A1099. 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

这道题是对前两道题的综合。因为是对权值进行排序，其从小到大顺序正是将BST中序遍历顺序。

输出为层序遍历，所以就用BFS即可。

#include<cstdio>#include<iostream>#include<cstring>#include<algorithm>#include<vector>#include<queue>#include<cmath>using namespace std;const int maxn=110;int v[maxn],num=0;struct node{int data;int lchild,rchild;}node[maxn];void inorder(int root){if(root==-1)return;inorder(node[root].lchild);node[root].data=v[num++];inorder(node[root].rchild);}void BFS(int root){queue<int> q;q.push(root);while(!q.empty()){int id=q.front();q.pop();printf("%d",node[id].data);if(node[id].lchild!=-1)q.push(node[id].lchild);if(node[id].rchild!=-1)q.push(node[id].rchild);if(!q.empty())printf(" ");else printf("\n");}}int main(){//freopen("data.in","r",stdin);int n;scanf("%d",&n);int l,r;for(int i=0;i<n;i++){scanf("%d %d",&l,&r);node[i].lchild=l;node[i].rchild=r;}for(int j=0;j<n;j++){scanf("%d",&v[j]);}sort(v,v+n);inorder(0);BFS(0);return 0;}