一. PSP表格
二. 项目要求:
- 能自动生成小学四则运算题目
- 除了整数以外，还要支持真分数的四则运算
三. 解题思路:
- 了解四则运算的基本法则
- 利用随机函数随机生成数字以及运算符
- 用户输入答案程序需要判断答案是否正确
- 支持真分数运算
四. 符号说明：
自然数：0, 1, 2, …。
- 真分数：1/2, 1/3, 2/3, 1/4, 1’1/2, …。
- 运算符：+, −, ×, ÷。
- 括号：(, )。
- 等号：=。
- 分隔符：空格（用于四则运算符和等号前后）。
- 算术表达式： e = n | e1 + e2 | e1 − e2 | e1 × e2 | e1 ÷ e2 | (e),
其中e, e1和e2为表达式，n为自然数或真分数。
- 四则运算题目：e = ，其中e为算术表达式。
五. 项目功能
由界面输入参数，实现了题目的生成以及去重，问题与答案的文件保存，用户输入答案文件与标准答案的校对以及结果文件生成
运行示例（Answerfile.txt为用户提交文件）：
六. 代码设计
1. 由于题目设计真分数运算，所以采用分数作为基本的运算单位。使用ExpressionResult类保存每条表达式以及它的运算结果
1 public class Fraction {
2 //分子
3 private Integer numerator;
4 //分母
5 private Integer denominator;
6
7 //取最大公因数化简
8 public Fraction(Integer n, Integer d) {
9 Integer GCD = Calculator.GCD(n, d);
10 this.numerator = n /= GCD;
11 this.denominator = d /= GCD;
12 }
13
14
15 //重写toString方法，以真分数形式表示
16 @Override
17 public String toString() {
18 if (this.numerator > this.denominator && this.denominator != 1 && this.getNumerator() > 0 && this.getDenominator() > 0) {
19 int num = numerator / denominator;
20 return num + "'" + numerator % denominator + "/" + denominator;
21 } else if (denominator == 1) {
22 return numerator.toString();
23 } else return numerator + "/" + denominator;
24 }
25 ｝
1 public class ExpressionResult {
2
3 private String expression;
4 private String result;
5
6 @Override
7 public String toString() {
8 return expression+"="+result;
9 }
10 }
2. 很多人采用二叉树生成表达式或者中缀转后缀表达式的思路，我则是直接进行表达式的生成与计算，在生成表达式时采用HashSet无法重复的特性来存放表达式达到去重的目的
1 //表达式的生成，采用HashSet存放表达式，直接去重，可以免去后续检测是否重复
2 public static HashSet<ExpressionResult> generateExpression(Integer r, Integer n) {
3 HashSet<ExpressionResult> expressionResultHashSet = new HashSet<>();
4 for (int i = 0; i < r; i++) {
5 //生成第一个操作符和操作数，在后面计算中使用firstNum存放计算的结果
6 char firstOps = GeneratorUtil.getOperator();
7 Fraction firstNum = GeneratorUtil.getFraction(n);
8 char secondOps = firstOps;
9 Fraction secondNum = firstNum;
10 ExpressionResult expressionResult = new ExpressionResult();
11 StringBuilder expression = new StringBuilder().append(firstNum);
12 //生成后续两个操作符并进行表达式的拼接
13 for (int j = 0; j < 2; j++) {
14 //获取第二个操作数
15 secondNum = GeneratorUtil.getFraction(n);
16 switch (secondOps) {
17 //加法则直接进行拼接，不需要额外操作
18 case '+':
19 //将当前运算符保存，后面在优先级比较中会使用到（下同）
20 firstOps = secondOps;
21 expression.append(secondOps).append(secondNum);
22 //保存运算的中间结果（下同）
23 firstNum = Calculator.ADD(firstNum, secondNum);
24 //获取下一个操作符（下同）
25 secondOps = GeneratorUtil.getOperator();
26 break;
27 case '-':
28 firstOps = secondOps;
29 //由于不能产生负数，所以在减法时要进行比较，如果前数小于后数则将表达式倒置拼接
30 if (Calculator.CMP(firstNum, secondNum)) {
31 firstNum = Calculator.SUB(firstNum, secondNum);
32 expression.append(secondOps).append(secondNum);
33 } else {
34 expression = new StringBuilder().append(secondNum).append(secondOps).append(expression);
35 firstNum = Calculator.SUB(secondNum, firstNum);
36 }
37 secondOps = GeneratorUtil.getOperator();
38 break;
39 case '×':
40 //乘法优先级大，在这里判断前面是否有优先级较小的加减操作，有的话将表达式带上括号再拼接乘法运算
41 if (firstOps == '+' || firstOps == '-') {
42 expression = new StringBuilder().append("(").append(expression).append(")").append(secondOps).append(secondNum);
