uva-712 S-Trees

A Strange Tree (S-tree) over the variable set $X_n = \{x_1, x_2, \dots, x_n\}$ is a binary tree representing a Boolean function$f: \{0, 1\}^n \rightarrow \{ 0, 1\}$. 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 $x_{i_1}, x_{i_2}, \dots, x_{i_n}$ 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 $x_1, x_2, \dots, x_n$, then it is quite simple to find out what $f(x_1, x_2, \dots, x_n)$ 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 $x_1 \wedge (x_2 \vee x_3)$

On the picture, two S-trees representing the same Boolean function, $f(x_1, x_2, x_3) = x_1 \wedge (x_2 \vee x_3)$, 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 $x_1, x_2, \dots, x_n$, are given as a Variable Values Assignment (VVA) 

 

\begin{displaymath}(x_1 = b_1, x_2 = b_2, \dots, x_n = b_n)\end{displaymath}

 

 

with  $b_1, b_2, \dots, b_n \in \{0,1\}$ . 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  $f(1, 1, 0) = 1 \wedge (1 \vee 0) = 1$ . 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 $f(x_1, x_2, \dots, x_n)$ 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 ,  $1 \le n \le 7$ , 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 $f(x_1, x_2, \dots, x_n)$  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
题目意思：给出叶子节点，给出遍历顺序，求遍历结果，对于011如果层次为X3,X1,X2则遍历顺序为101；
解题思路：用数组代替建树，模拟即可。
#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("\n");
    }
}


 

posted @ 2013-07-08 14:29  xinyuyuanm  阅读(247)  评论(0)  编辑  收藏  举报