uva 712-S-Trees

  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 callednon-terminal nodes. All non-terminal nodes have two children: the right childand the left child. Each non-terminal node is marked with some variable x_ifrom the variable set X_n. 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 x_i1corresponding to the root, a unique variable x_i2 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 terminalnodes. 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 x_i, 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, ( x₁ = 1, x₂ = 1 x₃ = 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 xi₁ xi₂ ...xi_n. (There will be exactly n different space-separated strings). So, for n = 3 and the variable ordering x₃, x₁, x₂, 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 mlines describing them. Each of the m lines contains exactly n 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 

3x1 x2 x30000011140000101111103x3 x1 x20001001140000101111100

Sample Output 

S-Tree #1:0011S-Tree #2:0011

  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 callednon-terminal nodes. All non-terminal nodes have two children: the right childand the left child. Each non-terminal node is marked with some variable x_ifrom the variable set X_n. 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 x_i1corresponding to the root, a unique variable x_i2 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 terminalnodes. 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 x_i, 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, ( x₁ = 1, x₂ = 1 x₃ = 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 xi₁ xi₂ ...xi_n. (There will be exactly n different space-separated strings). So, for n = 3 and the variable ordering x₃, x₁, x₂, 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 mlines describing them. Each of the m lines contains exactly n 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 

3x1 x2 x30000011140000101111103x3 x1 x20001001140000101111100

Sample Output 

S-Tree #1:0011S-Tree #2:0011

题目大概意思就是有一个二叉树，他每一层的值有xi决定，然后xi只能为1或者0，为1代表向右儿子走，0代表左儿子，让你求出最终到达底层叶节点的值为1或者0，输出答案即可，那么这样一来我值关心最后终点的位置，不用建树直接根据二叉树特点罗列数学表达式即可计算最后走向，具体代码如下：

#include<stdio.h>#include<stdlib.h>int main(){    int n,m,x1,x2,x3,pos,hash[150],ans[100000],kase=0;    char ch,s[7],str[300];    while(scanf("%d",&n)==1&&n){        getchar();        for(int i=0;i<n;i++)scanf("%c%c ",&ch,&s[i]);        scanf("%s",&str);        scanf("%d",&m);        for(int j=1;j<=m;j++){         for(int i=1;i<=n;i++)scanf("%1d",&hash[('0'+i)]);             pos=1;             for(int i=0;i<n;i++)pos=pos*2-(1-hash[s[i]]);//计算最终走向              ans[j]=str[pos-1]-48;        }        printf("S-Tree #%d:\n",++kase);        for(int i=1;i<=m;i++)printf("%d",ans[i]);        printf("\n\n");    }    return 0;}