技術標籤：PAT甲級

A 1123 Is It a Complete AVL Tree

題目連結

Problem Description

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

Now given a sequence of insertions, you are supposed to output the level-order traversal sequence of the resulting AVL tree, and to tell if it is a complete binary tree.

Input

Each input file contains one test case. For each case, the first line contains a positive integer N (≤ 20). Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output

For each test case, insert the keys one by one into an initially empty AVL tree. Then first print in a line the level-order traversal sequence of the resulting AVL 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. Then in the next line, print YES

Sample Input 1:

5
88 70 61 63 65

Sample Output 1:

70 63 88 61 65
YES

Sample Input 2:

8
88 70 61 96 120 90 65 68

Sample Output 2:

88 65 96 61 70 90 120 68
NO

AC程式碼
程式碼實現參照《演算法筆記》

#include<bits/stdc++.h>
using namespace std;
const int maxn = 25;
int level[maxn],n,key,ind=0,isComplete=1,flag=0;
struct node{
    int v,h;
    node* l;
    node* r;
};
node* newnode(int x){
    node* root = new node;
    root->v=x;
    root->h=1;
    root->l=root->r=NULL;
    return root;
}
int getHeight(node* root){
    if(root==NULL) return 0;
    return root->h;
}
int getBalanceFactor(node* root){
    return getHeight(root->l)-getHeight(root->r);
}
void updataHeight(node* root){
    root->h=max(getHeight(root->l),getHeight(root->r))+1;
}
void L(node* &root){
    node* temp = root->r;
    root->r=temp->l;
    temp->l=root;
    updataHeight(root);
    updataHeight(temp);
    root=temp;
}
void R(node* &root){
    node* temp = root->l;
    root->l=temp->r;
    temp->r=root;
    updataHeight(root);
    updataHeight(temp);
    root=temp;
}
void insert(node* &root,int x){
    if(root==NULL){
        root=newnode(x);
        return ;
    }
    if(x<root->v){
        insert(root->l,x);
        updataHeight(root);
        if(getBalanceFactor(root)==2){
            if(getBalanceFactor(root->l)==1){
                R(root);
            }else if(getBalanceFactor(root->l)==-1){
                L(root->l);
                R(root);
            }
        }
    }else{
        insert(root->r,x);
        updataHeight(root);
        if(getBalanceFactor(root)==-2){
            if(getBalanceFactor(root->r)==-1){
                L(root);
            }else if(getBalanceFactor(root->r)==1){
                R(root->r);
                L(root);
            }
        }
    }
}
void bfs(node* root){
    queue<node*>q;
    q.push(root);
    while(!q.empty()){
        node* now=q.front();
        q.pop();
        level[ind++]=now->v;
        if(now->l!=NULL){
            if(flag) isComplete=0;
            q.push(now->l);
        }else{
            flag=1;
        }
        if(now->r!=NULL){
            if(flag) isComplete=0;
            q.push(now->r);
        }else{
            flag=1;
        }
    }
}
int main(){
    scanf("%d",&n);
    node* root=NULL;
    for(int i=0;i<n;i++){
        scanf("%d",&key);
        insert(root,key);
    }
    bfs(root);
    for(int i=0;i<ind;i++){
        if(i>0) printf(" ");
        printf("%d",level[i]);
    }
    printf("\n%s",isComplete ? "YES" : "NO");
    return 0;
}