算法答疑---递归实现表达式求值

算法答疑---递归实现表达式求值

一、总结

一句话总结：表达式求值除了日常的栈做法，也可以用递归。

1、递归的核心是什么？

递推公式和边界条件

递推公式就是递归的逻辑，有时候不一定方便写出来

2、c++中int factor();形式的代码是做什么用的？

函数声明，c++中的函数声明是有带函数返回值的，也就是最前面那个int。

 1 #include<iostream>
 2 #include<cstring>
 3 using namespace std;
 4 int term();
 5 int expr();
 6 int factor();

二、3.1 表达式求值（递归实现）

#include<iostream>
#include<cstring>
using namespace std;
int term();
int expr();
int factor();

int expr()
{
	int result = term();
	bool more = true;	
	while(more)
	{
		char c = cin.peek();
		if(c == '+' || c == '-')
		{
			cin.get();
			int value = term();
			if(c == '+')
				result += value;
			else if(c == '-')
				result -= value;
		}
		else more = false; 
	}	
	return result;
}

int term()
{
	int result = factor();
	bool more = true;
	while(more)
	{
		char c = cin.peek();
		if(c == '*' || c == '/')
		{
			cin.get();
			int value = factor();
			if(c == '*')
				result *= value;
			else
				result /= value;
		}
		else
			more = false;
	}
	return result;
}

int factor()
{
	int result = 0;
	char c = cin.peek();
	if(c == '(')
	{
		cin.get();//去掉左括号 
		result = expr();
		cin.get();//去掉右括号 
	}
	else
	{
		while(isdigit(c))
		{
			result = result*10 + c - '0';
			cin.get();
			c = cin.peek() ;
		}
	} 
	return result;
}
int main()
{
	cout << expr() << endl;
	//cout << term() << endl;
//	cout << factor() << endl; 
	return 0;
} 

还有一种方法是通过栈来实现，后面更新~

 

 

 

三、代码测试（代码的中间结果）

测试代码：

#include<iostream>
#include<cstring>
using namespace std;
int term();
int expr();
int factor();
 
int expr()
{
    cout<<"---expr---"<<endl;
    int result = term();
    cout<<"expr_first_result: "<<result<<endl;
    bool more = true;    
    while(more)
    {
        char c = cin.peek();
        cout<<"expr_cin.peek(): "<<c<<endl;
        if(c == '+' || c == '-')
        {
            cin.get();
            int value = term();
            if(c == '+')
                result += value;
            else if(c == '-')
                result -= value;
        }
        else more = false; 
    }
    cout<<"expr_return_result: "<<result<<endl;    
    cout<<"---expr---END"<<endl;
    cout<<endl;
    return result;
}
 
int term()
{
    cout<<"---term---"<<endl;
    int result = factor();
    cout<<"term_first_result: "<<result<<endl;
    bool more = true;
    while(more)
    {
        char c = cin.peek();
        cout<<"term_cin.peek(): "<<c<<endl;
        if(c == '*' || c == '/')
        {
            cin.get();
            int value = factor();
            if(c == '*')
                result *= value;
            else
                result /= value;
        }
        else
            more = false;
    }
    cout<<"term_return_result: "<<result<<endl;
    cout<<"---term---END"<<endl;
    cout<<endl;
    return result;
}
 
int factor()
{
    cout<<"---factor---"<<endl;
    int result = 0;
    char c = cin.peek();
    cout<<"factor_cin.peek(): "<<c<<endl;
    if(c == '(')
    {
        cin.get();//去掉左括号 
        result = expr();
        cin.get();//去掉右括号 
    }
    else
    {
        while(isdigit(c))
        {
            result = result*10 + c - '0';
            cin.get();
            c = cin.peek() ;
        }
    } 
    cout<<"factor_return_result: "<<result<<endl;    
    cout<<"---factor---END"<<endl;
    cout<<endl;
    return result;
}
int main()
{
    freopen("in.txt","r",stdin); 
    freopen("out.txt","w",stdout); 
    cout << expr() << endl;
    //cout << term() << endl;
//    cout << factor() << endl; 
    return 0;
} 

in.txt

(2+3)+(5+7)+9/3

out.txt

---expr---
---term---
---factor---
factor_cin.peek(): (
---expr---
---term---
---factor---
factor_cin.peek(): 2
factor_return_result: 2
---factor---END

term_first_result: 2
term_cin.peek(): +
term_return_result: 2
---term---END

expr_first_result: 2
expr_cin.peek(): +
---term---
---factor---
factor_cin.peek(): 3
factor_return_result: 3
---factor---END

term_first_result: 3
term_cin.peek(): )
term_return_result: 3
---term---END

expr_cin.peek(): )
expr_return_result: 5
---expr---END

factor_return_result: 5
---factor---END

term_first_result: 5
term_cin.peek(): +
term_return_result: 5
---term---END

expr_first_result: 5
expr_cin.peek(): +
---term---
---factor---
factor_cin.peek(): (
---expr---
---term---
---factor---
factor_cin.peek(): 5
factor_return_result: 5
---factor---END

term_first_result: 5
term_cin.peek(): +
term_return_result: 5
---term---END

expr_first_result: 5
expr_cin.peek(): +
---term---
---factor---
factor_cin.peek(): 7
factor_return_result: 7
---factor---END

term_first_result: 7
term_cin.peek(): )
term_return_result: 7
---term---END

expr_cin.peek(): )
expr_return_result: 12
---expr---END

factor_return_result: 12
---factor---END

term_first_result: 12
term_cin.peek(): +
term_return_result: 12
---term---END

expr_cin.peek(): +
---term---
---factor---
factor_cin.peek(): 9
factor_return_result: 9
---factor---END

term_first_result: 9
term_cin.peek(): /
---factor---
factor_cin.peek(): 3
factor_return_result: 3
---factor---END

term_cin.peek(): 
term_return_result: 3
---term---END

expr_cin.peek(): 
expr_return_result: 20
---expr---END

20