1086. Tree Traversals Again (树的遍历,前序中序转后序)
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.
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
题目大意:用栈的形式给出一棵二叉树的建立的顺序,求这棵二叉树的后序遍历
需要一个堆结构s,一个child变量(表示该节点是其父亲节点的左孩子还是右孩子),父亲节点fa
对于push v操作:
1).第一个push肯定是根节点root。
2).根据child变量,建立fa与v的父子关系。
3).由于是中序遍历,所以接下来的节点必定是v的left(如果有的话),child=left,fa=v;
4).然后进行push操作
对于pop操作:
1).根据中序遍历性质,可知接下来的节点必定是pop节点的右孩子(如果有的话),child=right,fa=s.top()
2).进行pop操作。
#include<iostream>
#include<algorithm>
#include<string.h>
#include<stack>
#define LEFT 0
#define RIGHT 1
#define maxn 100
using namespace std;
stack<int> s;
//着重注意这题考查的是"建树"的技巧
struct NODE
{
int left=-1;
int right=-1;
}node[maxn];
bool first=true;
void postOrder(int u){//虽然建树时是按中序建的树
if(u==-1) //但是按后序扫的
return;
postOrder(node[u].left);
postOrder(node[u].right);
if(first){
first=false;
printf("%d",u);
}
else{
printf(" %d",u);
}
}
int main()
{
int n,v;
int root=-1,fa;
//fa是为了记录当前结点
//以便把各个node结点相连
int child=LEFT;
//child变量记录的是,
//当前父节点往左走,还是往右走
char str[10];
scanf("%d",&n);
while(scanf("%s",str)!=EOF)
{
if(strcmp(str,"Push")==0)
{
scanf("%d",&v);
if(root==-1)//为这棵树找根节点,入口
root=v;
else
{
if(child==LEFT)
node[fa].left=v;
else node[fa].right=v;
}
fa=v;//更新父节点
child=LEFT;
s.push(v);
}//对于入栈的操作,
//由于是中序,新节点优先进左子树
else//出栈后在改变方向,
//再次push时向右子树push
{
child=RIGHT;
fa=s.top();
s.pop();
}
}
postOrder(root);
return 0;
}