第四章 数学函数、字符和字符串 程序设计练习

其他 2020-10-16 23:21:35 阅读次数: 0

4.1（几何：五边形面积）编写程序，提示用户输入从五边形的中心到边的距离r，计算五边形的面积。计算五边形面积的公式为：

Area=\frac{5\times s^2}{4\times \tan \left ( \frac{\pi}{5} \right )},其中s为边长。边长可用s=2r\sin\frac{\pi}{5}来计算，其中r为从五边形中心到边的距离。精确到小数点后两位。

#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;

int main()
{
	const double PI = 3.1416;//定义PI为常量

	//请求用户输入五边形中心到边的距离
	cout << "Enter the length from the center to a vertex:";
	double r = 0.0;
	cin >> r;

	double s = 2 * r * sin(PI / 5);//根据r计算五边形边长s
	double area = 5 * pow(s, 2) / 4 / tan(PI / 5);//计算面积

	cout << "The area of the pentagon is " <<fixed<<setprecision(2)<< area;//格式化输出，保留两位小数

	return 0;
}

4.2（几何：大圆距离）大圆距离为一球体表面两个点之间的距离。让（x1，y1）与（x2，y2）为两点的地理纬度与经度。两点间的大圆距离可由下列公式计算：

d=radius\times\arccos\left ( \sin\left(x_1)\right\times\sin\left(x_2)\right +\cos(x_1)\times\left\cos(x_2)\times\cos\left(y_1-y_2 \right ) \right ) \right } \right ) \right )

编写程序，提示用户输入以度为单位的地球上的两个点的经度和维度，输出大圆距离。平均地球半径为6378.1km。公式中的维度和经度为北纬和西经。因此用负数代表南纬和东经。

#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;

int main()
{
	const double RADIUS = 6378.1;//平均地球半径
	const double PI = 3.1416;//定义π

	//输入第一个点的经纬度
	cout << "Enter point 1(latitude and longitude) in degrees:" << endl;
	double x1 = 0.0, y1 = 0.0;
	cin >> x1 >> y1;
	//输入第二个点的经纬度
	cout << "Enter point 2(latitude and longitude) in degrees:" << endl;
	double x2 = 0.0, y2 = 0.0;
	cin >> x2 >> y2;
	//计算两点的距离
	double distance = RADIUS * acos(sin(x1 / 180 * PI) * sin(x2 / 180 * PI) + cos(x1 / 180 * PI) * cos(x2 / 180 * PI) * cos((y1 - y2) / 180 * PI));
	cout << "The distance between the two points is " << fixed << distance;

	return 0;
}

4.3（几何：估算面积）从www.gps-data-team.com/map/中为亚特兰大，佐治亚州；奥兰多，弗洛里达州；萨凡纳，佐治亚州；以及夏洛特，北卡罗来纳州找出GPS位置，计算4个城市范围之内的结算面积。（提示：使用程序设计练习4.2中的公式计算两个城市之间的距离。将多边形拆分为两个三角形，用程序设计练习2.19中的公式计算三角形的面积）。

亚特兰大：北纬33°46’西经84°25’；奥兰多：北纬28°32′18″, 西经82°37′15″；萨凡纳：北纬32°5′1″, 西经82°54′1″；夏洛特：北纬35°13′38″, 西经81°9′25″

4.4（几何：六边形面积）六边形（hexagon）面积可用下列公式计算（s为边长）：Area=\frac{6\times s^2}{4\times \tan \left ( \frac{\pi}{6} \right )}。编写程序，提示用户输入六边形的边长，输出它的面积。

#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;

int main()
{
	const double PI = 3.1416;
	cout << "Enter the side:";
	double side = 0.0;
	cin >> side;

	double area = 0.0;
	area = side * side * 6 / 4 / tan(PI / 6);

	cout << "The area of the hexagon is " << fixed << setprecision(2) << area << endl;

	return 0;
}

4.5（几何：正多边形的面积）正多边形为一个所有边长相同，所有角的大小相同的n条边的多边形（即多边形既为等边的又为等角的）。计算正多边形面积的公式为

Area=\frac{n\times s^2}{4\times \tan \left ( \frac{\pi}{n} \right )}，其中s为边长。编写程序，提示用户输入边数以及正多边形的边长，输出它的面积。

