本文概述
给定二叉搜索树, 编写一个函数, 该函数以以下三个作为参数：
1)树的根
2)旧键值
3)新的关键值
该功能应将旧键值更改为新键值。该函数可以假定二叉搜索树中始终存在旧键值。
例子：
Input: Root of below tree
50
/ \
30 70
/ \ / \
20 40 60 80
Old key value: 40
New key value: 10
Output: BST should be modified to following
50
/ \
30 70
/ / \
20 60 80
/
10我们强烈建议你最小化浏览器, 然后先尝试一下
这个想法是为旧键值调用delete, 然后为新键值调用insert。以下是该想法的C ++实现。
C ++
//C++ program to demonstrate decrease
//key operation on binary search tree
#include<bits/stdc++.h>
using namespace std;
class node
{
public :
int key;
node *left, *right;
};
//A utility function to
//create a new BST node
node *newNode( int item)
{
node *temp = new node;
temp->key = item;
temp->left = temp->right = NULL;
return temp;
}
//A utility function to
//do inorder traversal of BST
void inorder(node *root)
{
if (root != NULL)
{
inorder(root->left);
cout <<root->key <<" " ;
inorder(root->right);
}
}
/* A utility function to insert
a new node with given key in BST */
node* insert(node* node, int key)
{
/* If the tree is empty, return a new node */
if (node == NULL) return newNode(key);
/* Otherwise, recur down the tree */
if (key <node->key)
node->left = insert(node->left, key);
else
node->right = insert(node->right, key);
/* 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. */
node * minValueNode(node* Node)
{
node* current = Node;
/* loop down to find the leftmost leaf */
while (current->left != NULL)
current = current->left;
return current;
}
/* Given a binary search tree and
a key, this function deletes the key
and returns the new root */
node* deleteNode(node* root, int key)
{
//base case
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 = deleteNode(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 = deleteNode(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)
{
node *temp = root->right;
free (root);
return temp;
}
else if (root->right == NULL)
{
node *temp = root->left;
free (root);
return temp;
}
//node with two children: Get
//the inorder successor (smallest
//in the right subtree)
node* temp = minValueNode(root->right);
//Copy the inorder successor's
//content to this node
root->key = temp->key;
//Delete the inorder successor
root->right = deleteNode(root->right, temp->key);
}
return root;
}
//Function to decrease a key
//value in Binary Search Tree
node *changeKey(node *root, int oldVal, int newVal)
{
//First delete old key value
root = deleteNode(root, oldVal);
//Then insert new key value
root = insert(root, newVal);
//Return new root
return root;
}
//Driver code
int main()
{
/* Let us create following BST
50
/\
30 70
/\ /\
20 40 60 80 */
node *root = NULL;
root = insert(root, 50);
root = insert(root, 30);
root = insert(root, 20);
root = insert(root, 40);
root = insert(root, 70);
root = insert(root, 60);
root = insert(root, 80);
cout <<"Inorder traversal of the given tree \n" ;
inorder(root);
root = changeKey(root, 40, 10);
/* BST is modified to
50
/\
30 70
//\
20 60 80
/
10 */
cout <<"\nInorder traversal of the modified tree \n" ;
inorder(root);
return 0;
}
//This code is contributed by rathbhupendraC
//C program to demonstrate decrease key operation on binary search tree
#include<stdio.h>
#include<stdlib.h>
struct node
{
int key;
struct node *left, *right;
};
//A utility function to create a new BST node
struct node *newNode( int item)
{
struct node *temp = ( struct node *) malloc ( sizeof ( struct node));
temp->key = item;
temp->left = temp->right = NULL;
return temp;
}
//A utility function to do inorder traversal of BST
void inorder( struct node *root)
{
if (root != NULL)
{
inorder(root->left);
printf ( "%d " , root->key);
inorder(root->right);
}
}
/* A utility function to insert a new node with given key in BST */
struct node* insert( struct node* node, int key)
{
/* If the tree is empty, return a new node */
if (node == NULL) return newNode(key);
/* Otherwise, recur down the tree */
if (key <node->key)
node->left = insert(node->left, key);
else
node->right = insert(node->right, key);
/* 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;
}
/* Given a binary search tree and a key, this function deletes the key
and returns the new root */
struct node* deleteNode( struct node* root, int key)
{
//base case
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 = deleteNode(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 = deleteNode(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)
{
struct node *temp = root->right;
free (root);
return temp;
}
else if (root->right == NULL)
{
struct node *temp = root->left;
free (root);
return temp;
}
