A1086

1086 Tree Traversals Again (25分)

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.

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



#include<bits/stdc++.h>
using namespace std;
struct node{
    node *lchild,*rchild;
    int data;
};
vector<int>preorder,inorder;
node *creat(int preL,int preR,int InL,int InR){
    if(preL>preR)return NULL;
    node *root=new node;
    root->data=preorder[preL];
    int i;
    for(i=InL;i<=InR;i++){
        if(inorder[i]==preorder[preL])break;
    }
    int num=i-InL;
    root->lchild=creat(preL+1,preL+num,InL,i-1);
    root->rchild=creat(preL+num+1,preR,i+1,InR);
    return root;
}
int ok=0;
void postorder(node *root){
    if(root==NULL)return;
    postorder(root->lchild);
    postorder(root->rchild);
    if(ok++)cout<<' ';
    cout<<root->data;
}
int main(){
    stack<int>s;
    string str,push="Push",pop="Pop";
    int N,data,n=0;
    cin>>N;
    while(n!=N){
        scanf("%s",str.c_str());
        if(str.c_str()==push){
            cin>>data;
            preorder.push_back(data);
            s.push(data);
        }
        else if(str.c_str()==pop){
            int x=s.top();
            s.pop();
            inorder.push_back(x);
            n++;
        }
    }
    node *root=creat(0,preorder.size()-1,0,inorder.size()-1);
    postorder(root);
    return 0;
}