20175316盛茂淞 2018-2019-2《Java程序設計》結對編程項目-四則運算 第一周 階段性總結

需求分析

• 自動生成四則運算題目（加、減、乘、除）。
• 既可以用前綴算法（波蘭算法）實現加減乘除也可以用後綴算法實現。
• 支持復合運算。

設計思路

• 首先我們先實現前綴表達式的方法，通過閱讀材料大致了解到如下方法：
• 前綴表達式的計算機求值：
  從右至左掃描表達式，遇到數字時，將數字壓入堆棧，遇到運算符時，彈出棧頂的兩個數，用運算符對它們做相應的計算（棧頂元素 op 次頂元素），並將結果入棧；重復上述過程直到表達式最左端，最後運算得出的值即為表達式的結果。
  例如前綴表達式“- × + 3 4 5 6”：

(1) 從右至左掃描，將6、5、4、3壓入堆棧；

(2) 遇到+運算符，因此彈出3和4（3為棧頂元素，4為次頂元素，註意與後綴表達式做比較），計算出3+4的值，得7，再將7入棧；

(3) 接下來是×運算符，因此彈出7和5，計算出7×5=35，將35入棧；

(4) 最後是-運算符，計算出35-6的值，即29，由此得出最終結果。
可以看出，用計算機計算前綴表達式的值是很容易的。

• 隨後後綴表達式實現方法上與前綴有異同之處：
• 後綴表達式的計算機求值：
  與前綴表達式類似，只是順序是從左至右：
  從左至右掃描表達式，遇到數字時，將數字壓入堆棧，遇到運算符時，彈出棧頂的兩個數，用運算符對它們做相應的計算（次頂元素 op 棧頂元素），並將結果入棧；重復上述過程直到表達式最右端，最後運算得出的值即為表達式的結果。
  
