四则运算 Java 杨辉鹏，郑冠华
GitHub链接：https://github.com/yanghuipeng/arithmetic
项目相关要求
使用 -n 参数控制生成题目的个数，例如
-n 10 将生成10个题目。
使用 -r 参数控制题目中数值（自然数、真分数）的范围，例如
-r 10
将生成10以内（不包括10）的四则运算题目。该参数可以设置为1或其他自然数。该参数必须给定，否则程序报错并给出帮助信息。
生成的题目中计算过程不能产生负数，也就是说算术表达式中如果存在形如e1 − e2的子表达式，那么e1 ≥ e2。
生成的题目中如果存在形如e1 ÷ e2的子表达式，那么其结果应是真分数。
每道题目中出现的运算符个数不超过3个。
程序一次运行生成的题目不能重复，即任何两道题目不能通过有限次交换+和×左右的算术表达式变换为同一道题目。
生成的题目存入执行程序的当前目录下的Exercises.txt文件，格式如下：
四则运算题目1
四则运算题目2
其中真分数在输入输出时采用如下格式，真分数五分之三表示为3/5，真分数二又八分之三表示为2’3/8。
-
在生成题目的同时，计算出所有题目的答案，并存入执行程序的当前目录下的Answers.txt文件，格式如下：
1.答案1
2.答案2
特别的，真分数的运算如下例所示：1/6 + 1/8 = 7/24。
程序应能支持一万道题目的生成。
程序支持对给定的题目文件和答案文件，判定答案中的对错并进行数量统计，输入参数如下：
Myapp.exe -e <exercisefile>.txt -a <answerfile>.txt
统计结果输出到文件Grade.txt，格式如下：
Correct: 5 (1, 3, 5, 7, 9)
Wrong: 5 (2, 4, 6, 8, 10)
其中“:”后面的数字5表示对/错的题目的数量，括号内的是对/错题目的编号。为简单起见，假设输入的题目都是按照顺序编号的符合规范的题目。
PSP开发耗时
PSP2.1
|
PSP2.1 |
Personal Software Process Stages |
预估耗时（分钟） |
实际耗时（分钟） |
|
Planning |
计划 |
30 | 50 |
|
· Estimate |
· 估计这个任务需要多少时间 |
30 | 50 |
|
Development |
开发 |
1100 | 2260 |
|
· Analysis |
· 需求分析 (包括学习新技术) |
80 | 180 |
|
· Design Spec |
· 生成设计文档 |
60 | 100 |
|
· Design Review |
· 设计复审 (和同事审核设计文档) |
30 | 40 |
|
· Coding Standard |
· 代码规范 (为目前的开发制定合适的规范) |
30 | 30 |
|
· Design |
· 具体设计 |
100 | 150 |
|
· Coding |
· 具体编码 |
600 | 1500 |
|
· Code Review |
· 代码复审 |
50 | 60 |
|
· Test |
· 测试（自我测试，修改代码，提交修改） |
150 | 200 |
|
Reporting |
报告 |
80 | 80 |
|
· Test Report |
· 测试报告 |
30 | 40 |
|
· Size Measurement |
· 计算工作量 |
20 | 20 |
|
· Postmortem & Process Improvement Plan |
· 事后总结, 并提出过程改进计划 |
30 | 20 |
|
合计 |
1210 | 2390 |
解题思路：
生成随机操作数
取随机操作符
生成表达式
- 计算
判重
结果写入文件
设计实现过程
Fraction分数类定义一个分数及分数的基本操作
- Expression表达式类定义一个表达式及计算表达式的结果
Function输出功能类输出结果
代码
项目目录：
主函数：（启动程序）Main.java
package TwoProject; import java.io.*;
import java.util.Scanner; public class Main { public static void main(String[] args) throws IOException {
// TODO 自动生成的方法存根
int titleNum; // 定义题目个数
int parameterRange; // 定义参数范围
System.out.println("**** -n [数值] 使用 -n 参数控制生成题目的个数");
System.out.println("**** -e <exercisefile>.txt -a <answerfile>.txt 对给定的题目文件和答案文件，判定答案中的对错并进行数量统计");
System.out.print("请输入命令：");
Scanner s = new Scanner(System.in);
String m = s.nextLine();
String str[] = m.split("\\s");
switch (str[0]) {
case "-n":
titleNum = Integer.valueOf(str[1].toString());
System.out.println("**** -r [数值] 使用 -r 参数控制题目中数值（自然数、真分数）的范围(数值应大于1)");
System.out.print("请输入命令：");
Scanner ss = new Scanner(System.in);
String n = ss.nextLine();
String strr[] = n.split("\\s");
if (strr[0].equals("-r")) {
parameterRange = Integer.valueOf(strr[1].toString());
Function function = new Function(titleNum, parameterRange);
function.outputExercises();
break;
} else {
System.out.println("输入的命令有误!");
break;
}
case "-e":
Function function0 = new Function();
String gradePath = "Grade.txt";
function0.outputGrade(str[1], str[3], gradePath);
break;
default:
System.out.println("输入的命令有误!");
break;
}
s.close(); } }
分数类 Fraction
package TwoProject;
public class Fraction {
private int a; // 定义分子
private int b; // 定义分母
public Fraction(String string) { // 将数字的字符串形式转换为整数、分数形式
string = string.trim(); // 清除前后空格
int c = string.indexOf("'"); // 求带分数标志“'”的索引
int d = string.indexOf("/"); // 求分数标志“/”的索引
if (c != -1) { // 数字为带分数
int z = Integer.valueOf(string.substring(0, c));
b = Integer.valueOf(string.substring(d + 1));
a = z * b + Integer.valueOf(string.substring(c + 1, d));
} else if (d != -1) { // 数字为真分数
b = Integer.valueOf(string.substring(d + 1));
