【PAT】1099. Build A Binary Search Tree (30)

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

The left subtree of a node contains only nodes with keys less than the node's key.

The right subtree of a node contains only nodes with keys greater than or equal to the node's key.

Both the left and right subtrees must also be binary search trees.

Given the structure of a binary tree and a sequence of distinct integer keys, there is only one way to fill these keys into the tree so that the resulting tree satisfies the definition of a BST. You are supposed to output the level order traversal sequence of that tree. The sample is illustrated by Figure 1 and 2.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (<=100) which is the total number of nodes in the tree. The next N lines each contains the left and the right children of a node in the format "left_index right_index", provided that the nodes are numbered from 0 to N-1, and 0 is always the root. If one child is missing, then -1 will represent the NULL child pointer. Finally N distinct integer keys are given in the last line.

Output Specification:

For each test case, print in one line the level order traversal sequence of that tree. All the numbers must be separated by a space, with no extra space at the end of the line.

Sample Input:

91 62 3-1 -1-1 45 -1-1 -17 -1-1 8-1 -173 45 11 58 82 25 67 38 42

Sample Output:

58 25 82 11 38 67 45 73 42

分析：

（1）给出“固定结构”的二叉搜索树，然后给出树中的数组，要求还原这棵树；

（2）将数组从小到大排列正好是二叉搜索树的中序遍历结果，因此可以借此来还原整棵树；

（3）树还原之后，就可以利用队列轻松的进行层序遍历了；

这道题目关键还是在于上述的第二点。

正确代码如下：

#include <iostream>#include <vector>#include <algorithm>#include <queue>using namespace std;vector<int> val;int index = 0;struct node{int val;int left; int right;};bool cmp(int a, int b){return a<b;}vector<node> tree;bool inOrder(node& root){if(root.left != -1){inOrder( tree[root.left] );}root.val = val[index++];if(root.right != -1){inOrder(tree[root.right]);}}bool  levelOrder(node root){queue<node> que;que.push(root);bool isFirst = true;while(!que.empty()){   node t = que.front();   if(isFirst){      cout<<t.val;      isFirst = false;   }else{   cout<<" "<<t.val;   }   if(t.left != -1){     que.push(tree[t.left]);   }   if(t.right!=-1){      que.push(tree[t.right]);   }   que.pop();   }cout<<endl;}int main(){int n, i;scanf("%d",&n);tree.resize(n);for(i=0; i<n; i++){scanf("%d%d",&tree[i].left,&tree[i].right);}val.resize(n);for(i=0; i<n; i++){scanf("%d",&val[i]);}sort(val.begin(), val.end(), cmp);inOrder(tree[0]);levelOrder(tree[0]);return 0;}