PAT甲级——A1127 ZigZagging on a Tree【30】

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

首先通过后续遍历和中序遍历重构二叉树
然后在层序遍历的基础上，进行元素逆序

 #include <iostream>
 #include <vector>
 #include <queue>
 #include <algorithm>
 using namespace std;
 struct Node
 {
     int v;
     Node *l, *r;
     Node(int a = -) :v(a), l(nullptr), r(nullptr) {}
 };
 int n;
 vector<int>inOrder, posOrder, zigOrder;
 Node* reCreatTree(int inL, int inR, int posL, int posR)
 {
     if (posL > posR)
         return nullptr;
     Node* root = new Node(posOrder[posR]);
     int k = inL;
     while (k<=inR && inOrder[k] != posOrder[posR])++k;//找到根节点
     int numL = k - inL;//左子树节点个数
     root->l = reCreatTree(inL, k - , posL, posL + numL - );
     root->r = reCreatTree(k + , inR, posL + numL, posR - );
     return root;
 }
 void zigOrderTravel(Node* root)
 {
     if (root == nullptr)
         return;
     queue<Node*>q;
     q.push(root);
     zigOrder.push_back(root->v);
     bool flag = false;
     while (!q.empty())
     {
         queue<Node*>temp;
         vector<int>tt;
         while (!q.empty())
         {
             Node* p = q.front();
             q.pop();
             if (p->l != nullptr)
             {
                 temp.push(p->l);
                 tt.push_back(p->l->v);
             }
             if (p->r != nullptr)
             {
                 temp.push(p->r);
                 tt.push_back(p->r->v);
             }
         }
         if (flag)
             reverse(tt.begin(), tt.end());
         zigOrder.insert(zigOrder.end(), tt.begin(), tt.end());
         flag = !flag;
         q = temp;
     }
 }
 int main()
 {
     cin >> n;
     inOrder.resize(n);
     posOrder.resize(n);
     for (int i = ; i < n; ++i)
         cin >> inOrder[i];
     for (int i = ; i < n; ++i)
         cin >> posOrder[i];
     Node* root = reCreatTree(, n - , , n - );
     zigOrderTravel(root);
     for (int i = ; i < zigOrder.size(); ++i)
         cout << (i >  ? " " : "") << zigOrder[i];
     return ;
 }