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 "iostream"
#include "string"
#include "string.h"
#include "stack"
using namespace std;
struct node{
int data;
node* lchild;
node* rchild;
};
const int maxn=50;
int n;
int pre[maxn];
int 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]==root->data) {
break;
}
}
int num=k-inL;
root->lchild=create(preL+1, preL+num, inL, k-1);
root->rchild=create(preL+num+1, preR, k+1, inR);
return root;
}
int number=0;
void POT(node* root){
if (root->lchild!=NULL) {
POT(root->lchild);
}
if (root->rchild!=NULL) {
POT(root->rchild);
}
printf("%d",root->data);
number++;
if (number<n) {
printf(" ");
}
}
int main(){
scanf("%d",&n);
char s[5];
stack<int> temp;
int x=0,preIndex=0,inIndex=0;
for (int i=0; i<n*2; i++) {
scanf("%s",s);
if (strcmp(s,"Push")==0) {
scanf("%d",&x);
pre[preIndex++]=x;
temp.push(x);
}
else{
in[inIndex++]=temp.top();
temp.pop();
}
}
node* root=create(0, n-1, 0, n-1);
POT(root);
}
