Suppose that all the keys in a binary tree are distinct positive integers. A unique binary tree can be determined by a given pair of postorder and inorder traversal sequences. And it is a simple standard routine to print the numbers in level-order. However, if you think the problem is too simple, then you are too naive. This time you are supposed to print the numbers in "zigzagging order" -- that is, starting from the root, print the numbers level-by-level, alternating between left to right and right to left. For example, for the following tree you must output: 1 11 5 8 17 12 20 15.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (<= 30), the total number of nodes in the binary tree. The second line gives the inorder sequence and the third line gives the postorder sequence. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the zigzagging sequence of the tree in a line. All the numbers in a line must be separated by exactly one space, and there must be no extra space at the end of the line.

Sample Input:

8

12 11 20 17 1 15 8 5

12 20 17 11 15 8 5 1

Sample Output:

1 11 5 8 17 12 20 15

思路

类似Pat1029，根据中序遍历和后序遍历序列确定树，以层次遍历的形式存入vector<vector<int>>中，然后按每一层往返输出就行。

代码

#include<iostream>

#include<vector>

#include<queue>

using namespace std;

vector<int> postorder(31);

vector<int> inorder(31);

vector<vector<int>> levels(31);

void buildTree(const int pl,const int pr,const int il,const int ir,const int level)

{

    if(pl > pr || il > ir)

        return;

    int root = postorder[pr],i = 0;

    while( inorder[il + i ] !=  root) i++;

    levels[level].push_back(root);

    buildTree(pl,pl + i - 1,il,il + i - 1,level + 1);

    buildTree(pl + i ,pr - 1,il + i + 1,ir,level + 1);

}

void zigzag()

{

    cout << levels[0][0];

    bool zigzag = false;

    for(int i = 1; i < levels.size() && !levels[i].empty();i++)

    {

        if(zigzag)

        {

            for(int j = levels[i].size() - 1;j >= 0;j--)

            {

                cout << " " << levels[i][j];

            }

        }

        else

        {

           for(int j = 0;j < levels[i].size();j++)

           {

               cout << " " << levels[i][j];

           }

        }

        zigzag = !zigzag;

    }

}

int main()

{

    int N;

    while(cin >> N)

    {

       for(int i = 0;i < N;i++)

         cin >> inorder[i];

       for(int i = 0;i < N;i++)

         cin >> postorder[i];

       buildTree(0,N - 1,0, N - 1,0);

       zigzag();

    }

}