03-树3 Tree Traversals Again (25分)
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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 NN (\le 30≤30) which is the total number of nodes in a tree (and hence the nodes are numbered from 1 to NN). Then 2N2N 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
AC代码:
#include <iostream>using namespace std;struct Node{ int tag; //第几次进栈 int num;};/*先序遍历对应进栈顺序,中序遍历对应出栈顺序; 后序遍历与中序遍历不同的是节点出栈后要马上再入栈(tag做第二次入栈标记),等右儿子遍历完后再出栈; 具体实现上,每次中序遍历的pop时,如果栈顶是标记过的节点(tag=2),循环弹出;如果没有标记过(tag=1),做标记,即弹出再压栈) 栈顶tag=2的节点对应中序遍历中已弹出的节点;循环弹出后碰到的第一个tag=1的节点才对应中序遍历当前pop的节点 */int main(){ int N; cin>>N; struct Node stack[30]; int flag = 0; int size = 0; //栈元素大小,指向栈顶的下一个位置 for ( int i = 0 ; i < 2*N ; i++){ string str; cin>>str; if(str[1] == 'u'){ cin>>stack[size].num; //入栈 stack[size].tag = 1; //标记第一次入栈 size++; }else{ //循环弹出栈顶tag=2的节点 while(size > 0 && stack[size-1].tag == 2){ if( flag){ cout<<" "; } flag = 1; cout<<stack[--size].num; } //将中序遍历中应该要弹出的节点弹出再压栈,做标记即可 if ( size>0){ stack[size-1].tag = 2; } } } while(size){ if ( flag ){ cout<<" "; } flag = 1; cout<<stack[--size].num; } return 0;}
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