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：
1 #include<iostream> 2 #include<cstring> 3 using namespace std; 4 int term(); 5 int expr(); 6 int factor(); 7 8 int expr() 9 { 10 cout<<"---expr---"<<endl; 11 int result = term(); 12 cout<<"expr_first_result: "<<result<<endl; 13 bool more = true; 14 while(more) 15 { 16 char c = cin.peek(); 17 cout<<"expr_cin.peek(): "<<c<<endl; 18 if(c == '+' || c == '-') 19 { 20 cin.get(); 21 int value = term(); 22 if(c == '+') 23 result += value; 24 else if(c == '-') 25 result -= value; 26 } 27 else more = false; 28 } 29 cout<<"expr_return_result: "<<result<<endl; 30 cout<<"---expr---END"<<endl; 31 cout<<endl; 32 return result; 33 } 34 35 int term() 36 { 37 cout<<"---term---"<<endl; 38 int result = factor(); 39 cout<<"term_first_result: "<<result<<endl; 40 bool more = true; 41 while(more) 42 { 43 char c = cin.peek(); 44 cout<<"term_cin.peek(): "<<c<<endl; 45 if(c == '*' || c == '/') 46 { 47 cin.get(); 48 int value = factor(); 49 if(c == '*') 50 result *= value; 51 else 52 result /= value; 53 } 54 else 55 more = false; 56 } 57 cout<<"term_return_result: "<<result<<endl; 58 cout<<"---term---END"<<endl; 59 cout<<endl; 60 return result; 61 } 62 63 int factor() 64 { 65 cout<<"---factor---"<<endl; 66 int result = 0; 67 char c = cin.peek(); 68 cout<<"factor_cin.peek(): "<<c<<endl; 69 if(c == '(') 70 { 71 cin.get();//去掉左括号 72 result = expr(); 73 cin.get();//去掉右括号 74 } 75 else 76 { 77 while(isdigit(c)) 78 { 79 result = result*10 + c - '0'; 80 cin.get(); 81 c = cin.peek() ; 82 } 83 } 84 cout<<"factor_return_result: "<<result<<endl; 85 cout<<"---factor---END"<<endl; 86 cout<<endl; 87 return result; 88 } 89 int main() 90 { 91 freopen("in.txt","r",stdin); 92 freopen("out.txt","w",stdout); 93 cout << expr() << endl; 94 //cout << term() << endl; 95 // cout << factor() << endl; 96 return 0; 97 }
in.txt
(2+3)+(5+7)+9/3
out.txt
1 ---expr--- 2 ---term--- 3 ---factor--- 4 factor_cin.peek(): ( 5 ---expr--- 6 ---term--- 7 ---factor--- 8 factor_cin.peek(): 2 9 factor_return_result: 2 10 ---factor---END 11 12 term_first_result: 2 13 term_cin.peek(): + 14 term_return_result: 2 15 ---term---END 16 17 expr_first_result: 2 18 expr_cin.peek(): + 19 ---term--- 20 ---factor--- 21 factor_cin.peek(): 3 22 factor_return_result: 3 23 ---factor---END 24 25 term_first_result: 3 26 term_cin.peek(): ) 27 term_return_result: 3 28 ---term---END 29 30 expr_cin.peek(): ) 31 expr_return_result: 5 32 ---expr---END 33 34 factor_return_result: 5 35 ---factor---END 36 37 term_first_result: 5 38 term_cin.peek(): + 39 term_return_result: 5 40 ---term---END 41 42 expr_first_result: 5 43 expr_cin.peek(): + 44 ---term--- 45 ---factor--- 46 factor_cin.peek(): ( 47 ---expr--- 48 ---term--- 49 ---factor--- 50 factor_cin.peek(): 5 51 factor_return_result: 5 52 ---factor---END 53 54 term_first_result: 5 55 term_cin.peek(): + 56 term_return_result: 5 57 ---term---END 58 59 expr_first_result: 5 60 expr_cin.peek(): + 61 ---term--- 62 ---factor--- 63 factor_cin.peek(): 7 64 factor_return_result: 7 65 ---factor---END 66 67 term_first_result: 7 68 term_cin.peek(): ) 69 term_return_result: 7 70 ---term---END 71 72 expr_cin.peek(): ) 73 expr_return_result: 12 74 ---expr---END 75 76 factor_return_result: 12 77 ---factor---END 78 79 term_first_result: 12 80 term_cin.peek(): + 81 term_return_result: 12 82 ---term---END 83 84 expr_cin.peek(): + 85 ---term--- 86 ---factor--- 87 factor_cin.peek(): 9 88 factor_return_result: 9 89 ---factor---END 90 91 term_first_result: 9 92 term_cin.peek(): / 93 ---factor--- 94 factor_cin.peek(): 3 95 factor_return_result: 3 96 ---factor---END 97 98 term_cin.peek(): 99 term_return_result: 3 100 ---term---END 101 102 expr_cin.peek(): 103 expr_return_result: 20 104 ---expr---END 105 106 20