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
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, ( 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 ...xin.
(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 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

题意：输入n代表树有n层 接着输入xi代表每层的名字。。然后输入一串代表叶子节点。
然后输入一个k，接下来输入k个串，代表遍历顺序。。0往左，1往右。

这题直接用数组模拟就可以了。。存下叶子节点。

然后根据遍历顺序。遇到1就在叶子节点往右移动 2 ^(总层数 - 当前层数) 个位置。。

然后逐个输出就可以了。。

#include <stdio.h>
#include <string.h>
#include <math.h>
int n;
int m;
int i;
int x[10];
char dd[10];
int d[10];
char ddi[205];
int di[205];
int main()
{
int tt = 1;
while (scanf("%d", &n) != EOF && n)
{
getchar();
for (i = 1; i <= n ; i++)
{
int sbb;
scanf("%*c%d%*c", &sbb);
x[sbb] = i;
}
gets(ddi);
int lenddi = strlen(ddi);
for (i = 1; i <= lenddi; i ++)
di[i] = ddi[i - 1] - '0';
printf("S-Tree #%d:\n", tt ++);
scanf("%d", &m);
getchar();
while (m --)
{
gets(dd);
memset(d, 0, sizeof(0));
int lendd = strlen(dd);
for (i = 1; i <= lendd; i ++)
{
d[x[i]] = dd[i - 1] - '0';
}
int sb = 1;
for (i = n; i >= 1; i --)
{
if (d[i] == 1)
{
sb += int(pow(2, n - i) + 0.5);
}
}
printf("%d", di[sb]);
}
printf("\n\n");
}
return 0;
}