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UVA 712 - S-Trees

2024-07-06 13:45:42   229人阅读

题目如下：

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 theroot node and consists of n+1 nodes. Each of the S-tree‘s nodes has adepth, which is the amount of nodes between itself and the root (so the root has depth 0). The nodes with depth less thann are called non-terminal nodes. All non-terminal nodes have two children: theright child and the left child. Each non-terminal node is marked with some variablexi 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 variablexi2 corresponding to the nodes with depth 1, andso on. The sequence of the variables$x_{i_1}, x_{i_2}, \dots, x_{i_n}$is called thevariable 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 variablexi, 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 isx3, x1,x2.

The values of the variables $x_1, x_2, \dots, x_n$,are given as aVariable 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, (x1 = 1,x2 = 1 x3 = 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 integern, $1 \le n \le 7$,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 xi1 xi2 ...xin. (There will be exactlyn different space-separated strings).So, for n = 3 and the variable orderingx3, 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 bym lines 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 ofx1, 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 givenm VVAs, where f is thefunction 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

只要把题意搞清楚了这道题还是很简单的，按照正常思路先建树再遍历，直接模拟即可。遍历的时候遍历两次，第一次赋值，第二次得出结果，输入的时候我是把X忽略，根据X的下标确定每个节点的位置，然后在遍历赋值的时候就可以根据这个下标给节点赋值。把建树放在循环中使每次的数据互不干扰。

AC的代码如下：

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