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 or equal to the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- Both the left and right subtrees must also be binary search trees.
Insert a sequence of numbers into an initially empty binary search tree. Then you are supposed to count the total number of nodes in the lowest 2 levels of the resulting tree.
Input Specification:
Each input file contains one test case. For each case, the first line gives a positive integer N (<=1000) which is the size of the input sequence. Then given in the next line are the N integers in [-1000 1000] which are supposed to be inserted into an initially empty binary search tree.
Output Specification:
For each case, print in one line the numbers of nodes in the lowest 2 levels of the resulting tree in the format:
n1 + n2 = n
where n1 is the number of nodes in the lowest level, n2 is that of the level above, and n is the sum.
Sample Input:
9 25 30 42 16 20 20 35 -5 28
Sample Output:
2 + 4 = 6
1 #include<cstdio> 2 #include<iostream> 3 #include<algorithm> 4 #include<string> 5 #include<queue> 6 using namespace std; 7 typedef struct NODE{ 8 struct NODE *lchild, *rchild; 9 int data; 10 int level; 11 }node; 12 void insert(node* &root, int x){ 13 if(root == NULL){ 14 node* temp = new node; 15 temp->lchild = NULL; 16 temp->rchild = NULL; 17 temp->data = x; 18 root = temp; 19 return; 20 } 21 if(x <= root->data) 22 insert(root->lchild, x); 23 else insert(root->rchild, x); 24 } 25 int depth = 0, n1, n2; 26 void levelOrder(node* root){ 27 queue<node*> Q; 28 root->level = 1; 29 Q.push(root); 30 while(Q.empty() == false){ 31 node* temp = Q.front(); 32 depth = temp->level; 33 Q.pop(); 34 if(temp->lchild != NULL){ 35 temp->lchild->level = temp->level + 1; 36 Q.push(temp->lchild); 37 } 38 if(temp->rchild != NULL){ 39 temp->rchild->level = temp->level + 1; 40 Q.push(temp->rchild); 41 } 42 } 43 } 44 void DFS(node * root){ 45 if(root == NULL) 46 return; 47 if(root->level == depth) 48 n1++; 49 else if(root->level == depth -1) 50 n2++; 51 DFS(root->lchild); 52 DFS(root->rchild); 53 } 54 int main(){ 55 int N, temp; 56 node* root = NULL; 57 scanf("%d", &N); 58 for(int i = 0; i < N; i++){ 59 scanf("%d", &temp); 60 insert(root, temp); 61 } 62 levelOrder(root); 63 DFS(root); 64 printf("%d + %d = %d", n1, n2, n1 + n2); 65 cin >> N; 66 return 0; 67 }
总结：
1、注意最下面两层，和叶节点+叶节点上一层节点个数是不一样的。