a = Integer.valueOf(string.substring(0, d));
} else { // 数字为整数
a = Integer.valueOf(string);
b = 1;
}
build(a, b);
}
public Fraction(int a, int b) {
build(a, b);
}
// 数字形式转换为字符串形式
public String toString() {
if (b == 1) {
return String.valueOf(a);
} else {
int i = a / b;
if (i != 0) {
return String.format("%d'%d/%d", i, a - b * i, b);
} else {
return String.format("%d/%d", a, b);
}
}
}
// 给定分子分母构造分数
private void build(int a, int b) {
if (b == 0) {
throw new RuntimeException("分母不能为0");
}
int c = comfactor(a, b);
this.a = a / c;
this.b = b / c;
}
// 求公因子
private int comfactor(int a, int b) {
int mod = a % b;
return mod == 0 ? b : comfactor(b, mod);
}
// 加法 a + b
public Fraction add(Fraction fraction) {
return new Fraction(this.a * fraction.b + fraction.a * this.b, this.b * fraction.b);
}
// 减法 a - b
public Fraction subtraction(Fraction fraction) {
return new Fraction(this.a * fraction.b - fraction.a * this.b, this.b * fraction.b);
}
// 乘法 a x b
public Fraction multiplication(Fraction fraction) {
return new Fraction(this.a * fraction.a, this.b * fraction.b);
}
// 除法a/b
public Fraction division(Fraction fraction) {
return new Fraction(this.a * fraction.b, b * fraction.a);
}
public double getDouble() {
return a / b;
}
}
表达式类Expression
package TwoProject; import java.util.List;
import java.util.ArrayList;
import java.util.concurrent.ThreadLocalRandom; /**
*
* @author 辉鹏
* @param parameterRange
* 参数范围
*
*
*/
public class Expression {
int parameterRange;
char[] symbol = { '+', '-', '×', '÷' };
boolean isWrong = false;
String s;
ThreadLocalRandom random = ThreadLocalRandom.current();
public Expression(String string) {
s=string.trim();
expreGenerate(s);
}
public Expression(int parameterRange) {
super();
this.parameterRange = parameterRange;
int n = random.nextInt(1, 4);
char[] symchar = new char[n];
char[] symchar1 = new char[n];
for (int i = 0; i < n; i++) {
int j = random.nextInt(0, 4);
symchar[i] = symbol[j];
}
for (int i = 0; i < n; i++) {
if (symchar[i] == '+' || symchar[i] == '-') {
symchar1[i] = '1';
}
if (symchar[i] == '×' || symchar[i] == '÷') {
symchar1[i] = '2';
}
}
String string = symchar1.toString().trim();
if (n == 1) {
String[] str0 = new String[4];
str0[0] = createFraction().toString();
str0[1] = String.valueOf(symchar[0]);
str0[2] = createFraction().toString();
str0[3] = "=";
StringBuffer stringBuffer = new StringBuffer();
for (int i = 0; i < 4; i++) {
stringBuffer = stringBuffer.append(str0[i] + " ");
}
s = stringBuffer.toString();
} else if (n == 2) {
if (string == "12" || string == "22") {
Object[] str1 = new String[6];
str1[0] = createFraction().toString();
str1[1] = String.valueOf(symchar[0]);
str1[2] = createFraction().toString();
str1[3] = String.valueOf(symchar[1]);
str1[4] = createFraction().toString();
str1[5] = "=";
StringBuffer stringBuffer = new StringBuffer();
for (int i = 0; i < 6; i++) {
stringBuffer = stringBuffer.append(str1[i] + " ");
}
s = stringBuffer.toString();
} else {
String[] str2 = new String[8];
str2[0] = createFraction().toString();
str2[1] = String.valueOf(symchar[0]);
str2[2] = "(";
str2[3] = createFraction().toString();
str2[4] = String.valueOf(symchar[1]);
str2[5] = createFraction().toString();
str2[6] = ")";
str2[7] = "=";
StringBuffer stringBuffer = new StringBuffer();
for (int i = 0; i < 8; i++) {
stringBuffer = stringBuffer.append(str2[i] + " ");
}
s = stringBuffer.toString();
}
} else {
if (string == "221" || string == "222") {
