uva-712 S-Trees

A Strange Tree (S-tree) over the variable set  is a binary tree representing a Boolean function. Each path of the S-tree begins at the root node and consists of n+1 nodes. Each of the S-tree's nodes has a depth, which is the amount of nodes between itself and the root (so the root has depth 0). The nodes with depth less than n are called non-terminal nodes. All non-terminal nodes have two children: the right child and the left child. Each non-terminal node is marked with some variable xi from the variable set Xn. All non-terminal nodes with the same depth are marked with the same variable, and non-terminal nodes with different depth are marked with different variables. So, there is a unique variable xi1 corresponding to the root, a unique variable xi2 corresponding to the nodes with depth 1, and so on. The sequence of the variables  is called the variable ordering. The nodes having depth n are called terminal nodes. They have no children and are marked with either 0 or 1. Note that the variable ordering and the distribution of 0's and 1's on terminal nodes are sufficient to completely describe an S-tree.
As stated earlier, each S-tree represents a Boolean function f. If you have an S-tree and values for the variables , then it is quite simple to find out what  is: start with the root. Now repeat the following: if the node you are at is labelled with a variable xi, then depending on whether the value of the variable is 1 or 0, you go its right or left child, respectively. Once you reach a terminal node, its label gives the value of the function.
 
 
Figure 1: S-trees for the function 
On the picture, two S-trees representing the same Boolean function, , are shown. For the left tree, the variable ordering is x1, x2, x3, and for the right tree it is x3, x1, x2.
The values of the variables , are given as a Variable Values Assignment (VVA) 
 
 
 
with  . For instance, (  x 1  = 1,  x 2  = 1  x 3  = 0) would be a valid VVA for  n  = 3, resulting for the sample function above in the value  . The corresponding paths are shown bold in the picture.
Your task is to write a program which takes an S-tree and some VVAs and computes  as described above.
 

Input 

The input file contains the description of several S-trees with associated VVAs which you have to process. Each description begins with a line containing a single integer  n ,  , the depth of the S-tree. This is followed by a line describing the variable ordering of the S-tree. The format of that line is  x i 1   x i 2  ... x i n . (There will be exactly  n  different space-separated strings). So, for  n  = 3 and the variable ordering  x 3 ,  x 1 ,  x 2 , this line would look as follows:
x3 x1 x2
In the next line the distribution of 0's and 1's over the terminal nodes is given. There will be exactly 2n characters (each of which can be 0 or 1), followed by the new-line character. The characters are given in the order in which they appear in the S-tree, the first character corresponds to the leftmost terminal node of the S-tree, the last one to its rightmost terminal node.
The next line contains a single integer m, the number of VVAs, followed by m lines describing them. Each of the m lines contains exactlyn characters (each of which can be 0 or 1), followed by a new-line character. Regardless of the variable ordering of the S-tree, the first character always describes the value of x1, the second character describes the value of x2, and so on. So, the line
110
corresponds to the VVA ( x1 = 1, x2 = 1, x3 = 0).
The input is terminated by a test case starting with n = 0. This test case should not be processed.
 

Output 

For each S-tree, output the line `` S-Tree # j : ", where  j  is the number of the S-tree. Then print a line that contains the value of  for each of the given  m  VVAs, where  f  is the function defined by the S-tree.
Output a blank line after each test case.
 

Sample Input 

 

3

x1 x2 x3

00000111

4

000

010

111

110

3

x3 x1 x2

00010011

4

000

010

111

110

0

 

Sample Output 

S-Tree #1:

0011



S-Tree #2:

0011

제목 의미: 잎 노드를 제시하고 역행 순서를 제시하며 역행 결과를 구한다. 011에 대해 만약에 차원이 X3, X1, X2이면 역행 순서는 101이다.
문제 풀이 사고방식: 트리 대신 수조로 시뮬레이션하면 된다.

#include<iostream>



using namespace std;

#include<cstdio>



int main()

{

    int n;

    int cas=1;

    int tab[20];

    int terminal[300];

    while(cin>>n,n)

    {

        char order[20];

        for(int i=1;i<=n;i++)

        {

            scanf("%s",order);

            sscanf(&order[1],"%1d",&tab[i]);

        }

        int num=1;

        for(int i=1;i<=n;i++)

            num*=2;

        for(int i=1;i<=num;i++)

            scanf("%1d",&terminal[i]);

        int m;

        scanf("%d",&m);

        string ans;

        for(int i=0;i<m;i++)

        {

            int index=1;

            int step[20];

            for(int j=1;j<=n;j++)

            {

                scanf("%1d",&step[j]);

            }

            for(int j=1;j<=n;j++)

            {

                if(step[tab[j]])

                    index*=2;

                else index=index*2-1;

            }

            ans+=terminal[index]+'0';

            //printf("%d",terminal[index]);

        }

        cout<<"S-Tree #"<<cas++<<":"<<endl;

        cout<<ans<<endl<<endl;

        //printf("
");

    }

}