2016/11/10 1003. AVL Tree

最新推荐文章于 2023-11-09 20:44:13 发布

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本文介绍了一种在AVL树中进行节点插入并保持树平衡的方法。通过定义L、R、LR、RL四种旋转操作，确保每次插入新节点后都能通过相应的旋转使树重新达到平衡状态。该实现包括了节点的创建、前序遍历等功能。

边插入边平衡。首先写好L,R,LR,RL的函数，并在每一步插入时更新balance的情况，按balance的情况，调用函数即可平衡。

// Problem#: 19624
// Submission#: 4906418
// The source code is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License
// URI: http://creativecommons.org/licenses/by-nc-sa/3.0/
// All Copyright reserved by Informatic Lab of Sun Yat-sen University
// Problem#: 19624
// Submission#: 4906311
// The source code is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License
// URI: http://creativecommons.org/licenses/by-nc-sa/3.0/
// All Copyright reserved by Informatic Lab of Sun Yat-sen University
#include<iostream>
using namespace std;
struct tree {
    int data;
    int balance;
    tree* left;
    tree* right;
    tree(int e) {
        data=e;
        balance=0;
        left=right=NULL;
    }
};
void preorder(tree*& t) {
    if(t==NULL) return;
    else {
        cout<<t->data<<" ";
        preorder(t->left);
        preorder(t->right);
    }
}
void L(tree* &p) {
    tree* re;
    re=p->right;
    p->right=re->left ;
    re->left=p;
    p=re;
}
void R(tree* &p) {
    tree* re;
    re=p->left;
    p->left=re->right ;
    re->right=p;
    p=re;
}
void LR(tree* &p) {
    tree*& lt=p->left;
    switch(lt->balance) {
        case -1:
            p->balance=0;
            lt->balance=0;
            R(p);
            break;
        case 1: {
            tree* rd=lt->right;
            switch(rd->balance) {
                case -1:
                    p->balance=1;
                    lt->balance=0;
                    break;
                case 0:
                    p->balance=0;
                    lt->balance=0;
                    break;
                case 1:
                    p->balance=0;
                    lt->balance=-1;
                    break;
            }
            rd->balance=0;
            L(lt);
            R(p);
            break;
        }
    }
}
void RL(tree* &p) {
    tree*& rt=p->right;
    switch(rt->balance) {
        case 1:
            p->balance=0;
            rt->balance=0;
            L(p);
            break;
        case -1: {
            tree* rd=rt->left;
            switch(rd->balance) {
                case -1:
                    p->balance=0;
                    rt->balance=1;
                    break;
                case 0:
                    p->balance=0;
                    rt->balance=0;
                    break;
                case 1:
                    p->balance=-1;
                    rt->balance=0;
                    break;
            }
            rd->balance=0;
            R(rt);
            L(p);
            break;
        }
    }
}
void insert(tree* &p,int& n,bool& m) {//m¡À¨º?????¨¨¨º?¡¤?¡À??¡¥
    if(p==NULL) {
        p=new tree(n);
        m=1;
    } else if(n<=p->data) {
        insert(p->left,n,m);
        if(m==1) {
            switch(p->balance) {
                case -1:
                    LR(p);
                    m=false;
                    break;
                case 0:
                    p->balance=-1;
                    break;
                case 1:
                    p->balance=0;
                    m=false;
                    break;
            }
        }
    } else {
        insert(p->right,n,m);
        if(m==1) {
            switch(p->balance) {
                case 1:
                    RL(p);
                    m=false;
                    break;
                case 0:
                    p->balance=1;
                    break;
                case -1:
                    p->balance=0;
                    m=false;
                    break;
            }
        }
    }
}
void deletetree(tree* &p) {
    if(p==NULL) return;
    else {
        deletetree(p->left);
        deletetree(p->right);
        delete p;
    }
}
int main() {
    int t;
    cin>>t;
    while(t--) {
        int n,e;
        cin>>n;
        tree* p=NULL;
        bool m=true;
        for(int i=0 ; i<n ; i++) {
            cin>>e;
            insert(p,e,m);
        }
        preorder(p);
        cout<<endl;
        deletetree(p);
    }
    return 0;
}