43 } else {
44 expression.append(secondOps).append(secondNum);
45 }
46 //保存运算结果
47 firstNum = Calculator.MUL(firstNum, secondNum);
48 firstOps = secondOps;
49 secondOps = GeneratorUtil.getOperator();
50 break;
51 case '÷':
52 //除法优先级大，在这里判断前面是否有优先级较小的加减操作，有的话将表达式带上括号再拼接乘法运算
53 if (firstOps == '+' || firstOps == '-') {
54 expression = new StringBuilder().append("(").append(expression).append(")").append(secondOps).append(secondNum);
55 firstNum = Calculator.DIV(secondNum, firstNum);
56 } else {
57 expression.append(secondOps).append(secondNum);
58 firstNum = Calculator.DIV(firstNum, secondNum);
59 }
60 firstOps = secondOps;
61 secondOps = GeneratorUtil.getOperator();
62 break;
63 }
64 }
65 //将表达式和结果保存，放进HashSet
66 expressionResult.setExpression(expression.toString());
67 expressionResult.setResult(firstNum.toString());
68 expressionResultHashSet.add(expressionResult);
69 }
70 return expressionResultHashSet;
71 }
3. 随机数和操作符的获取
1 public class GeneratorUtil {
2
3 private static final char OPERATORS[] = {'+', '-', '×', '÷'};
4 private static final Random R = new Random();
5
6 public static Fraction getFraction(int maximum) {
7 //调整随机数为整数或者分数
8 boolean isFraction = R.nextBoolean();
9 return isFraction ? new Fraction(R.nextInt(maximum) + 1, R.nextInt(maximum) + 1) : new Fraction(R.nextInt(maximum) + 1, 1);
10 }
11
12 public static char getOperator() {
13 return OPERATORS[R.nextInt(4)];
14 }
15
16 }
4. 分数的运算操作
1 public class Calculator {
2
3 /**
4 * 化简
5 */
6 public static Integer simplify(Integer numerator, Integer denominator) {
7 if (denominator == 0) return numerator;
8 return numerator % denominator == 0 ? denominator : simplify(denominator, numerator % denominator);
9 }
10
11 //相加
12 public static Fraction ADD(Fraction first, Fraction second) {
13 return new Fraction(first.getNumerator() * second.getDenominator() + first.getDenominator() * second.getNumerator(),
14 first.getDenominator() * second.getDenominator());
15 }
16
17 //相减
18 public static Fraction SUB(Fraction first, Fraction second) {
19 return new Fraction(first.getNumerator() * second.getDenominator() - first.getDenominator() * second.getNumerator(), first.getDenominator() * second.getDenominator());
20 }
21
22 //相乘
23 public static Fraction MUL(Fraction first, Fraction second) {
24 return new Fraction(first.getNumerator() * second.getNumerator(), first.getDenominator() * second.getDenominator());
25 }
26
27 //相除
28 public static Fraction DIV(Fraction first, Fraction second) {
29 return MUL(first, Countdown(second));
30 }
31 //取倒
32 public static Fraction Countdown(Fraction fraction) {
33 return new Fraction(fraction.getDenominator(), fraction.getNumerator());
34 }
35
36 //比较大小
37 public static boolean CMP(Fraction first, Fraction second) {
38 Fraction result = DIV(first, second);
39 return result.getNumerator() > result.getDenominator() && result.getNumerator() > 0 ? true : false;
40 }
41 //获取最大公因数并约去（辗转相除法）
42 public static int GCD(int a, int b) {
43 if (b == 0) return a;
44 return a % b == 0 ? b : GCD(b, a % b);
45 }
46 }
5. 题目、答案文件和答案比对结果文件的生成
