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
#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");
}
}