UVA 11234 – Expressions

Description

2007/2008 ACM International Collegiate Programming Contest 
University of Ulm Local Contest

Problem E: Expressions

Arithmetic expressions are usually written with the operators in between the two operands (which is called infix notation). For example,(x+y)*(z-w) is an arithmetic expression in infix notation. However,
it is easier to write a program to evaluate an expression if the expression is written in postfix notation (also known as reverse polish notation). In postfix notation, an operator is written behind its two operands, which may be expressions themselves. For
example, x y + z w - * is a postfix notation of the arithmetic expression given above. Note that in this case parentheses are not required.

To evaluate an expression written in postfix notation, an algorithm operating on a stack can be used. A stack is a data structure which supports two operations:

1. push: a number is inserted at the top of the stack.
2. pop: the number from the top of the stack is taken out.

During the evaluation, we process the expression from left to right. If we encounter a number, we push it onto the stack. If we encounter an operator, we pop the first two numbers from the stack, apply the operator
on them, and push the result back onto the stack. More specifically, the following pseudocode shows how to handle the case when we encounter an operator O:

a := pop();b := pop();push(b O a);

The result of the expression will be left as the only number on the stack.

Now imagine that we use a queue instead of the stack. A queue also has a push and pop operation, but their meaning is different:

1. push: a number is inserted at the end of the queue.
2. pop: the number from the front of the queue is taken out of the queue.

Can you rewrite the given expression such that the result of the algorithm using the queue is the same as the result of the original expression evaluated using the algorithm with the stack?

Input Specification

The first line of the input contains a number T (T ≤ 200). The following T lines each contain one expression in postfix notation. Arithmetic operators are represented
by uppercase letters, numbers are represented by lowercase letters. You may assume that the length of each expression is less than 10000 characters.

Output Specification

For each given expression, print the expression with the equivalent result when using the algorithm with the queue instead of the stack. To make the solution unique, you are not allowed to assume that the operators
are associative or commutative.

Sample Input

2xyPzwIMabcABdefgCDEF

Sample Output

wzyxIPMgfCecbDdAaEBF

規則：遇到數字push進線性表中，遇到操作符，從線性表中pop()出兩元素，計算後再push進去。

這個題的意思是讓你求一表達示，使用隊列按照上面規則操作得到的結果與給定的字串用棧按上面規則操作得到的結果相同。
剛開始看到這個題一點思路也沒有。後來到網上查了下，說是要建樹，後來就明白了。
首先利用後輟運算式建好樹，然後寬度優先遍曆就行了。
language:c++
code:
#include<iostream>#include<vector>#include<string>#include<stack>#include<queue>#include<cctype>using namespace std;struct node{    char data;    node* left,*right;    node(char d=0,node*l=0,node*r=0):data(d),left(l),right(r){}};node *build(char data,node* left,node* right){    node*father=new node(data,left,right);    return father;}int main(){    string s;    int cas;    cin>>cas;    while(cas--)    {        cin>>s;        stack<node*>stck;        queue<node*>que;        string ans;        for(size_t i=0;i!=s.size();i++)        {            if(islower(s[i]))            {                node* tree=new node(s[i],0,0);                stck.push(tree);            }            else            {                node* r=stck.top();stck.pop();                node* l=stck.top();stck.pop();                stck.push(build(s[i],l,r));            }        }        que.push(stck.top());        while(!que.empty())        {            node* cur=que.front();que.pop();            ans+=cur->data;            if(cur->left)que.push(cur->left);            if(cur->right)que.push(cur->right);        }        for(int i=ans.size()-1;i>-1;i--)            cout<<ans[i];        cout<<endl;    }    return 0;}