1064 Complete Binary Search Tree (30分)
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.
A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.
Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.
Each input file contains one test case. For each case, the first line contains a positive integer N (≤1000). Then N distinct non-negative integer keys are given in the next line. All the numbers in a line are separated by a space and are no greater than 2000.
For each test case, print in one line the level order traversal sequence of the corresponding complete binary search tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.
解题思路：先按层序遍历建一课空的完全二叉树，然后将输入序列从小到大排序，之后按中序遍历依次将已排好序的序列插入建好的空树中，最后层序遍历建好的树。
#include<iostream> #include<queue> #include<algorithm> #define Null -1 using namespace std; struct node{ int val; struct node *left, *right; int flag = 0; }; node *nodeTemp; int nodeFlag = 0; node *newNode(int v){ node *root = new node(); root->val = v; root->left = root->right = NULL; return root; } void findNode(node *root){ if(root->left){ findNode(root->left); } if(!nodeFlag){ if((root->left == NULL && root->val == Null) || (root->left != NULL && root->val == Null)){ nodeTemp = root; nodeFlag = 1; return; } } if(root->right){ findNode(root->right); } } void insert(node *root, int v){ nodeFlag = 0; findNode(root); nodeTemp->val = v; } node *makeTree(int n){ node *root = newNode(Null); queue<node*> q; q.push(root); for(int i = 1; i < n; i++){ node *temp; temp = q.front(); temp->left = newNode(Null); q.pop(); q.push(temp->left); i++; if(i >= n){ break; } temp->right = newNode(Null); q.push(temp->right); } return root; } void levelTravel(node *root){ queue<node*> q; q.push(root); printf("%d", root->val); if(root->left){ q.push(root->left); } if(root->right){ q.push(root->right); } q.pop(); while(!q.empty()){ node *temp = q.front(); printf(" %d", temp->val); if(temp->left){ q.push(temp->left); } if(temp->right){ q.push(temp->right); } q.pop(); } } int main(){ int n, val; int a[1005]; scanf("%d", &n); //建树 node *root = makeTree(n); //填入值 for(int i = 0; i < n; i++){ scanf("%d", &a[i]); } sort(a, a + n); for(int i = 0; i < n; i++){ insert(root, a[i]); } //层序遍历输出 levelTravel(root); return 0; }