#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;

int main()
{
	const double PI = 3.1416;
	//获取正多边形边的数量
	cout << "Enter the number of sides:";
	int sideNumber = 0;
	cin >> sideNumber;
	//获取边的长度
	cout << "Enter the side:";
	double side = 0;
	cin >> side;
	//计算面积
	double area = 0.0;
	area = sideNumber * side * side / 4 / tan(PI / sideNumber);
	//格式化输出，保留两位小数
	cout << "The area of the polygon is " << fixed << setprecision(2) << area << endl;

	return 0;
}

4.6（圆上的随机点）编写程序，生成以（0,0）为圆心，半径为40的圆上的3个随机点，显示由这三个点形成的三角形的3个内角度数。（提示：随机生成一个弧度在0~2π之间的角度α，由这个角决定的点为（r*cos（α），r*sin（α）））。

#include <iostream>
#include <cmath>
#include <cstdio>
#include <ctime>
using namespace std;

int main()
{
	const double PI = 3.1416;
	const double R = 40;
	srand(time(0));
	double x1 = 0.0, x2 = 0.0, x3 = 0.0, y1 = 0.0,
		y2 = 0.0, y3 = 0.0, a1 = 0.0, a2 = 0.0, a3 = 0.0;
	//随机生成一个弧度在0~2π之间的角度α，由这个角决定的点为（r*cos（α），r*sin（α）））
	a1 = rand() * 1.0 / RAND_MAX * PI * 2;
	a2 = rand() * 1.0 / RAND_MAX * PI * 2;
	a3 = rand() * 1.0 / RAND_MAX * PI * 2;
	//确定三个点的坐标
	x1 = R * cos(a1), y1 = R * sin(a1);
	x2 = R * cos(a2), y2 = R * sin(a2);
	x3 = R * cos(a3), y3 = R * sin(a3);

	double a, b, c;//定义三角形的三条边
	//计算三条边的长度
	a = pow(pow(x1 - x2, 2) + pow(y1 - y2, 2), 0.5);
	b = pow(pow(x1 - x3, 2) + pow(y1 - y3, 2), 0.5);
	c = pow(pow(x2 - x3, 2) + pow(y2 - y3, 2), 0.5);

	double innerAngle1, innerAngle2, innerAngle3;//定义三个内角
	//计算三个内角值
	innerAngle1 = acos((a * a - b * b - c * c) / (-2 * b * c));
	innerAngle2 = acos((b * b - a * a - c * c) / (-2 * a * c));
	innerAngle3 = acos((c * c - b * b - a * a) / (-2 * a * b));

	cout << "三角形的三个内角度数为：" << innerAngle1/PI*180 << "° , " 
		<< innerAngle2/PI*180 << "° , " << innerAngle3/PI*180 <<"°"<< endl;
	system("pause");
	return 0;
}

4.7（拐角点坐标）假设一五边形以（0,0）为中心，一个点在0点位置。编写程序，提示用户输入五边形的外接圆的半径，输出该五边形的5个拐角点的坐标。

#include <iostream>
#include <cmath>
using namespace std;

int main()
{
	const double PI(3.1416);
	//输入五边形外接圆的半径
	cout << "Enter the radius of the bounding circle: ";
	double boundingCircleRadius = 0.0;
	cin >> boundingCircleRadius;
	//输出坐标
	cout << "The coordinates of five points on the pentagon are" << endl;
	//输出第一个点的坐标
	cout << "(0" << "," << boundingCircleRadius << ")" << endl;
	//输出第二~五个点的坐标
	cout << "(" << boundingCircleRadius * cos(PI / 2 + PI * 2 / 5) << "," << boundingCircleRadius * sin(PI / 2 + PI * 2 / 5) << ")" << endl;
	cout << "(" << boundingCircleRadius * cos(PI / 2 + PI * 4 / 5) << "," << boundingCircleRadius * sin(PI / 2 + PI * 4 / 5) << ")" << endl;
	cout << "(" << boundingCircleRadius * cos(PI / 2 + PI * 6 / 5) << "," << boundingCircleRadius * sin(PI / 2 + PI * 6 / 5) << ")" << endl;
	cout << "(" << boundingCircleRadius * cos(PI / 2 + PI * 8 / 5) << "," << boundingCircleRadius * sin(PI / 2 + PI * 8 / 5) << ")" << endl;