//node with two children: Get the inorder successor (smallest
//in the right subtree)
struct node* temp = minValueNode(root->right);
//Copy the inorder successor's content to this node
root->key = temp->key;
//Delete the inorder successor
root->right = deleteNode(root->right, temp->key);
}
return root;
}
//Function to decrease a key value in Binary Search Tree
struct node *changeKey( struct node *root, int oldVal, int newVal)
{
// First delete old key value
root = deleteNode(root, oldVal);
//Then insert new key value
root = insert(root, newVal);
//Return new root
return root;
}
//Driver Program to test above functions
int main()
{
/* Let us create following BST
50
/ \
30 70
/ \ / \
20 40 60 80 */
struct node *root = NULL;
root = insert(root, 50);
root = insert(root, 30);
root = insert(root, 20);
root = insert(root, 40);
root = insert(root, 70);
root = insert(root, 60);
root = insert(root, 80);
printf ( "Inorder traversal of the given tree \n" );
inorder(root);
root = changeKey(root, 40, 10);
/* BST is modified to
50
/ \
30 70
/ / \
20 60 80
/
10 */
printf ( "\nInorder traversal of the modified tree \n" );
inorder(root);
return 0;
}Java
//Java program to demonstrate decrease
//key operation on binary search tree
class GfG
{
static class node
{
int key;
node left, right;
}
static node root = null ;
//A utility function to
//create a new BST node
static node newNode( int item)
{
node temp = new node();
temp.key = item;
temp.left = null ;
temp.right = null ;
return temp;
}
//A utility function to
//do inorder traversal of BST
static void inorder(node root)
{
if (root != null )
{
inorder(root.left);
System.out.print(root.key + " " );
inorder(root.right);
}
}
/* A utility function to insert
a new node with given key in BST */
static node insert(node node, int key)
{
/* If the tree is empty, return a new node */
if (node == null ) return newNode(key);
/* Otherwise, recur down the tree */
if (key <node.key)
node.left = insert(node.left, key);
else
node.right = insert(node.right, key);
/* 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. */
static node minValueNode(node Node)
{
node current = Node;
/* loop down to find the leftmost leaf */
while (current.left != null )
current = current.left;
return current;
}
/* Given a binary search tree and
a key, this function deletes the key
and returns the new root */
static node deleteNode(node root, int key)
{
//base case
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 = deleteNode(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 = deleteNode(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 )
{
node temp = root.right;
return temp;
}
else if (root.right == null )
{
node temp = root.left;
return temp;
}
//node with two children: Get
//the inorder successor (smallest
//in the right subtree)
node temp = minValueNode(root.right);
//Copy the inorder successor's
//content to this node
root.key = temp.key;
//Delete the inorder successor
root.right = deleteNode(root.right, temp.key);
}
return root;
}
//Function to decrease a key
//value in Binary Search Tree
static node changeKey(node root, int oldVal, int newVal)
{
//First delete old key value
root = deleteNode(root, oldVal);
//Then insert new key value
root = insert(root, newVal);
//Return new root
return root;
}
//Driver code
public static void main(String[] args)
{
/* Let us create following BST
50
/\
30 70
/\ /\
20 40 60 80 */
root = insert(root, 50 );
root = insert(root, 30 );
root = insert(root, 20 );
root = insert(root, 40 );
root = insert(root, 70 );
root = insert(root, 60 );
root = insert(root, 80 );
System.out.println( "Inorder traversal of the given tree" );
inorder(root);
root = changeKey(root, 40 , 10 );
/* BST is modified to
50
/\
30 70
//\
20 60 80
/
10 */
System.out.println( "\nInorder traversal of the modified tree " );
inorder(root);
}
}
//This code is contributed by Prerna sainiPython3
# Python3 program to demonstrate decrease key
# operation on binary search tree
# A utility function to create a new BST node
class newNode:
def __init__( self , key):
self .key = key
self .left = self .right = None
# A utility function to do inorder
# traversal of BST
def inorder(root):
if root ! = None :
inorder(root.left)
print (root.key, end = " " )
inorder(root.right)
# A utility function to insert a new
# node with given key in BST
def insert(node, key):
# If the tree is empty, return a new node
if node = = None :
return newNode(key)
# Otherwise, recur down the tree
if key <node.key:
node.left = insert(node.left, key)
else :
node.right = insert(node.right, key)