  例如後綴表達式“3 4 + 5 × 6 -”：

(1) 從左至右掃描，將3和4壓入堆棧；

(2) 遇到+運算符，因此彈出4和3（4為棧頂元素，3為次頂元素，註意與前綴表達式做比較），計算出3+4的值，得7，再將7入棧；

(3) 將5入棧；

(4) 接下來是×運算符，因此彈出5和7，計算出7×5=35，將35入棧；

(5) 將6入棧；

(6) 最後是-運算符，計算出35-6的值，即29，由此得出最終結果。

代碼

import java.util.Scanner;
import java.util.Stack;
public class sizeyunsuan {
    public static final String USAGE = "== usage ==\n"
            + "input the expressions, and then the program "
            + "will calculate them and show the result.\n"
            + "input 'bye' to exit.\n";
    /**
     * @param args
     */
    public static void main(String[] args) {
        System.out.println(USAGE);
        Scanner scanner = new Scanner(System.in);
        String input = "";
        final String CLOSE_MARK = "bye";
        System.out.println("input an expression:");
        input = scanner.nextLine();
        while (input.length() != 0
                && !CLOSE_MARK.equals((input))) {
            System.out.print("Polish Notation (PN):");
            try {
                toPolishNotation(input);
            } catch (NumberFormatException e) {
                System.out.println("\ninput error, not a number.");
            } catch (IllegalArgumentException e) {
                System.out.println("\ninput error:" + e.getMessage());
            } catch (Exception e) {
                System.out.println("\ninput error, invalid expression.");
            }
            System.out.print("Reverse Polish Notation (RPN):");
            try {
                toReversePolishNotation(input);
            } catch (NumberFormatException e) {
                System.out.println("\ninput error, not a number.");
            } catch (IllegalArgumentException e) {
                System.out.println("\ninput error:" + e.getMessage());
            } catch (Exception e) {
                System.out.println("\ninput error, invalid expression.");
            }
            System.out.println("input a new expression:");
            input = scanner.nextLine();
        }
        System.out.println("program exits");
    }
    /**
     * parse the expression , and calculate it.
     * @param input
     * @throws IllegalArgumentException
     * @throws NumberFormatException
     */
    private static void toPolishNotation(String input)
            throws IllegalArgumentException, NumberFormatException {
        int len = input.length();
        char c, tempChar;
        Stack<Character> s1 = new Stack<Character>();
        Stack<Double> s2 = new Stack<Double>();
        Stack<Object> expression = new Stack<Object>();
        double number;
        int lastIndex = -1;
        for (int i=len-1; i>=0; --i) {
            c = input.charAt(i);
            if (Character.isDigit(c)) {
                lastIndex = readDoubleReverse(input, i);
                number = Double.parseDouble(input.substring(lastIndex, i+1));
                s2.push(number);
                i = lastIndex;
                if ((int) number == number)
                    expression.push((int) number);
                else
                    expression.push(number);
            } else if (isOperator(c)) {
                while (!s1.isEmpty()
                        && s1.peek() != ')'
                        && priorityCompare(c, s1.peek()) < 0) {
                    expression.push(s1.peek());
                    s2.push(calc(s2.pop(), s2.pop(), s1.pop()));
                }
                s1.push(c);
            } else if (c == ')') {
                s1.push(c);
            } else if (c == '(') {
                while ((tempChar=s1.pop()) != ')') {
                    expression.push(tempChar);
                    s2.push(calc(s2.pop(), s2.pop(), tempChar));
                    if (s1.isEmpty()) {
                        throw new IllegalArgumentException(
                                "bracket dosen't match, missing right bracket ')'.");
                    }
                }
            } else if (c == ' ') {
                // ignore
            } else {
                throw new IllegalArgumentException(
                        "wrong character '" + c + "'");
            }
        }
        while (!s1.isEmpty()) {
            tempChar = s1.pop();
            expression.push(tempChar);
            s2.push(calc(s2.pop(), s2.pop(), tempChar));
        }
        while (!expression.isEmpty()) {
            System.out.print(expression.pop() + " ");
        }
        double result = s2.pop();
        if (!s2.isEmpty())
            throw new IllegalArgumentException("input is a wrong expression.");
        System.out.println();
        if ((int) result == result)
            System.out.println("the result is " + (int) result);
        else
            System.out.println("the result is " + result);
    }
    /**
     * parse the expression, and calculate it.
     * @param input
     * @throws IllegalArgumentException
     * @throws NumberFormatException
     */
    private static void toReversePolishNotation(String input)
            throws IllegalArgumentException, NumberFormatException {
        int len = input.length();
        char c, tempChar;
        Stack<Character> s1 = new Stack<Character>();
        Stack<Double> s2 = new Stack<Double>();
        double number;
        int lastIndex = -1;
        for (int i=0; i<len; ++i) {
            c = input.charAt(i);
            if (Character.isDigit(c) || c == '.') {
                lastIndex = readDouble(input, i);
                number = Double.parseDouble(input.substring(i, lastIndex));
                s2.push(number);
                i = lastIndex - 1;
                if ((int) number == number)
                    System.out.print((int) number + " ");
                else
                    System.out.print(number + " ");
            } else if (isOperator(c)) {
                while (!s1.isEmpty()
                        && s1.peek() != '('
                        && priorityCompare(c, s1.peek()) <= 0) {
                    System.out.print(s1.peek() + " ");
                    double num1 = s2.pop();
                    double num2 = s2.pop();
                    s2.push(calc(num2, num1, s1.pop()));
                }
                s1.push(c);
            } else if (c == '(') {
                s1.push(c);
            } else if (c == ')') {
                while ((tempChar=s1.pop()) != '(') {
                    System.out.print(tempChar + " ");
                    double num1 = s2.pop();
                    double num2 = s2.pop();
                    s2.push(calc(num2, num1, tempChar));
                    if (s1.isEmpty()) {
                        throw new IllegalArgumentException(
                                "bracket dosen't match, missing left bracket '('.");
                    }
                }
            } else if (c == ' ') {
                // ignore
            } else {
                throw new IllegalArgumentException(
                        "wrong character '" + c + "'");
            }
        }
        while (!s1.isEmpty()) {
            tempChar = s1.pop();
            System.out.print(tempChar + " ");
            double num1 = s2.pop();
            double num2 = s2.pop();
            s2.push(calc(num2, num1, tempChar));
        }
        double result = s2.pop();
        if (!s2.isEmpty())
            throw new IllegalArgumentException("input is a wrong expression.");
        System.out.println();
        if ((int) result == result)
            System.out.println("the result is " + (int) result);
        else
            System.out.println("the result is " + result);
    }
    /**
     * calculate the two number with the operation.
     * @param num1
     * @param num2
     * @param op
     * @return
     * @throws IllegalArgumentException
     */
    private static double calc(double num1, double num2, char op)
            throws IllegalArgumentException {
        switch (op) {
            case '+':
                return num1 + num2;
            case '-':
                return num1 - num2;
            case '*':
                return num1 * num2;
            case '/':
                if (num2 == 0) throw new IllegalArgumentException("divisor can't be 0.");
                return num1 / num2;
            default:
                return 0; // will never catch up here
        }
    }
    /**
     * compare the two operations' priority.
     * @param c
     * @param peek
     * @return
     */
    private static int priorityCompare(char op1, char op2) {
        switch (op1) {
            case '+': case '-':
                return (op2 == '*' || op2 == '/' ? -1 : 0);
            case '*': case '/':
                return (op2 == '+' || op2 == '-' ? 1 : 0);
        }
        return 1;
    }
    /**
     * read the next number (reverse)
     * @param input
     * @param start
     * @return
     * @throws IllegalArgumentException
     */
    private static int readDoubleReverse(String input, int start)
            throws IllegalArgumentException {
        int dotIndex = -1;
        char c;
        for (int i=start; i>=0; --i) {
            c = input.charAt(i);
            if (c == '.') {
                if (dotIndex != -1)
                    throw new IllegalArgumentException(
                            "there have more than 1 dots in the number.");
                else
                    dotIndex = i;
            } else if (!Character.isDigit(c)) {
                return i + 1;
            } else if (i == 0) {
                return 0;
            }
        }
        throw new IllegalArgumentException("not a number.");
    }

