P1090 [NOIP2004 提高组] 合并果子 / [USACO06NOV] Fence Repair G AVL题解

P1090 [NOIP2004 提高组] 合并果子 / [USACO06NOV] Fence Repair G

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#include<bits/stdc++.h>
using namespace std;
typedef struct AVLTreeNode{
    int key;
    int height;
    AVLTreeNode* left;
    AVLTreeNode* right;
    AVLTreeNode(int val,AVLTreeNode* l,AVLTreeNode* r):
        key(val),height(0),left(l),right(r){
        }
}AVLTreeNode;
int height(AVLTreeNode* tree)
{
    if (tree!=NULL)
    {
        return tree->height;
    }
    return 0;
}
//LL型 右旋 
AVLTreeNode* leftLeftRotation(AVLTreeNode* k2)
{
    AVLTreeNode* k1;
    k1=k2->left;
    k2->left=k1->right;
    k1->right=k2;
    k2->height=max(height(k2->left),height(k2->right))+1;
    k1->height=max(height(k1->left),k2->height)+1;
    return k1;
}
//RR型 左旋
AVLTreeNode* rightRightRotation(AVLTreeNode* k1)
{
    AVLTreeNode* k2;
    k2=k1->right;
    k1->right=k2->left;
    k2->left=k1;
    k1->height=max(height(k1->left),height(k1->right))+1;
    k2->height=max(height(k2->right),k1->height)+1;
    return k2;  
}
//LR型 双旋 先左旋再右旋
AVLTreeNode* leftRightRotation(AVLTreeNode* k3)
{
    k3->left=rightRightRotation(k3->left);
    return leftLeftRotation(k3);    
} 
//RL型 双旋 先右旋再左旋
AVLTreeNode* rightLeftRotation(AVLTreeNode* k1)
{
    k1->right=leftLeftRotation(k1->right);
    return rightRightRotation(k1);  
}
//插入
void Insert(AVLTreeNode* &tree,int key)
{
    if (tree==NULL)
    {
        tree=new AVLTreeNode(key,NULL,NULL);
    }
    else if(key<tree->key)
    {
        Insert(tree->left,key);
        if (height(tree->left)-height(tree->right)==2)
        {
            AVLTreeNode* l;
            l=tree->left;
            if (height(l->left)>height(l->right))
            {
                tree=leftLeftRotation(tree);
            }
            else
            {
                tree=leftRightRotation(tree); 
            }
        }
    }
    else
    {
        Insert(tree->right,key);
        if(height(tree->right)-height(tree->left)==2)
        {
            AVLTreeNode* r;
            r=tree->right;
            if (height(r->right)>height(r->left))
            {
                tree=rightRightRotation(tree);
            }
            else
            {
                tree=rightLeftRotation(tree); 
            }
        }
    }
    tree->height=max(height(tree->left),height(tree->right))+1;
} 
AVLTreeNode* Maximum(AVLTreeNode* tree)
{
    if (tree==NULL)
    {
        return tree; 
    }
    while(tree->right!=NULL)
    {
        tree=tree->right;
    }
    return tree;
} 
AVLTreeNode* Minimum(AVLTreeNode* tree)
{
    if(tree==NULL)
    {
        return tree; 
    }
    while(tree->left!=NULL)
    {
        tree=tree->left;
    }
    return tree;
}
AVLTreeNode* Search(AVLTreeNode* tree,int key)
{
    if (tree==NULL||tree->key==key)
    {
        return tree;
    }
    if(key<tree->key)
    {
        return Search(tree->left,key); 
    }
    else
    {
        return Search(tree->right,key);
    }
}
void Remove(AVLTreeNode* &tree,int key)
{
    AVLTreeNode* z;
    if((z=Search(tree,key))!=NULL)
    {
        if (z->key<tree->key)
        {
            Remove(tree->left,key);
            if(height(tree->right)-height(tree->left)==2)
            {
                AVLTreeNode *r=tree->right;
                if (height(r->left)>height(r->right))
                {
                    tree=rightLeftRotation(tree);
                }
                else
                {
                    tree=rightRightRotation(tree);
                }
                     
            }   
        }
        else if(z->key>tree->key)
        {
            Remove(tree->right,key);
            if(height(tree->left)-height(tree->right)==2)
            {
                AVLTreeNode *l=tree->left;
                if(height(l->right)>height(l->left))
                {
                    tree=leftRightRotation(tree); 
                }
                else
                {
                    tree=leftLeftRotation(tree); 
                }
            }
        }
        else
        {
            if (tree->left!=NULL&&tree->right!=NULL)
            {
                if(height(tree->left)>height(tree->right))
                {
                    AVLTreeNode* Max=Maximum(tree->left);
                    tree->key=Max->key;
                    Remove(tree->left,Max->key); 
                }
                else
                {
                    AVLTreeNode* Min=Minimum(tree->right);
                    tree->key=Min->key;
                    Remove(tree->right,Min->key); 
                }
            }
            else
            {
                AVLTreeNode* tmp=tree;
                tree=(tree->left!=NULL)?tree->left:tree->right;
                delete tmp; 
            }
        }
    }   
}
void PreOrder(AVLTreeNode* root)
{
    if (root!=NULL)
    {
        cout<<root<<",left:"<<root->left<<",right:"<<root->right<<",height:"<<root->height<<",key:"<<root->key<<endl;
        PreOrder(root->left);
        PreOrder(root->right);       
    }
}
void InOrder(AVLTreeNode* root)
{
    if (root!=NULL)
    {
        InOrder(root->left);
        cout<<root->key<<" ";
        InOrder(root->right);
    }
}
int main()
{
    int n;
    cin>>n;
    AVLTreeNode* root=NULL;
    for(int i=1;i<=n;i++)
    {
        int x;
        cin>>x;
        Insert(root,x);
    }
    int ans=0,cur;
    for (int i=1;i<n;i++)
    {
        AVLTreeNode* Min;
        Min=Minimum(root);
        cur=Min->key;
        Remove(root,Min->key);
        Min=Minimum(root);
        cur+=Min->key;
        ans+=cur;
        Remove(root,Min->key);
        Insert(root,cur);
    }
    cout<<ans<<endl;
}