1 public static void generateFile(HashSet<ExpressionResult> expressionResultHashSet) throws IOException {
2 File questionFile = new File("Exercises.txt");
3 File answerFile = new File("Answers.txt");
4 if (!questionFile.exists()) {
5 questionFile.createNewFile();
6 }
7 if (!answerFile.createNewFile()) {
8 answerFile.createNewFile();
9 }
10 try (BufferedWriter abw = new BufferedWriter(new FileWriter(answerFile));
11 BufferedWriter qbw = new BufferedWriter(new FileWriter(questionFile))) {
12
13 int count = 1;
14 for (ExpressionResult e : expressionResultHashSet) {
15 try {
16 qbw.write(count + "." + e.getExpression());
17 qbw.newLine();
18 abw.write(count + "." + e.getResult());
19 abw.newLine();
20 //将表达式放入队列，在监听线程中拼接到界面中去
21 GuiForOperator.queue.add(count + "." + e.getExpression() + "=" + e.getResult());
22 count++;
23 } catch (IOException e1) {
24 e1.printStackTrace();
25 }
26 }
27
28 }
29 }
1 public static void CompareAnswers(File answerFile) throws IOException {
2 List<String> correctList = new ArrayList<>();
3 List<String> wrongList = new ArrayList<>();
4 try (BufferedReader qrAnswer = new BufferedReader(new FileReader(answerFile));
5 BufferedReader qrExercise = new BufferedReader(new FileReader("Answers.txt"))) {
6 String eStr = null;
7 String aStr = null;
8 while ((eStr = qrExercise.readLine()) != null && (aStr = qrAnswer.readLine()) != null) {
9 String orderNum = eStr.substring(0, eStr.indexOf("."));
10 String standardAnswer = aStr.substring(2, aStr.length());
11 String submitAnswer = eStr.substring(2, eStr.length());
12 if (standardAnswer.equals(submitAnswer)) {
13 correctList.add(orderNum);
14 } else {
15 wrongList.add(orderNum);
16 }
17 }
18 }
19 File gradeFile = new File("Grade.txt");
20 if (!gradeFile.exists()) {
21 gradeFile.createNewFile();
22 }
23 try (BufferedWriter bw = new BufferedWriter(new FileWriter(gradeFile))) {
24 StringBuilder correctStr = new StringBuilder().append("Correct: ").append(correctList.size()).append(" (");
25 StringBuilder wrongStr = new StringBuilder().append("Wrong: ").append(wrongList.size()).append(" (");
26 correctList.forEach((e) -> {
27 correctStr.append(e + ",");
28 });
29 wrongList.forEach((e) -> {
30 wrongStr.append(e + ",");
31 });
32 bw.write(correctStr.toString().substring(0, correctStr.lastIndexOf(",")) + ")");
33 bw.newLine();
34 if (wrongList.size() != 0) {
35 bw.write(wrongStr.toString().substring(0, wrongStr.lastIndexOf(",")) + ")");
36 } else {
37 bw.write(wrongStr.append(")").toString());
38 }
39 //将比对结果放入队列，在监听线程中拼接到界面中去
40 GuiForOperator.queue.add(correctStr.toString().substring(0, correctStr.lastIndexOf(",")) + ")");
41 GuiForOperator.queue.add(wrongStr.toString().substring(0, wrongStr.lastIndexOf(",")) + ")");
42
43 }
44 }
6. 界面：包括传入参数、文件以及结果显示
1 public class GuiForOperator extends JFrame {
2 // 使用队列存放表达式，起线程监听，有则取出并显示
3 public static BlockingQueue<String> queue = new LinkedBlockingQueue<>();
4
5 private JPanel contentPane;
6 private JTextField textField;
7 private JTextField textField_1;
8 public JTextArea textArea;
9 public JScrollPane scrollPane;
10
11
12 /**
13 * Create the frame.
