PAT1127:ZigZagging on a Tree
1127. 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.
![](http://nos.patest.cn/nc_ol5xekjcdy4.jpg)
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 1Sample 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(); } }