1099. Build A Binary Search Tree (30)

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:

  9
  1 6
  2 3
  -1 -1
  -1 4
  5 -1
  -1 -1
  7 -1
  -1 8
  -1 -1
  73 45 11 58 82 25 67 38 42
  

  Sample Output:

  58 25 82 11 38 67 45 73 42

• 【自己写的没有AC的代码】

• 我的想法比较暴力：先序建树；数组排序；中序填数；层序输出

• #include <iostream>
  using namespace std;
  #include <vector>
  #include <algorithm>
  #include <queue>
  vector<int> arr;//值组
  int n;
  int value;//赋值时用
  int i;
  struct Node{
  	int data;
  	int lchild;
  	int rchild;
  };
  typedef struct Node Node;
  void PreOrderTravel(Node* bst,int index){
  	if(index!=-1){
  		cin>>bst[index].lchild>>bst[index].rchild;
  		PreOrderTravel(bst,bst[index].lchild);
  		PreOrderTravel(bst,bst[index].rchild);
  	}else return;
  }
  void InOrderTravel(Node* bst,int index){
  	if(bst[index].lchild!=-1){//左到头
  		InOrderTravel(bst,bst[index].lchild);
  	}
  	bst[index].data=arr[value++];
  	if(bst[index].rchild!=-1){
  		InOrderTravel(bst,bst[index].rchild);
  	}
  }
  
  void LevelOrderTravel(Node* bst){
  	queue<Node> q;
  	Node node=bst[0];
  	q.push(node);
  	while(!q.empty()){
  		node=q.front();
  		q.pop();
  		cout<<node.data;
  		if(++i!=n){
  			cout<<" ";
  		}
  		if(node.lchild!=-1){
  			q.push(bst[node.lchild]);
  		}
  		if(node.rchild!=-1){
  			q.push(bst[node.rchild]);
  		}
  	}
  
  }
  int main(){
  	cin>>n;
  	Node* bst=new Node[n];//顺序表存储
  	PreOrderTravel(bst,0);//先序建树
  	int a;
  	for(int i=0;i<n;i++){
  		cin>>a;
  		arr.push_back(a);
  	}
  	sort(arr.begin(),arr.end());//对数进行排序
  	value=0;
  	InOrderTravel(bst,0);//中序填数
  	i=0;
  	LevelOrderTravel(bst);//层序输出
  	system("pause");
  
  }

• 测试点

  测试点	结果	用时(ms)	内存(kB)	得分/满分
  0	答案正确	3	384	18/18
  1	答案错误	3	384	0/3
  2	答案正确	2	384	3/3
  3	答案正确	2	384	1/1
  4	答案错误	3	384	0/5

• 【据说AC的代码】
  

  #include <iostream>
  #include <algorithm>
  #include <queue>
  using namespace std;
  
  
  int Left[105];
  int Right[105];
  int a[105];
  int b[105];
  
  
  void DFS(int now ,int &x){
      if(now < 0)
          return;
      DFS(Left[now],x);
      b[now] = a[x++];
      DFS(Right[now],x);
  }
  
  int main(){
      int N ;
      cin >> N;
      for(int i = 0; i < N ; i ++){
          cin >> Left[i] >> Right[i];
      }
      for(int i = 0; i < N ; i ++){
          cin >> a[i];
      }
      sort(a,a+N);
      int n = 0;
      DFS(0,n);
      queue<int> q;
      q.push(0);
      vector<int> answer;
      while(!q.empty()){
          int node = q.front();
          q.pop();
          answer.push_back(b[node]);
          if(Left[node] != -1) q.push(Left[node]);
          if(Right[node] != -1) q.push(Right[node]);
      }
      for(int i = 0; i < answer.size(); i ++){
          cout << answer[i] << (i == answer.size() - 1?"":" ");
      }
      return 0;
  }