PAT 甲级 1086. Tree Traversals Again (25)

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:

6Push 1Push 2Push 3PopPopPush 4PopPopPush 5Push 6PopPop

Sample Output:

3 4 2 6 5 1

#include <algorithm>#include <stack>#include <cstring>#include <iostream>#include <vector>using namespace std;vector<int> pre, in, post;void postorder(int root, int start, int end) {if (start > end) return;int i = start;while (i < end && in[i] != pre[root]) i++;postorder(root + 1, start, i - 1);postorder(root + 1 + i - start, i + 1, end);post.push_back(pre[root]);}int main() {int n;scanf("%d", &n);char str[5];stack<int> s;while (~scanf("%s", str)) {if (strlen(str) == 4) {int num;scanf("%d", &num);pre.push_back(num);s.push(num);}else {in.push_back(s.top());s.pop();}}postorder(0, 0, n - 1);printf("%d", post[0]);for (int i = 1; i < n; i++)printf(" %d", post[i]);cin >> n;return 0;}