	return 0;
}

4.8（找出ASCII码对应的字符）编写程序，接收ASCII码（0~127之间的整数），输出它的字符。

#include <iostream>
using namespace std;

int main()
{
	cout << "Enter an ASCII code:";
	int number;
	cin >> number;

	if (number < 0 || number>127)
		cout << "Error";
	else
		cout << "The character is "<<static_cast<char>(number) << endl;

	return 0;
}

4.9（找出字符对应的ASCII码）编写程序，接收字符，输出它的ASCII码。

#include <iostream>
using namespace std;

int main()
{
	cout << "Enter a character : ";
	char c;
	cin >> c;

	cout << "The ASCII code for the character is " << static_cast<int>(c) << endl;

	return 0;
}

4.10（元音还是辅音？）假设字母A/a、E/e、I/i、O/o、U/u为元音。编写程序，提示用户输入字母，判断字母是元音还是辅音。

#include <iostream>
using namespace std;

int main()
{
	cout << "Enter a letter: ";
	char letter;
	cin >> letter;

	if ('a' <= letter && 'z' >= letter || 'A' <= letter && 'Z' >= letter)//判断输出字符是否合法
	{//输入确实是字母
		switch (letter)
		{//当输入字母为元音时，打印
		case 'a':case 'e':case 'i':case 'o':case 'u':
		case 'A':case 'E':case 'I':case 'O':case 'U':
			cout << letter << " is a vowel" << endl;
			break;
		//其他非元音情况情况
		default:cout << letter << " is a consonant" << endl;
			break;
		}
	}
	else//输入不是字母
		cout << letter << " is an invalid input" << endl;

	return 0;
}

4.11（将大写字母转换为小写字母）编写程序，提示用户输入1个大写字母，将其转换为小写字母。

#include <iostream>
#include <cctype>
using namespace std;

int main()
{
	cout << "Enter an uppercase letter: ";
	char letter;
	cin >> letter;

	if (isupper(letter) && isalpha(letter))//判断输入字符确实是字母且确实是大写字母
		cout << static_cast<char>(letter - 'A' + 'a') << endl;
	else
		cout << letter << " is an invalid input" << endl;

	return 0;
}

4.12（将字母等级转换为数字）编写程序，提示用户输入字母A/a、B/b、C/c、D/d、F/f，输出其相应的数字值4/3/2/1/0。

#include <iostream>
#include <cctype>
using namespace std;

int main()
{
	//输入字母
	cout << "Enter a letter grade: ";
	char letter;
	cin >> letter;

	int value = -1;//字母对应的数字值
	if (isalpha(letter))//判断输入是否为字母
	{
		switch (letter)
		{
		case 'A':case 'a':value = 4; break;//字母为A、a时数字值为4
		case 'B':case 'b':value = 3; break;
		case 'C':case 'c':value = 2; break;
		case 'D':case 'd':value = 1; break;
		case 'F':case 'f':value = 0; break;
		default:value = -1;break;//输入字母非法时，数字值为-1
		}
		if (value == -1)//如果数字值为-1，输出输入为非法值
			cout << letter << " is an invalid input";
		else//输入合法时输出相应等级
			cout << "The numeric value for grade " << letter << " is " << value;
	}
	else//输入不是字母时，输出输入为非法值
		cout << letter << " is an invalid input";

	return 0;
}

4.13（十六进制到二进制）编写程序，提示用 户输入一个十六进制的数字，输出它对应的二进制数字。

#include <iostream>
#include <cctype>
using namespace std;

int main()
{
	//提示用户输入一个十六进制整数
	cout << "Enter a hex digit: ";
	char digit;//因为输入有数字有字符所以用char类型
	cin >> digit;