    /**
     * read the next number
     * @param input
     * @param start
     * @return
     * @throws IllegalArgumentException
     */
    private static int readDouble(String input, int start)
            throws IllegalArgumentException {
        int len = input.length();
        int dotIndex = -1;
        char c;
        for (int i=start; i<len; ++i) {
            c = input.charAt(i);
            if (c == '.') {
                if (dotIndex != -1)
                    throw new IllegalArgumentException(
                            "there have more than 1 dots in the number.");
                else if (i == len - 1)
                    throw new IllegalArgumentException(
                            "not a number, dot can't be the last part of a number.");
                else
                    dotIndex = i;
            } else if (!Character.isDigit(c)) {
                if (dotIndex == -1 || i - dotIndex > 1)
                    return i;
                else
                    throw new IllegalArgumentException(
                            "not a number, dot can't be the last part of a number.");
            } else if (i == len - 1) {
                return len;
            }
        }

        throw new IllegalArgumentException("not a number.");
    }
    /**
     * return true if the character is an operator.
     * @param c
     * @return
     */
    private static boolean isOperator(char c) {
        return (c=='+' || c=='-' || c=='*' || c=='/');
    }
}
 

測試說明

• 正常測試
• 異常測試
• 邊界測試

碼雲鏈接

[碼雲連接]https://gitee.com/shengmaosong/java-besti-20175316/blob/master/jiedui/jiedui1/sizeyunsuan.java

UML圖

## 參考資料

• 逆波蘭算法
• 前綴解析
• IDEA上傳至碼雲

結對學習照片

20175316盛茂淞 2018-2019-2《Java程序設計》結對編程項目-四則運算 第一周 階段性總結