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如何在Binary Search Tree中实现减小键或更改键?

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 rathbhupendra

C

//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 saini

Python3

# 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 PranchalK

C#

//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。

如果发现任何不正确的地方, 或者想分享有关上述主题的更多信息, 请发表评论。

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