# 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.
def minValueNode(node):
current = node
# loop down to find the leftmost leaf
while current.left ! = None :
current = current.left
return current
# Given a binary search tree and a key, this
# function deletes the key and returns the new root
def deleteNode(root, key):
# base case
if root = = None :
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 = deleteNode(root.left, key)
# If the key to be deleted is greater than
# the root's key, then it lies in right subtree
elif key> root.key:
root.right = deleteNode(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 = = None :
temp = root.right
return temp
elif root.right = = None :
temp = root.left
return temp
# node with two children: Get the inorder
# successor (smallest in the right subtree)
temp = minValueNode(root.right)
# Copy the inorder successor's content
# to this node
root.key = temp.key
# Delete the inorder successor
root.right = deleteNode(root.right, temp.key)
return root
# Function to decrease a key value in
# Binary Search Tree
def changeKey(root, oldVal, newVal):
# First delete old key value
root = deleteNode(root, oldVal)
# Then insert new key value
root = insert(root, newVal)
# Return new root
return root
# Driver Code
if __name__ = = '__main__' :
# Let us create following BST
# 50
# / \
# 30 70
# /\ /\
# 20 40 60 80
root = None
root = insert(root, 50 )
root = insert(root, 30 )
root = insert(root, 20 )
root = insert(root, 40 )
root = insert(root, 70 )
root = insert(root, 60 )
root = insert(root, 80 )
print ( "Inorder traversal of the given tree" )
inorder(root)
root = changeKey(root, 40 , 10 )
print ()
# BST is modified to
# 50
# / \
# 30 70
# / /\
# 20 60 80
# /
# 10
print ( "Inorder traversal of the modified tree" )
inorder(root)
# This code is contributed by PranchalKC#
//C# program to demonstrate decrease
//key operation on binary search tree
using System;
class GFG
{
public class node
{
public int key;
public node left, right;
}
static node root = null ;
//A utility function to
//create a new BST node
static node newNode( int item)
{
node temp = new node();
temp.key = item;
temp.left = null ;
temp.right = null ;
return temp;
}
//A utility function to
//do inorder traversal of BST
static void inorder(node root)
{
if (root != null )
{
inorder(root.left);
Console.Write(root.key + " " );
inorder(root.right);
}
}
/* A utility function to insert
a new node with given key in BST */
static node insert(node node, int key)
{
/* If the tree is empty, return a new node */
if (node == null ) return newNode(key);
/* Otherwise, recur down the tree */
if (key <node.key)
node.left = insert(node.left, key);
else
node.right = insert(node.right, key);
/* 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. */
static node minValueNode(node Node)
{
node current = Node;
/* loop down to find the leftmost leaf */
while (current.left != null )
current = current.left;
return current;
}
/* Given a binary search tree and
a key, this function deletes the key
and returns the new root */
static node deleteNode(node root, int key)
{
node temp = null ;
//base case
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 = deleteNode(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 = deleteNode(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 )
{
temp = root.right;
return temp;
}
else if (root.right == null )
{
temp = root.left;
return temp;
}
//node with two children: Get
//the inorder successor (smallest
//in the right subtree)
temp = minValueNode(root.right);
//Copy the inorder successor's
//content to this node
root.key = temp.key;
//Delete the inorder successor
root.right = deleteNode(root.right, temp.key);
}
return root;
}
//Function to decrease a key
//value in Binary Search Tree
static node changeKey(node root, int oldVal, int newVal)
{
//First delete old key value
root = deleteNode(root, oldVal);
//Then insert new key value
root = insert(root, newVal);
//Return new root
return root;
}
//Driver code
public static void Main(String[] args)
{
/* Let us create following BST
50
/\
30 70
/\ /\
20 40 60 80 */
root = insert(root, 50);
root = insert(root, 30);
root = insert(root, 20);
root = insert(root, 40);
root = insert(root, 70);
root = insert(root, 60);
root = insert(root, 80);
Console.WriteLine( "Inorder traversal " +
"of the given tree " );
inorder(root);
root = changeKey(root, 40, 10);
/* BST is modified to
50
/\
30 70
//\
20 60 80
/
10 */
Console.WriteLine( "\nInorder traversal " +
"of the modified tree" );
inorder(root);
}
}
//This code is contributed by 29AjayKumar输出如下：
Inorder traversal of the given tree
20 30 40 50 60 70 80
Inorder traversal of the modified tree
10 20 30 50 60 70 80上述changeKey()的时间复杂度为O(h), 其中h是BST的高度。
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