14 */
15 public GuiForOperator() {
16 setTitle("\u56DB\u5219\u8FD0\u7B97");
17 setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
18 setBounds(100, 100, 706, 495);
19 contentPane = new JPanel();
20 contentPane.setBorder(new EmptyBorder(5, 5, 5, 5));
21 setContentPane(contentPane);
22 contentPane.setLayout(null);
23
24 JLabel label = new JLabel("\u9898\u76EE\u6570\u91CF\uFF1A");
25 label.setBounds(55, 43, 76, 18);
26 contentPane.add(label);
27
28 textField = new JTextField();
29 textField.setBounds(163, 35, 282, 35);
30 contentPane.add(textField);
31 textField.setColumns(10);
32
33 JLabel label_1 = new JLabel("\u6700\u5927\u968F\u673A\u6570\uFF1A");
34 label_1.setBounds(55, 91, 125, 18);
35 contentPane.add(label_1);
36
37 textField_1 = new JTextField();
38 textField_1.setBounds(163, 83, 282, 35);
39 contentPane.add(textField_1);
40 textField_1.setColumns(10);
41
42
43 scrollPane = new JScrollPane(textArea);
44 textArea = new JTextArea();
45 textArea.setEditable(false);
46 textArea.setBounds(55, 167, 591, 255);
47 textArea.setLineWrap(true);
48 scrollPane.setBounds(55, 167, 591, 255);
49 scrollPane.setVerticalScrollBarPolicy(JScrollPane.VERTICAL_SCROLLBAR_ALWAYS);
50 contentPane.add(scrollPane);
51 scrollPane.setViewportView(textArea);
52
53
54 JButton button = new JButton("\u786E\u5B9A");
55 button.addActionListener(e -> {
56 String r = textField.getText();
57 String n = textField_1.getText();
58 textArea.setText("");
59 try {
60 //传入参数生成表达式写入文件
61 HashSet<ExpressionResult> expressionResults = Generator.generateExpression(Integer.valueOf(r), Integer.valueOf(n));
62 Generator.generateFile(expressionResults);
63 } catch (IOException e1) {
64 e1.printStackTrace();
65 }
66 });
67 button.setBounds(533, 87, 113, 27);
68 contentPane.add(button);
69 JButton btnNewButton = new JButton("选择文件");
70 btnNewButton.addActionListener(arg0 -> {
71
72 JFileChooser jfc = new JFileChooser();
73 jfc.setFileSelectionMode(JFileChooser.FILES_AND_DIRECTORIES);
74 jfc.showDialog(new JLabel(), "选择");
75 File file = jfc.getSelectedFile();//得到文件
76 if (file.isDirectory()) {
77 System.out.println("文件夹:" + file.getAbsolutePath());
78 } else if (file.isFile()) {
79 System.out.println("文件:" + file.getAbsolutePath());
80 }
81 try {
82 //传入比对文件
83 Generator.CompareAnswers(file);
84 } catch (IOException e) {
85 e.printStackTrace();
86 }
87 });
88 btnNewButton.setBounds(533, 39, 113, 27);
89 contentPane.add(btnNewButton);
90 }
7. 程序入口
1 public class AppEntry {
2 public static void main(String[] args) {
3 //新建窗口并显示
4 GuiForOperator frame = new GuiForOperator();
5 frame.setVisible(true);
6 //启动线程监听队列取出表达式进行显示
7 new Thread(() -> {
8 while (true) {
9 try {
10 String expression = GuiForOperator.queue.take();
11 if (expression != null) {
12 frame.textArea.append(expression + "\r\n");
13 }
14 } catch (InterruptedException e) {
15 e.printStackTrace();
16 }
17 }
18 }).start();
19 }
20 }
七. 性能分析
生成一万道题目，数值在一万以内；生成十万道题目，数值在十万以内；生成一百万道题目，数值在一百万以内；