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
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.
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 <queue>
#include <stack>
#include <cstring>
using namespace std;
struct node {
int data;
node* lchild;
node* rchild;
};
int n, num = 0;
int pre[51], post[51], in[51];
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;
}
void preTrave(node* root) {
if (root == NULL) return ;
preTrave(root->lchild);
preTrave(root->rchild);
printf("%d", root->data);
num++;
if (num < n) printf(" ");
}
int main() {
char str[10];
stack<int> s;
int prei = 0, ini = 0;
scanf("%d", &n);
while (scanf("%s", str) != EOF) {
int temp;
if (strcmp(str, "Push") == 0) {
scanf("%d", &temp);
pre[prei++] = temp;
s.push(temp);
}
else if (strcmp(str, "Pop") == 0) {
in[ini++] = s.top();
s.pop();
}
}
while (!s.empty()) {
in[ini++] = s.top();
s.pop();
}
node* root = create(0, n -1, 0, n - 1);
preTrave(root);
return 0;
}