	if (isalnum(digit))//判断输入是否为数字或字符，是则进行下列运算
	{
		switch (digit)
		{
		case '1':cout << "The binary value is " << 0001; break;
		case '2':cout << "The binary value is " << 0010; break;
		case '3':cout << "The binary value is " << 0011; break;
		case '4':cout << "The binary value is " << 0100; break;
		case '5':cout << "The binary value is " << 0101; break;
		case '6':cout << "The binary value is " << 0110; break;
		case '7':cout << "The binary value is " << 0111; break;
		case '8':cout << "The binary value is " << 1000; break;
		case '9':cout << "The binary value is " << 1001; break;
		case 'A':case 'a':cout << "The binary value is " << 1010; break;
		case 'B':case 'b':cout << "The binary value is " << 1011; break;
		case 'C':case 'c':cout << "The binary value is " << 1100; break;
		case 'D':case 'd':cout << "The binary value is " << 1101; break;
		case 'E':case 'e':cout << "The binary value is " << 1110; break;
		case 'F':case 'f':cout << "The binary value is " << 1111; break;
		default:cout << digit << " is an invalid input"; break;
		}
	}
	else//如果输入不是字符或数字，输出错误提示
		cout << digit << " is an invalid input";

	return 0;
}

4.14（将十进制转换为十六进制）编写程序，提示用户输入0~15之间的整数，输出相应的十六进制数。

#include <iostream>
using namespace std;

int main()
{
	cout << "Enter a decimal value (0 to 15): ";
	int value;
	cin >> value;
	//判断输入是否在0-15范围内
	if (value >= 0 && value <= 15)
	{
		cout << "The hex value is ";
		if (value < 10)//如果输入小于10直接输出
			cout << value;
		else//如果输入大于10输出字母
			cout << static_cast<char>(value - 10 + 'a');
	}
	else
		cout << value << " is an invalid input";

	return 0;
}

4.15（电话键面板）电话上匹配的国际标准字母/数字由下图所示：

编写程序，提示用户输入一个字母，输出它对应的数字。

#include <iostream>
#include <cctype>
using namespace std;

int main()
{
	cout << "Enter a letter : ";
	char letter;
	cin >> letter;

	if (isalpha(letter))//判断输入是否为字母
	{
		switch (letter)
		{
		case 'a':case 'b':case 'c':case 'A':case 'B':case 'C':
			cout << "The corresponding number is 2" << endl; break;
		case 'd':case 'e':case 'f':case 'D':case 'E':case 'F':
			cout << "The corresponding number is 3" << endl; break;
		case 'g': case 'h':case 'i':case 'G':case 'H':case 'I':
			cout << "The corresponding number is 4" << endl; break;
		case 'j':case 'k':case 'l':case 'J':case 'K':case 'L':
			cout << "The corresponding number is 5" << endl; break;
		case 'm':case 'n':case 'o':case 'M':case 'N':case 'O':
			cout << "The corresponding number is 6" << endl; break;
		case 'p':case 'q':case 'r':case 's':case 'P':case 'Q':case 'R':case 'S':
			cout << "The corresponding number is 7" << endl; break;
		case 't':case 'u':case 'v':case 'T':case 'U':case 'V':
			cout << "The corresponding number is 8" << endl; break;
		case 'w':case 'x':case 'y':case 'z':case 'W':case 'X':case 'Y':case 'Z':
			cout << "The corresponding number is 9" << endl; break;
		default:cout << letter << " is an invalid input"; break;
		}
	}
	else//输入为非字母，输出错误提示
		cout << letter << " is an invalid input" << endl;

	return 0;
}

4.16（处理一个字符串）编写程序，提示用户输入一个字符串，输出它的长度以及它的第一个字符。

#include <iostream>
#include <string>
using namespace std;

int main()
{
	cout << "Enter a string:";
	string str;
	getline(cin, str);

	cout << "The length of the string is " << str.length() << endl;
	if (str.length() != 0)//如果输入字符串不为空，输出第一个字符
		cout << "The first of the string is " << str[0] << endl;

	return 0;
}

4.17（商业：检验ISBN-10）重写程序设计练习3.35的程序，将ISBN数字输入为字符串。

#include <iostream>
#include <string>
using namespace std;

int main()
{
	//输入ISBN的前九位
	cout << "Enter the first 9 digits of an ISBN an integer: ";
	string ISBN_9;
	cin >> ISBN_9;

	int d10 = 0;
	//用循环进行公示中的加法运算
	for (int i = 0; i < 9; i++)
		d10 += (ISBN_9[i] - '0') * (i + 1);
	d10 %= 11;//公式中的最后一步取余运算

