Size Balance Tree（SBT模板整理）

 

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/* * tree[x].left   表示以 x 为节点的左儿子 * tree[x].right  表示以 x 为节点的右儿子 * tree[x].size   表示以 x 为根的节点的个数（大小） */     struct SBT {     int key,left,right,size; } tree[10010]; int root = 0,top = 0;   void left_rot(int &x)         // 左旋 {     int y = tree[x].right;     if (!y) return;     tree[x].right = tree[y].left;     tree[y].left = x;     tree[y].size = tree[x].size;     tree[x].size = tree[tree[x].left].size + tree[tree[x].right].size + 1;     x = y; }   void right_rot(int &x)        //右旋 {     int y = tree[x].left;     if (!y) return;     tree[x].left = tree[y].right;     tree[y].right = x;     tree[y].size = tree[x].size;     tree[x].size = tree[tree[x].left].size + tree[tree[x].right].size + 1;     x = y; }   void maintain(int &x,bool flag)  //维护SBT状态 {     if (!x) return;     if (flag == false)           //左边     {         if(tree[tree[tree[x].left].left].size > tree[tree[x].right].size)//左孩子的左孩子大于右孩子             right_rot(x);         else if (tree[tree[tree[x].left].right].size > tree[tree[x].right].size) //左孩子的右孩子大于右孩子         {             left_rot(tree[x].left);             right_rot(x);         }         else             return;     }     else                       //右边     {         if(tree[tree[tree[x].right].right].size > tree[tree[x].left].size)//右孩子的右孩子大于左孩子             left_rot(x);         else if(tree[tree[tree[x].right].left].size > tree[tree[x].left].size) //右孩子的左孩子大于左孩子         {             right_rot(tree[x].right);             left_rot(x);         }         else             return;     }     maintain(tree[x].left,false);     maintain(tree[x].right,true);     maintain(x,true);     maintain(x,false); }   void insert(int &x,int key)  //插入 {     if (x == 0)     {         x = ++top;         tree[x].left = 0;         tree[x].right = 0;         tree[x].size = 1;         tree[x].key = key;     }     else     {         tree[x].size++;         if(key < tree[x].key)             insert(tree[x].left,key);         else             insert(tree[x].right,key);//相同元素可插右子树         maintain(x,key >= tree[x].key);     } }   int remove(int &x,int key)  //利用后继删除 {     tree[x].size--;     if(key > tree[x].key)         remove(tree[x].right,key);     else  if(key < tree[x].key)         remove(tree[x].left,key);     else  if(tree[x].left !=0 && !tree[x].right) //有左子树，无右子树     {         int tmp = x;         x = tree[x].left;         return tmp;     }     else if(!tree[x].left && tree[x].right != 0) //有右子树，无左子树     {         int tmp = x;         x = tree[x].right;         return tmp;     }     else if(!tree[x].left && !tree[x].right)    //无左右子树     {         int tmp = x;         x = 0;         return tmp;     }     else                                      //左右子树都有     {         int tmp = tree[x].right;         while(tree[tmp].left)             tmp = tree[tmp].left;         tree[x].key = tree[temp].key;         remove(tree[x].right,tree[tmp].key);     } }   int getmin(int x)    //求最小值 {     while(tree[x].left)         x = tree[x].left;     return tree[x].key; }   int getmax(int x)    //求最大值 {     while(tree[x].right)         x = tree[x].right;     return tree[x].key; }   int pred(int &x,int y,int key)   //前驱，y初始前驱，从0开始, 最终要的是返回值的key值 {     if(x == 0)         return y;     if(key > tree[x].key)         return pred(tree[x].right,x,key);     else         return pred(tree[x].left,y,key); }   int succ(int &x,int y,int key)   //后继，同上 {     if(x == 0)         return y;     if(key < tree[x].key)         return succ(tree[x].left,x,key);     else         return succ(tree[x].right,y,key); }   int select(int &x,int k)   //查找第k小的数 {     int r = tree[tree[x].left].size + 1;     if(r == k)         return tree[x].key;     else if(r < k)         return select(tree[x].right,k - r);     else         return select(tree[x].left,k); }   int rank(int &x,int key)   //key排第几 {     if(key < tree[x].key)     {         return rank(tree[x].left,key);     }     else if(key > tree[x].key)         return rank(tree[x].right,key) + tree[tree[x].left].size + 1;     else         return tree[tree[x].left].size + 1; }   int main() {     //insert(root,key);     //delete(root,key)     return 0; }

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