No2. 字符串四則運算

問題描述：

給定四則運算字符串，輸出運算結果

輸入描述：

1/2*(3+(4-5))

輸出描述：

1.0

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1> 問題分析

使用棧將中綴表達式轉換爲後綴表達式，計算後綴表達式；

☞ 前綴：prefix

☞ 中綴：infix

☞ 後綴：postfix

2> 實現

• 中綴表達式轉後綴表達式

/*
 * 中綴轉後綴
 */
public static LinkedList<Character> convertToPostfix(String infix) {
	LinkedList<Character> valueStack = new LinkedList<Character>();
	LinkedList<Character> operatorStack = new LinkedList<Character>();
	HashMap<Character, Integer> baseOperatorMap = new HashMap<Character, Integer>();
	baseOperatorMap.put('(', 0);
	baseOperatorMap.put('+', 1);
	baseOperatorMap.put('-', 2);
	baseOperatorMap.put('*', 3);
	baseOperatorMap.put('/', 4);
	Character topOperator = null;

	while (!infix.isEmpty()) {
		int index = 0;
		char nextCharacter = infix.charAt(index);
		//System.out.println(nextCharacter + " " + valueStack + " " + operatorStack);
		if (Character.isDigit(nextCharacter)) {
			valueStack.push(nextCharacter);
		} else if (nextCharacter == '+' || nextCharacter == '-' || nextCharacter == '*' || nextCharacter == '/') {
			if (!operatorStack.isEmpty()) {
				if (baseOperatorMap.get(nextCharacter) <= baseOperatorMap.get(operatorStack.getFirst())) {
					topOperator = operatorStack.pop();
					operatorStack.push(nextCharacter);
					valueStack.push(topOperator);
				} else {
					operatorStack.push(nextCharacter);
				}
			}else{
				operatorStack.push(nextCharacter);
			}
		} else if (nextCharacter == '(') {
			operatorStack.push(nextCharacter);
		} else if (nextCharacter == ')') {
			topOperator = operatorStack.pop();
			while (topOperator != '(') {
				valueStack.push(topOperator);
				topOperator = operatorStack.pop();
			}
		} else if (nextCharacter == ' ') {

		} else {
			System.out.println("格式有誤！");
			return null;
		}
		index++;
		infix = infix.substring(index);
	}
	//operatorStack非空
	while(!operatorStack.isEmpty()){
		topOperator = operatorStack.pop();
		valueStack.push(topOperator);
	}
	return valueStack;
}

☞ 結果：[*, +, -, 5, 4, 3, /, 2, 1]

• 計算後綴表達式

☞ 由於上述棧頂到棧底的順序是後綴表達式的逆序，所以取值計算時要從最後開始取值。

/*
 * 求解後綴表達式
 */
public static double calculate(String infix) {
	String result = null;
	double firstNum = 0;
	double secondNum = 0;
	LinkedList<Character> postFix = convertToPostfix(infix);
	LinkedList<String> valueStack = new LinkedList<String>();
	while(!postFix.isEmpty()){
		//由於後綴棧爲反後綴表達式，從末尾進行彈出
		Character nextCharacter = postFix.pollLast();
		if(Character.isDigit(nextCharacter)){
			valueStack.push(nextCharacter.toString());
		}else if(nextCharacter == '+' || nextCharacter == '-' || nextCharacter == '*' || nextCharacter == '/'){
			switch(nextCharacter.toString()){
			case("+"):
				secondNum = Double.valueOf(valueStack.pop());
				firstNum = Double.valueOf(valueStack.pop());
				result = Double.valueOf((firstNum+secondNum)).toString();
				break;
			case("-"):
				secondNum = Double.valueOf(valueStack.pop());
				firstNum = Double.valueOf(valueStack.pop());
				result = Double.valueOf((firstNum-secondNum)).toString();
				break;
			case("*"):
				secondNum = Double.valueOf(valueStack.pop());
				firstNum = Double.valueOf(valueStack.pop());
				result = Double.valueOf((firstNum*secondNum)).toString();
				break;
			case("/"):
				secondNum = Double.valueOf(valueStack.pop());
				firstNum = Double.valueOf(valueStack.pop());
				result = Double.valueOf((firstNum/secondNum)).toString();
				break;
			}		
			valueStack.push(result);
		}
	}
	return Double.valueOf(valueStack.peek());
} 

• main測試

public static void main(String[] args) {
	String x = "1/2*(3+(4-5))";
	double result = calculate(x);
	System.out.println(result);
}