String[] str3 = new String[10];
str3[0] = createFraction().toString();
str3[1] = String.valueOf(symchar[0]);
str3[2] = createFraction().toString();
str3[3] = String.valueOf(symchar[1]);
str3[4] = "(";
str3[5] = createFraction().toString();
str3[6] = String.valueOf(symchar[2]);
str3[7] = createFraction().toString();
str3[8] = ")";
str3[9] = "=";
StringBuffer stringBuffer = new StringBuffer();
for (int i = 0; i < 10; i++) {
stringBuffer = stringBuffer.append(str3[i] + " ");
}
s = stringBuffer.toString().trim(); } else if (string == "111" || string == "112") {
Object[] str4 = new String[10];
str4[0] = createFraction().toString();
str4[1] = String.valueOf(symchar[0]);
str4[2] = "(";
str4[3] = createFraction().toString();
str4[4] = String.valueOf(symchar[1]);
str4[5] = createFraction().toString();
str4[6] = ")";
str4[7] = String.valueOf(symchar[2]);
str4[8] = createFraction().toString();
str4[9] = "=";
StringBuffer stringBuffer = new StringBuffer();
for (int i = 0; i < 10; i++) {
stringBuffer = stringBuffer.append(str4[i] + " ");
}
s = stringBuffer.toString().trim();
} else if (string == "121" || string == "122") {
Object[] str5 = new String[10];
str5[0] = "(";
str5[1] = createFraction().toString();
str5[2] = String.valueOf(symchar[0]);
str5[3] = createFraction().toString();
str5[4] = ")";
str5[5] = String.valueOf(symchar[1]);
str5[6] = createFraction().toString();
str5[7] = String.valueOf(symchar[2]);
str5[8] = createFraction().toString();
str5[9] = "=";
StringBuffer stringBuffer = new StringBuffer();
for (int i = 0; i < 10; i++) {
stringBuffer = stringBuffer.append(str5[i] + " ");
}
s = stringBuffer.toString().trim();
} else {
Object[] str6 = new String[8];
str6[0] = createFraction().toString();
str6[1] = String.valueOf(symchar[0]);
str6[2] = createFraction().toString();
str6[3] = String.valueOf(symchar[1]);
str6[4] = createFraction().toString();
str6[5] = String.valueOf(symchar[2]);
str6[6] = createFraction().toString();
str6[7] = "=";
StringBuffer stringBuffer = new StringBuffer();
for (int i = 0; i < 8; i++) {
stringBuffer = stringBuffer.append(str6[i] + " ");
}
s = stringBuffer.toString().trim();
}
}
expreGenerate(s);
} // 随机生成一个分数
Fraction createFraction() {
return new Fraction(random.nextInt(1, parameterRange), random.nextInt(1, 10));
} // 返回一个表达式
private String expreGenerate(String s) {
return s;
} // 表达式计算
private Fraction calculate(String symbol0, Fraction left0, Fraction right0) {
String symbol = symbol0;
Fraction left = left0;
Fraction right = right0;
switch (symbol) {
case "+":
return left.add(right);
case "-":
if (left.getDouble() <= right.getDouble()) {
isWrong = true;
return new Fraction(1, 1);
} else {
return left.subtraction(right);
}
case "×":
return left.multiplication(right);
default:
return left.division(right);
}
} // 表达式结果计算方法
public String getResult() {
String string = s;
String[] strings = string.split("\\s+");
List<String> list = new ArrayList<String>();
for (int i = 0; i < strings.length; i++) {
list.add(strings[i]);
}
if (string.indexOf("(") != -1) {
for (int i = 0; i < list.size(); i++) {
if (list.get(i).equals("="))
break;
if (list.get(i).equals("(")) {
list.set(i, calculate(list.get(i + 2), new Fraction(list.get(i + 1)), new Fraction(list.get(i + 3)))
.toString());
for (int j = 0; j < 4; j++) {
list.remove(i + 1);
}
}
}
}
if (string.indexOf("×") != -1 || string.indexOf("÷") != -1) {
for (int i = 0; i < list.size(); i++) {
if (list.get(i).equals("="))
