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 程式師世界 >> 編程語言 >> C語言 >> C++ >> C++入門知識 >> UVA 712 - S-Trees

UVA 712 - S-Trees

編輯:C++入門知識

題目如下:

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 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, andso 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 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 fZ喎?http://www.Bkjia.com/kf/ware/vc/" target="_blank" class="keylink">vciB0aGUgZnVuY3Rpb24gPGltZyBzcmM9"http://www.2cto.com/uploadfile/Collfiles/20140529/20140529092656200.gif" alt="$x_1 \wedge (x_2 \vee x_3)$" align="MIDDLE" border="0" height="34" width="109">

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 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, (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 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 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 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 $f(x_1, x_2, \dots, x_n)$for each of the given m 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

只要把題意搞清楚了這道題還是很簡單的,按照正常思路先建樹再遍歷,直接模擬即可。遍歷的時候遍歷兩次,第一次賦值,第二次得出結果,輸入的時候我是把X忽略,根據X的下標確定每個節點的位置,然後在遍歷賦值的時候就可以根據這個下標給節點賦值。把建樹放在循環中使每次的數據互不干擾。

AC的代碼如下:


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