	//首先输出前九位
	cout << "The ISBN-10 number is " << ISBN_9;
	if (d10 == 10)//如果第十位是10则输出X
		cout << 'X';
	else//不是10，直接打印数字
		cout << d10;

	return 0;
}

4.18（随机字符串）编写程序，随机生成一个带有3个大写字母的字符串。

#include <iostream>
#include <string>
#include <ctime>
#include <cstdio>
using namespace std;

int main()
{
	srand(time(0));//设置rand函数的种子
	string str;
	
	str += (char)('A' + rand() % 25);//生成第一个大写字母
	str += (char)('A' + rand() % 25);//生成第二个大写字母
	str += (char)('A' + rand() % 25);//生成第三个大写字母

	cout << "The random string is " << str;

	return 0;
}

4.19（排列三个城市）编写程序，提示用户输入3个城市，输出它们的升序排列。

#include <iostream>
#include <string>
using namespace std;

int main()
{
	//输入第一个城市名称
	cout << "Enter the first city:";
	string firCity;
	getline(cin, firCity);
	//输入第二个城市名称
	cout << "Enter the second city:";
	string senCity;
	getline(cin, senCity);
	//输入第三个城市名称
	cout << "Enter the third city:";
	string thiCity;
	getline(cin, thiCity);
	//输出城市排列提示信息
	cout << "The three cities in alphabetcal order are ";
	if (firCity <= senCity)//升序排列
	{
		if (firCity <= thiCity)
		{
			if (senCity <= thiCity)
				cout << firCity << " " << senCity << " " << thiCity;
			else
				cout << firCity << " " << thiCity << " " << senCity;
		}
		else
			cout << thiCity << " " << firCity << " " << senCity;
	}
	else
	{
		if (senCity <= thiCity)
		{
			if (firCity <= thiCity)
				cout << senCity << " " << firCity << " " << thiCity;
			else
				cout << senCity << " " << thiCity << " " << firCity;
		}
		else
			cout << thiCity << " " << senCity << " " << firCity;
	}

	return 0;
}

4.20（一个月的天数）编写程序，提示用户输入年份以及月份名称的前3个字母（第一个字母大写），输出此月的天数。

#include <iostream>
#include <string>
using namespace std;

int main()
{
	//提示用户输入年份
	cout << "Enter a year:";
	int year;
	cin >> year;
	//提示用户输入月份
	cout << "Enter a month:";
	string month;
	cin >> month;
	//1,3,5,7,8,10,12月为31天
	if (month == "Jan" || month == "Mar" || month == "May" || month == "Jul" || month == "Aug" || month == "Oct" || month == "Dec")
		cout << month << " " << year << " has " << 31 << " days";
	//4,6,8,11月为30天
	else if (month == "Apr" || month == "Jun" || month == "Sep" || month == "Nov")
		cout << month << " " << year << " has " << 30 << " days";
	//2月时对年份进行判断是闰年还是平年
	else if (month == "Feb")
		if (year % 4 == 0 && year % 100 != 0 || year % 400 == 0)
			cout << month << " " << year << " has " << 29 << " days";
		else
			cout << month << " " << year << " has " << 28 << " days";
	else//所以情况都不符合输出错误提示信息
		cout << month << " is not a correct month name";

	return 0;
}

4.21（学生专业和年纪）编写程序，提示用户输入两个字符，输出字符代表的专业以及年级。第一个字符代表专业，第二个为数字字符1/2/3/4，代表一个学生是大一、大二、大三还是大四。假设下列字符用来定义专业：

