由先序中序求后序

PAT  1086

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

题意：输入按照栈的形式，输入先序和中序，输出后序

#include <cstdio>
#include <iostream>
#include <cstring>
#include <stack>
#include <algorithm>
using namespace std;
const int maxn=50;
struct node{
	int data;
	node* ld;
	node* rd;
};
int pre[maxn],in[maxn],post[maxn];
int n;
node* create(int prel,int prer,int inl,int inr)   //由先序中序构建二叉树 
{
	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->ld =create(prel+1,prel+numleft,inl,k-1);
	root->rd =create(prel+numleft+1,prer,k+1,inr);
	return root;
}
int num;
void postorder(node* root)                //后序输出 
{
	if(root==NULL)
	return;
	postorder(root->ld);
	postorder(root->rd);
	printf("%d",root->data);
	num++;
	if(num<n) printf(" ");
}
int main()
{
	scanf("%d",&n);
	char str[5];
	stack<int> st;
	int x,prei=0,ini=0;
	for(int i=0;i<2*n;i++)   //输入处理，把栈转化为先序数组和中序数组 
	{
		scanf("%s",str);
		if(strcmp(str,"Push")==0)
		{
			scanf("%d",&x);
			pre[prei++]=x;
			st.push(x); 
		}
		else
		{
			in[ini++]=st.top();
			st.pop() ; 
		}
	}
	node* root=create(0,n-1,0,n-1);   //构建二叉树 
	postorder(root);                 //后序输出 
	return 0;
}