1086 Tree Traversals Again (25point(s))
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
#include<bits/stdc++.h>
using namespace std;
const int maxn=35;
struct node{
int data;
node *lchild,*rchild;
};
int pre[maxn],in[maxn];
node* create(int preL,int preR,int inL,int inR){
if(preL>preR) return NULL;
node* root=new node;
root->data=pre[preL];
int k;
for(k=inL;k<=inR;++k)
if(in[k]==pre[preL]) break;
int numLeft=k-inL;
root->lchild=create(preL+1,preL+numLeft,inL,k-1);
root->rchild=create(preL+numLeft+1,preR,k+1,inR);
return root;
}
int num=0;
void postOrder(node *root){
if(!root) return;
postOrder(root->lchild);
postOrder(root->rchild);
if(num!=0) printf(" ");
num++;
printf("%d",root->data);
}
int main(){
int n;
scanf("%d",&n);
stack<int> s;
int j=0,k=0;
string str;
int index;
for(int i=0;i<2*n;++i){
cin>>str;
if(str=="Push"){
scanf("%d",&index);
pre[j++]=index;
s.push(index);
}else{
in[k++]=s.top();
s.pop();
}
}
node* root=create(0,n-1,0,n-1);
postOrder(root);
}