uva-712 S-Trees

最新推荐文章于 2021-03-12 18:47:57 发布

ultimater

最新推荐文章于 2021-03-12 18:47:57 发布

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本文介绍了一种特殊的二叉树——S-树，并详细解释了如何通过给定的叶子节点标记和遍历顺序来确定遍历结果。通过具体的样例展示了如何使用数组模拟S-树的构建过程及遍历算法。

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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 x_i from 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_i₁ corresponding to the root, a unique variable x_i₂ corresponding to the nodes with depth 1, and so 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 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 $x_1 \wedge (x_2 \vee x_3)$

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 is x₃, 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 ...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 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 $f(x_1, x_2, \dots, x_n)$ 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

Sample Output

S-Tree #1:
0011

S-Tree #2:
0011

题目意思：给出叶子节点，给出遍历顺序，求遍历结果，对于011如果层次为X3,X1,X2则遍历顺序为101；

解题思路：用数组代替建树，模拟即可。

#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");
    }
}