An inorder binary tree traversal can be implemented in a non-recursive way with a stack. For example, suppose that when a 6-node binary tree (with the keys numbered from 1 to 6) is traversed, the stack operations are: push(1); push(2); push(3); pop(); pop(); push(4); pop(); pop(); push(5); push(6); pop(); pop(). Then a unique binary tree (shown in Figure 1) can be generated from this sequence of operations. Your task is to give the postorder traversal sequence of this tree.
Figure 1
Input Specification:
Each input file contains one test case. For each case, the first line contains a positive integer N (≤30) which is the total number of nodes in a tree (and hence the nodes are numbered from 1 to N). Then 2N lines follow, each describes a stack operation in the format: "Push X" where X is the index of the node being pushed onto the stack; or "Pop" meaning to pop one node from the stack.
Output Specification:
For each test case, print the postorder traversal sequence of the corresponding tree in one line. A solution is guaranteed to exist. All the numbers must be separated by exactly one space, and there must be no extra space at the end of the line.
Sample Input:
6
Push 1
Push 2
Push 3
Pop
Pop
Push 4
Pop
Pop
Push 5
Push 6
Pop
Pop
Sample Output:
3 4 2 6 5 1
思路:
题中给出了先序和中序遍历序列,可以唯一确定一颗树,所以首先可以进行建立树,然后后序遍历即可。
#include<iostream> #include<vector> #include<algorithm> #include<queue> #include<string> #include<map> #include<set> #include<stack> using namespace std; vector<int> po; struct Node { int data; Node *lchild=nullptr; Node *rchild=nullptr; }; void createTree(Node *&root,vector<int>preOrder,int pl,int pr, vector<int>inOrder,int il,int ir) { if(root==nullptr) { root=new Node; root->data=preOrder[pl]; } int index=0; while(inOrder[index]!=preOrder[pl]) index++; int len=index-il; int rlen=ir-index; if(len>0) createTree(root->lchild,preOrder,pl+1,pr-rlen,inOrder,il,index-1); if(rlen>0) createTree(root->rchild,preOrder,pr-rlen+1,pr,inOrder,index+1,ir); } vector<int> print; void postOrder(Node *root) { if(!root) return; postOrder(root->lchild); postOrder(root->rchild); print.push_back(root->data); } int main() { int n; cin>>n; vector<int>inOrder; vector<int>preOrder; stack<int> st; string str; int temp; for(int i=0;i<2*n;i++) { cin>>str; if(str=="Push") { cin>>temp; preOrder.push_back(temp); st.push(temp); } else { temp=st.top(); st.pop(); inOrder.push_back(temp); } } Node *root=nullptr; createTree(root,preOrder,0,preOrder.size()-1,inOrder,0,inOrder.size()-1); postOrder(root); cout<<print[0]; for(int i=1;i<print.size();i++) cout<<" "<<print[i]; return 0; }