M：Mathematics（数学）；C：Computer Science（计算机科学技术）；I：Information Technology（信息技术）

#include <iostream>
#include <string>
#include <cctype>
using namespace std;

int main()
{
	//提示用户输入两个字符
	cout << "Enter two characters:";
	string str;
	cin >> str;
	//输出字符代表的专业
	switch (str[0])
	{
	case 'M':cout << "Mathematics "; break;
	case 'C':cout << "Computer Science "; break;
	case 'I':cout << "Information Technology "; break;
	default:cout << "Invalid major code"; break;
	}
	//输出字符代表的年级
	switch (str[1])
	{
	case '1':cout << "Freshman"; break;
	case '2':cout << "Sophomore"; break;
	case '3':cout << "Junior"; break;
	case '4':cout << "Senior"; break;
	default:cout << "Invalid status code"; break;
	}

	return 0;
}

4.22（金融应用：工资单）编写程序，读取下列信息，输出工资表：

员工姓名（如Smith）

一周内的工作时间（如10）

小时工作率（如9.75）

联邦税收扣缴率（如9%）

#include <iostream>
#include <iomanip>
#include <string>
using namespace std;

int main()
{
	//输入员工姓名
	cout << "Enter employee,s name:";
	string name;
	getline(cin, name);
	//输入每周工作时长
	cout << "Enter number of hours worked in a week:";
	double hourWork;
	cin >> hourWork;
	//输入时薪
	cout << "Enter hourly pay rate:";
	double hourlyPayRate;
	cin >> hourlyPayRate;
	//输入联邦税率
	cout << "Enter federal tax withholding rate:";
	double federalTaxWithholdingRate;
	cin >> federalTaxWithholdingRate;
	//输入州税率
	cout << "Enter state tax withholding rate:";
	double stateTaxWithholdingRate;
	cin >> stateTaxWithholdingRate;

	double grossPay = hourlyPayRate * hourWork;//总收入
	double federalWithholding = federalTaxWithholdingRate * grossPay;//联邦税收
	double stateWithholding = stateTaxWithholdingRate * grossPay;//州税收
	double totalDedutions = federalWithholding + stateWithholding;//总税收
	double netPay = grossPay - totalDedutions;//实际收入

	cout<< fixed << setprecision(2)//强输出小数点，结果保留两位小数
		<< "Enployee Name: " << name << endl
		<< "Hours Worked: " << hourWork << endl
		<< "Pay Rate: $"  << hourlyPayRate << endl
		<< "Gross Pay: $" << grossPay << endl
		<< "Deductions:" << endl
		<< "\tFederal Withholding ("  << federalTaxWithholdingRate * 100.0 << "%): $" << fixed << setprecision(2) << federalWithholding << endl
		<< "\tState Withholding ("  << stateTaxWithholdingRate * 100.0 << "%): $" << fixed << setprecision(2) << stateWithholding << endl
		<< "\tTotal Deduction: $"  << totalDedutions << endl
		<< "Net Pay: $" << netPay;

	return 0;
}

4.23（检验SSN）编写程序，提示用户输入ddd-dd-dddd形式的社会保障号码，其中d为一个数字。程序应该检查输入是否有效。

#include <iostream>
#include <string>
#include <cctype>
using namespace std;

int main()
{
	cout << "Enter a SSN:";
	string ssn;
	cin >> ssn;

	if (isdigit(ssn[0]))
		if (isdigit(ssn[1]))
			if (isdigit(ssn[2]))
				if (ssn[3] == '-')
					if (isdigit(ssn[4]))
						if (isdigit(ssn[5]))
							if (ssn[6] == '-')
								if (isdigit(ssn[7]))
									if (isdigit(ssn[8]))
										if (isdigit(ssn[9]))
											cout << ssn << " is a valid social security number";
										else
											cout << ssn << " is an invalid social security number";
									else
										cout << ssn << " is an invalid social security number";
								else
									cout << ssn << " is an invalid social security number";
							else
								cout << ssn << " is an invalid social security number";
						else
							cout << ssn << " is an invalid social security number";
					else
						cout << ssn << " is an invalid social security number";
				else
					cout << ssn << " is an invalid social security number";
			else
				cout << ssn << " is an invalid social security number";
		else
			cout << ssn << " is an invalid social security number";
	return 0;
}

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