答案（第三章）

3.1、编写一个程序，利用球体半径作为输入，计算体积和表面积。

# File: 3.1.py
# -*- coding: utf-8 -*-
# Calculation of the surface area and volume of a sphere

import math
def calA_V():
	print("This program calculates the surface area and volume of a sphere.")
	r = eval(input("The radius is: "))
	PI = math.pi
	v = 4/3*PI*r**3            #**操作符进行指数运算
	s = 4*PI*r**2
	print("The surface area is: %.2f\nThe volume is: %.2f"%(s, v))

calA_V()

3.2、给定披萨饼的直径和价格，计算每平方英寸成本。

#  File: 3.2.py
# -*- coding: utf-8 -*-
# unit cost of pizza
import math
def unitCost():
	print("This program calculates the unit cost of\nthe pizza with given diameter and price.")
	print("*"*20)
	d = eval(input("The diameter of the pizza(inches): "))
	price, currency = input("The price of the pizza: ").split()   #从空格处分割字符串
	price = eval(price)
	Ucost = price / (math.pi*d/4)
	print("This pizza cost %.2f %s per suqare inch."%(Ucost, currency))

unitCost()

3.3、编写程序，计算碳水化合物分子量。

# File:3.3.py
# -*-coding:utf-8 -*-
#

def Counting():
	print("This program caculates the formula weight of carbohydrate.")
	h, o, c = eval(input("The number of hydrogens, oxygens and  carbons (separate by comma): "))
	carb=  1.00794*h + 12.1017*o + 15.9994*c
	print("The formula weight of carbohydrate is: ", carb)

Counting()

3.4、编写程序，根据闪光和雷声之间的时间差来确定雷击距离。声速1100英尺/秒，1英里=5280英尺。

3.5、Konditorei咖啡店售卖咖啡，每磅10.5美元加上运费。每份订单运费每磅0.86美元+固定成本1.5美元。编写计算订单费用的程序。

# File: 3.4.py
# -*- coding : utf-8 -*-

def thunderDis():
	print("This program cauculates the distance from a thunder.")
	t = eval(input("Enter the time interval between the lighting and thunder: "))
	print("The distance from the thunder is: %.5f"%(t*1100/5280), "miles.")

thunderDis()

def coffeePrice():
        w = eval(input("The weight of coffee (rating in pounds): "))
        price = w*(10.5+1.86) + 1.5
        print("The price of this order is %.3f dollars"%price)

coffeePrice()

3.6~3.7、使用坐标（x1, y1）和（x2, y2）指定平面中的两个点，编写程序，计算通过用户输入的两个点的（非垂直）的直线的斜率。编写程序，计算两点间距离。

# Flie: 3.6.py
# -*- coding: utf-8 -*-

def rateNdis(a, b):
	import math
	x1, y1 = a[0], a[1]
	x2, y2 = b[0], b[1]
	d = math.sqrt((x1 - x2)**2 + (y1 - y2)**2) #计算两点间距离
	if x1 == x2:
		r = "infinity"             #直线垂直于x轴，斜率无穷大
	elif y1 == y2:
		r = 0                      #直线平行于x轴，斜率为0
	else:
		r = (y1 - y2)/(x1 - x2)
	return r, d

p1 = eval(input("The coordinates of the first point: "))
p2 = eval(input("The coordinates of the second point: "))
r, d = rateNdis(p1, p2)                        #将函数的返回值赋给r, d
print("The rate of this line is: ",r, "\nThe distance of this segment is: ",d)

运行结果：

3.8、格里高利润余是从1月1日到前一个新月的天数。此值用于确定复活节的日期，它由下列公式计算（使用整型算术）：
C = year // 100
epact = (8 + (C // 4) - C + ((8C + 13)//25) + 11(year % 19))%30
编写程序，提示用户输入4位年份，然后输出润余的值。

# File:3.8.py
# -*- coding:utf-8 -*-

def main():
    year = eval(input("Enter the year: "))
    c = year//100
    epact = (8 + (c//4) - c +((8*c + 13)//25) + 11*(year%19))%30
    print("Epact: ",epact)

main()

3.9、使用以下公式编写程序以计算三角形的面积，其三边长度为a,b,c。
s = (a + b + c)/2
A = √s(s - a)(s - b)(s - c)

# Flie:3.9.py
# -*- coding: utf-8 -*-

import math #
def TriArea():
    "This program calculates the area of a triangle according the length of its sides."
    sides = eval(input("Enter the length of three sides of a triangle: ")) #此时sides为字典类型
    s = sum(sides)/2
    A = math.sqrt(s * (s - sides[0]) * (s - sides[1]) * (s - sides[2]))
    print("The area of the triangle is: %.2f"%A)
    
TriArea()

3.10、编写程序，确定梯子斜靠在房子上时，达到给定高度所需的长度，并使用公式进行转换。

# File: 3.10.py
# -*- coding: utf-8 -*-

import math #
def main():
    h = eval(input("The height of the ladder: "))
    a = eval(input("The angle between the latter and the wall: "))
    PI = math.pi
    print("The length of the ladder should be %.2f"%(h/math.sin(a/180*PI)))
    #计算时应将输入的角度转为弧度

main()

3.11~3.12、编写程序计算前n个自然数的和，n由用户提供。计算前n个自然数的立方和。

# File 3.11.py
# -*- coding: utf-8 -*-

import math #
def main():
    n = int(input("The number of the nature number is: "))
    a, b = 0, 0
    for i in range(n):
        a = a + i
        b = b + i**2
    print("The sum is: ", a)
    print("The sum of quadratic sum is: ", b)


main()

3.13~3.14、编写程序对用户输入的一系列数字求和。程序应首先提示用户有多少数字要求和，然后依次提示用户输入每个数字，并在输入所有数字后打印出总和。对用户输入的一系列数字求平均值。

# File: 3.14.py
# -*- coding: utf-8 -*-
# average

def main():
        n = eval(input("How many figures are there?\n"))
        s = 0
        for i in range(n):
            a = eval(input("Enter the figures: "))
            s = s + a
        print("The input figures added up to be: ", s)
        print("The average value of the input numbers is:", float(s/n))
main()

运行结果：

3.15、编写程序，通过对级数的项进行求和来求近似π值。

# File 3.15.py
# -*- coding: utf-8 -*-

import math #


def pi():
    p = 0
    n = eval(input("The length of the series is: "))
    for i in range(n):
        p =p + 4/(2*i+1)*(-1)**i

    print("The Approximate value of π is: ",p, "\nThe deviation is: ", (math.pi-p))

pi()

运行结果：

3.16、计算第n个斐波那契数

# File: 3.16.py
# -*- coding: utf-8 -*-

def main():
    "This program calculates the n-th Fibonacci number."
    n = int(input("Enter the index: "))
    
    if n > 2:
        f = [1, 1]
        for i in range(n-2):
            f.append(f[-1] + f[-2])         #append方法在列表末尾增添一项,增添项为当前数列最后两项之和
        fi = f[-1]    
    else:
        fi = 1

    print("The %d-th Fibonacci number is: %d"%(n,fi))
    
main()

运行结果：

3.17、你已经看到math库包含了一个计算数字平方根的函数。在本练习中，你讲编写自己的算法来计算平方根。解决这个问题的一种方法是使用猜测和检查。你首先猜测平方根可能是什么，然后看看你的猜测是多么接近。一个好的猜测法是使用牛顿法。猜测x是我们希望的根，guess是当前猜测的答案。猜测可以通过使用下一个猜测来改进：(guess+x/guess)/2。编程实现牛顿方法。程序应提示用户找到值的平方根（x）和改进猜测的次数。从猜测值x/2开始，程序应指定猜测的次数，并报告猜测的终值。

# File:3.17.py
# -*- coding: utf-8 -*-

import math #
def main():
    x = float(input("Enter a positive number: "))
    n = int(input("Enter the number of iterations: "))
    guess = x/2
    for i in range(n):
        guess = (guess+x/guess)/2            #迭代计算平方根
    e = abs(math.sqrt(x) - guess)            #计算猜测值与真实值间误差
    print("The guess value is: %f\nThe error is: %f"%(guess, e))
    if e > 0.001:                            #如果误差过大，则增加迭代次数
        print("You may want to increase the number of iterations to get a more accurate value.")