递归在代数表达式中的运用

//postfix expression test whether the postfix expression is right

#include<string>
#include<iostream>
using namespace std;
int postfix(const string &str,int cur,int size);
int main()
{
	string str;
	cout<<"please the computing expression :";
	cin>>str;
	int size=str.size();
	int index=postfix(str,size-1,size);
	cout<<str<<endl;
	if(index>-1&&index==0)
		cout<<"the postifix expression is right !"<<endl;	
	else
          	cout<<"the postfix expression is wrong !"<<endl;
	return 0;
}
int postfix(const string &str,int cur,int size)
//find the first of postfix,if one exists
//precondition :the substring of str from the index cur
//through the first of the string contains no blanks character
//postcondition :returns the index of the first character
//int the postfix expression that begins at index end of str
//firstPtr should rturns -1 if no such prefix expression exists
{
	if(cur<0||cur>=size)
		return -1;
	if(str[cur]>='a'&&str[cur]<='z')
		return cur;
	else if(str[cur]=='*'||str[cur]=='+'||str[cur]=='-'||str[cur]=='/')
	{
		int pre=postfix(str,cur-1,size);
		if(pre>-1)
			return postfix(str,pre-1,size);
		else
			return -1;
	}
	else
		return -1;
}

bool infix(const string &str,int first,int last)
{
	if((first==last)&&(str[first]>='a')&&(str[first]<='z'))
		return true;
	else
	{
		int mid=findO(str,first,last);
		if(mid==-1)
			return false;
		else
		{
			bool ok=infix(str,first,mid-1);
			if(ok)
				return infix(str,mid+1,last);
			else
				return false;
		}
	}
}

//prefix expression test whether the prefix expression is right

#include<string>
#include<iostream>
using namespace std;
int prefix(const string &str,int cur,int size);
int main()
{
	string str;
	cout<<"please enter prefix expression :";
	cin>>str;
	int size=str.size();
	int index=prefix(str,0,size);
	cout<<str<<endl;
	if(index>-1&&index==size-1)
		cout<<"prefix expression success !"<<endl;
	else
		cout<<"prefix expression failed !"<<endl;
}

int prefix(const string &str,int cur,int size)
//Finds the end of a prefix expression ,if one exists.
//precondition :the substring of str from index cur
//through the end of the string contains no blank characters
//Postcondition :return the index of the lase character
//int the prefix expression that begins at index first of 
//strExp endPtr should returns -1 if no such prefix expression exist
{
	if(cur<0||cur>=size)
		return -1;
	if(str[cur]>='a'&&str[cur]<='z')
		return cur;
	else if(str[cur]=='*'||str[cur]=='+'||str[cur]=='-'||str[cur]=='/')
	{
		int post=prefix(str,cur+1,size);
		if(post>-1)
			return prefix(str,post+1,size);
		else
			return -1;
	}
	else
		return -1;
}

//and turn the postfix expression to the prefix expression 

#include<iostream>
#include<string>
using namespace std;
void pre2post(const string &str,string &post,int &index);
int main()
{
	cout<<"please enter a right prefix expression :";
	string str,post;
	cin>>str;
	cout<<endl<<str<<endl;
	int size=0;
	pre2post(str,post,size);
	cout<<" covert to postfix expression :"<<post<<endl;
	return 0;
}
void pre2post(const string &str,string &post,int &index)
{
	if(index<str.size())
	{
            	char ch=str[index];
		index++;
         	if(ch>='a'&&ch<='z')
	          	post=post+ch;
          	else
	        {
         		 pre2post(str,post,index);
			 pre2post(str,post,index);
			 post=post+ch;
        	}
                

      	}
}