break;
if (list.get(i).equals("×") || list.get(i).equals("÷")) {
list.set(i - 1, calculate(list.get(i), new Fraction(list.get(i - 1)), new Fraction(list.get(i + 1)))
.toString());
for (int j = 0; j < 2; j++) {
list.remove(i);
}
i--;
}
}
}
if (string.indexOf("+") != -1 || string.indexOf("-") != -1) {
for (int i = 0; i < list.size(); i++) {
if (list.get(i).equals("="))
break;
if (list.get(i).equals("+") || list.get(i).equals("-")) {
list.set(i - 1, calculate(list.get(i), new Fraction(list.get(i - 1)), new Fraction(list.get(i + 1)))
.toString());
for (int j = 0; j < 2; j++) {
list.remove(i);
}
i--;
}
}
}
return list.get(0);
} public String toString() {
return s;
}
}
输出功能类Function
package TwoProject; import java.io.BufferedReader;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Set; /**
* @param titleNum
* 题目个数
* @param parameterRange
* 参数范围
*/
public class Function {
int titleNum;
int parameterRange;
Set<String> set = new HashSet<>(); public Function() { } public Function(int titleNum, int parameterRange) {
this.titleNum = titleNum;
this.parameterRange = parameterRange;
} public void outputExercises() {
try {
PrintWriter exercisesWriter = new PrintWriter(new FileWriter("Exercises.txt"));
PrintWriter answerWriter = new PrintWriter(new FileWriter("Answers.txt"));
for (int i = 1; i < titleNum + 1;) {
Expression expression = new Expression(parameterRange);
String string = expression.getResult();
if (expression.isWrong == false && !(set.contains(string))) {
set.add(string);
exercisesWriter.println(i + ". " + expression.toString());
answerWriter.println((i + ". " + string));
i++;
}
}
exercisesWriter.close();
answerWriter.close();
} catch (IOException e) {
e.printStackTrace();
}
System.out.println("已经生成题目和答案");
} /**
* 输出结果
*
* @param exercisePath
* 表达式文件路径
* @param answerPath
* 结果文件路径
* @param gradePath
* 输出结果文件路径
*/
public void outputGrade(String exercisePath, String answerPath, String gradePath) { try {
BufferedReader exercisesReader = new BufferedReader(new FileReader(exercisePath));
BufferedReader answerReader = new BufferedReader(new FileReader(answerPath));
PrintWriter gradeWriter = new PrintWriter(new FileWriter(gradePath));
String exercises, answer;
int c = 0, w = 0;
StringBuilder correct = new StringBuilder("Correct: %d (");
StringBuilder wrong = new StringBuilder("Wrong: %d (");
while ((exercises = exercisesReader.readLine()) != null && (answer = answerReader.readLine()) != null) {
int exercisesPoint = exercises.indexOf(".");
int answerPoint = answer.indexOf(".");
if (exercisesPoint != -1 && answerPoint != -1) {
int i = Integer.valueOf(exercises.substring(0, exercisesPoint).trim());
Expression expression = new Expression(exercises.substring(exercisesPoint + 1));
Fraction ans = new Fraction(answer.substring(answerPoint + 1));
if (expression.getResult().equals(ans.toString())) {
c++;
correct.append(" " + i);
if (c % 30 == 0) {
correct.append("\r\n");
}
} else {
w++;
wrong.append(" " + i);
if (w % 30 == 0) {
wrong.append("-r\n");
}
}
}
}
gradeWriter.println(String.format(correct.append(" )").toString(), c));
gradeWriter.println(String.format(wrong.append(" )").toString(), w));
gradeWriter.flush();
exercisesReader.close();
answerReader.close();
gradeWriter.close();
} catch (IOException e) {
e.printStackTrace();
}
System.out.println("已经比较完成，并生成输出文件");
}
}
测试
表达式的输出
随机输出10条20范围以内的表达式和答案
表达式： 结果：
对比上面输出的10条表达式和答案，结果
然后故意修改第2，5，6，7道题的答案，再重新运行一遍，结果如下
随机输出10000条20范围以内的表达式和答案: