嘿，我必须通过给出位置来找到最有效的打印数字的方法。输入是这样的：
8 (N-> N Numbers)
INS 100 (Add 100 to the tree)
INS 200 (Add 200 to the tree)
INS 300 (Add 300 to the tree)
REM 200 (Remove the number 200 from the tree)
PER 1 (Have to output the biggest number in the tree-> Shoud print 300)
INS 1000 (Add 1000 to the tree)
PER 1 ((Have to output the biggest number in the tree-> Shoud print 1000))
PER 2 (I have to output the second biggest number so: 300)
我有办法像这样打印，但速度很慢，我必须维持一个O（N * log（N））。
这是我的完整代码
#include<stdio.h>
#include<stdlib.h>
#include<iostream>
using namespace std;
// An AVL tree node
struct node
{
int key;
struct node *left;
struct node *right;
int height;
};
// A utility function to get maximum of two integers
int max(int a, int b);
// A utility function to get height of the tree
int height(struct node *N)
{
if (N == NULL)
return 0;
return N->height;
}
// A utility function to get maximum of two integers
int max(int a, int b)
{
return (a > b)? a : b;
}
/* Helper function that allocates a new node with the given key and
NULL left and right pointers. */
struct node* newNode(int key)
{
struct node* node = (struct node*)
malloc(sizeof(struct node));
node->key = key;
node->left = NULL;
node->right = NULL;
node->height = 1; // new node is initially added at leaf
return(node);
}
// A utility function to right rotate subtree rooted with y
// See the diagram given above.
struct node *rightRotate(struct node *y)
{
struct node *x = y->left;
struct node *T2 = x->right;
// Perform rotation
x->right = y;
y->left = T2;
// Update heights
y->height = max(height(y->left), height(y->right))+1;
x->height = max(height(x->left), height(x->right))+1;
// Return new root
return x;
}
// A utility function to left rotate subtree rooted with x
// See the diagram given above.
struct node *leftRotate(struct node *x)
{
struct node *y = x->right;
struct node *T2 = y->left;
// Perform rotation
y->left = x;
x->right = T2;
// Update heights
x->height = max(height(x->left), height(x->right))+1;
y->height = max(height(y->left), height(y->right))+1;
// Return new root
return y;
}
// Get Balance factor of node N
int getBalance(struct node *N)
{
if (N == NULL)
return 0;
return height(N->left) - height(N->right);
}
struct node* insert(struct node* node, int key)
{
/* 1. Perform the normal BST rotation */
if (node == NULL)
return(newNode(key));
if (key < node->key)
node->left = insert(node->left, key);
else
node->right = insert(node->right, key);
/* 2. Update height of this ancestor node */
node->height = max(height(node->left), height(node->right)) + 1;
/* 3. Get the balance factor of this ancestor node to check whether
this node became unbalanced */
int balance = getBalance(node);
// If this node becomes unbalanced, then there are 4 cases
// Left Left Case
if (balance > 1 && key < node->left->key)
return rightRotate(node);
// Right Right Case
if (balance < -1 && key > node->right->key)
return leftRotate(node);
// Left Right Case
if (balance > 1 && key > node->left->key)
{
node->left = leftRotate(node->left);
return rightRotate(node);
}
// Right Left Case
if (balance < -1 && key < node->right->key)
{
node->right = rightRotate(node->right);
return leftRotate(node);
}
/* return the (unchanged) node pointer */
return node;
}
/* Given a non-empty binary search tree, return the node with minimum
key value found in that tree. Note that the entire tree does not
need to be searched. */
struct node * minValueNode(struct node* node)
{
struct node* current = node;
/* loop down to find the leftmost leaf */
while (current->left != NULL)
current = current->left;
return current;
}
struct node* apagaNode(struct node* root, int key)
{
// STEP 1: PERFORM STANDARD BST DELETE
if (root == NULL)
return root;
// If the key to be deleted is smaller than the root's key,
// then it lies in left subtree
if ( key < root->key )
root->left = apagaNode(root->left, key);
// If the key to be deleted is greater than the root's key,
// then it lies in right subtree
else if( key > root->key )
root->right = apagaNode(root->right, key);
// if key is same as root's key, then This is the node
// to be deleted
else
{
// node with only one child or no child
if( (root->left == NULL) || (root->right == NULL) )
{
struct node *temp = root->left ? root->left : root->right;
// No child case
if(temp == NULL)
{
temp = root;
root = NULL;
}
else // One child case
*root = *temp; // Copy the contents of the non-empty child
free(temp);
}
else
{
// node with two children: Get the inorder successor (smallest
// in the right subtree)
struct node* temp = minValueNode(root->right);
// Copy the inorder successor's data to this node
root->key = temp->key;
// Delete the inorder successor
root->right = apagaNode(root->right, temp->key);
}
}
// If the tree had only one node then return
if (root == NULL)
return root;
// STEP 2: UPDATE HEIGHT OF THE CURRENT NODE
root->height = max(height(root->left), height(root->right)) + 1;
// STEP 3: GET THE BALANCE FACTOR OF THIS NODE (to check whether
// this node became unbalanced)
int balance = getBalance(root);
// If this node becomes unbalanced, then there are 4 cases
// Left Left Case
if (balance > 1 && getBalance(root->left) >= 0)
return rightRotate(root);
// Left Right Case
if (balance > 1 && getBalance(root->left) < 0)
{
root->left = leftRotate(root->left);
return rightRotate(root);
}
// Right Right Case
if (balance < -1 && getBalance(root->right) <= 0)
return leftRotate(root);
// Right Left Case
if (balance < -1 && getBalance(root->right) > 0)
{
root->right = rightRotate(root->right);
return leftRotate(root);
}
return root;
}
int imprime(struct node *root,int targetPos,int curPos)
{
if(root != NULL)
{
int newPos = imprime(root->left, targetPos, curPos);
newPos++;
if (newPos == targetPos)
{
printf("%d\n", root->key);
}
return imprime(root->right, targetPos, newPos);
}
else
{
return curPos;
}
}
int main()
{
struct node *root = NULL;
int total=0;
int n,b;
string a;
cin >> n;
for (int i=0; i<n; i++)
{
cin >> a >> b;
if(a=="INS")
{root = insert(root, b);total=total+1;}
else
if(a=="REM")
{root = apagaNode(root, b);total=total-1;}
else
imprime(root, total-b+1, 0);
}
return 0;
}
我发现打印值的方式：
int imprime(struct node *root,int targetPos,int curPos)
{
if(root != NULL)
{
int newPos = imprime(root->left, targetPos, curPos);
newPos++;
if (newPos == targetPos)
{
printf("%d\n", root->key);
}
return imprime(root->right, targetPos, newPos);
}
else
{
return curPos;
}
}
问题是这个功能很慢，我不能用它。如何通过这样的给定位置打印的最佳方式是什么？ （听说过，计算n_nodes，在轮换期间我必须增加，减少，我真的不明白。请帮帮我！给我一些提示和建议）（PS：我不是这种算法的专家）
答案 0 :(得分：1)
您听到的建议是正确的：您应该在node结构中添加一个节点计数器：
struct node
{
int key;
struct node *left;
struct node *right;
int height;
int n_nodes;
};
它应该保存树中的节点数。假设它是正确的，您可以改进查找具有目标位置的节点的算法：它将准确知道要查看的树的哪个分支（left或right），这将是使搜索更快（当前imprime实现是O（n））。
那么，如何使n_nodes字段保持正确的价值呢？幸运的是，您已经有一个例子：height。查看现有代码对其进行更改的位置;这些大致是您必须更新n_nodes的地方。他们中的大多数都是微不足道的（只需加1）;更有趣的是旋转功能：
struct node *rightRotate(struct node *y)
{
struct node *x = y->left;
struct node *T2 = x->right;
// Perform rotation
x->right = y;
y->left = T2;
// Update heights
y->height = max(height(y->left), height(y->right))+1;
x->height = max(height(x->left), height(x->right))+1;
// Update numbers of nodes
x->n_nodes = ...;
y->n_nodes = ...;
T2->n_nodes = ...;
// Return new root
return x;
}
所以它会像这样转换树：
y x
/ \ / \
x D A y
/ \ ==> / \
A T2 T2 D
/ \ / \
B C B C
此处A，B，C和D是您的计划所知大小的树;我们将其大小表示为a，b，c和d。因此，转换会改变这些大小：
size of x: from a+b+c+2 to a+b+c+d+3
size of y: from a+b+c+d+3 to b+c+d+2
size of T2: unchanged
所以只需将其转换为代码。