问：二叉树所有节点求和程序

17 Mar 2025 | 6 分钟阅读

说明

在此程序中，我们需要计算二叉树中存在的节点的总和。首先，我们将遍历左子树并计算左子树中存在的节点的总和。类似地，我们计算右子树中存在的节点的总和，并通过添加根节点的数据来计算总和。

Program to find the sum of all the nodes of a Binary Tree

对于给定的树，二叉树节点的总和将是 1 + 2 + 5 + 8 + 6 + 9 = 31。

算法

定义 Node 类，该类包含三个属性：data、left 和 right。这里，left 表示节点的左子节点，right 表示节点的右子节点。
创建节点时，数据将传递到节点的 data 属性，left 和 right 都将设置为 null。
定义另一个类，该类有一个 root 属性。
1. 根表示树的根节点，并将其初始化为 null。
calculateSum() 将计算二叉树中存在的节点的总和
1. 它检查 root 是否为空，这意味着树为空。
2. 如果树不为空，则遍历左子树，计算节点总和并将其存储在 sumLeft 中。
3. 然后，遍历右子树，计算节点总和并将其存储在 sumRight 中。
4. 最后，计算总和 = temp.data + sumLeft + sumRight。

解决方案

Python

#Represent a node of binary tree
class Node:
    def __init__(self,data):
        #Assign data to the new node, set left and right children to None
        self.data = data;
        self.left = None;
        self.right = None;
 
class SumOfNodes:
    def __init__(self):
        #Represent the root of binary tree
        self.root = None;
    
    #calculateSum() will calculate the sum of all the nodes present in the binary tree
    def calculateSum(self, temp):
        sum = sumRight = sumLeft = 0;
        
        #Check whether tree is empty
        if(self.root == None):
            print("Tree is empty");
            return 0;
        else:
            #Calculate the sum of nodes present in left subtree
            if(temp.left != None):
                sumLeft = self.calculateSum(temp.left);
            
            #Calculate the sum of nodes present in right subtree
            if(temp.right != None):
                sumRight = self.calculateSum(temp.right);
            
            #Calculate the sum of all nodes by adding sumLeft, sumRight and root node's data
            sum = temp.data + sumLeft + sumRight; 
        return sum;
 
bt = SumOfNodes();
#Add nodes to the binary tree
bt.root = Node(5);
bt.root.left = Node(2);
bt.root.right = Node(9);
bt.root.left.left = Node(1);
bt.root.right.left = Node(8);
bt.root.right.right = Node(6);
 
#Display the sum of all the nodes in the given binary tree
print("Sum of all nodes of binary tree: " + str(bt.calculateSum(bt.root)));

输出

Sum of all nodes of binary tree: 31

C

#include <stdio.h>
#include <stdlib.h>
 
//Represent a node of binary tree
struct node{
    int data;
    struct node *left;
    struct node *right;
};
 
//Represent the root of binary tree
struct node *root = NULL;
 
//createNode() will create a new node
struct node* createNode(int data){
    //Create a new node
    struct node *newNode = (struct node*)malloc(sizeof(struct node));
    //Assign data to newNode, set left and right children to NULL
    newNode->data = data;
    newNode->left = NULL;
    newNode->right = NULL;
    
    return newNode;
}
 
//calculateSum() will calculate the sum of all the nodes present in the binary tree
int calculateSum(struct node *temp){
    int sum, sumLeft, sumRight;
    sum = sumRight = sumLeft = 0;
    
    //Check whether tree is empty
    if(root == NULL) {
        printf("Tree is empty\n");
        return 0;
    }
    else {
        //Calculate the sum of nodes present in left subtree
        if(temp->left != NULL)
            sumLeft = calculateSum(temp->left);
        
        //Calculate the sum of nodes present in right subtree
        if(temp->right != NULL)
              sumRight = calculateSum(temp->right);
        
        //Calculate the sum of all nodes by adding sumLeft, sumRight and root node's data
        sum = temp->data + sumLeft + sumRight; 
        return sum;
  }    
}
 
int main()
{
    //Add nodes to the binary tree
    root = createNode(5);
    root->left = createNode(2);
    root->right = createNode(9);
    root->left->left = createNode(1);
    root->right->left = createNode(8);
    root->right->right = createNode(6);
    
    //Display the sum of all the nodes in the given binary tree
    printf("Sum of all nodes of binary tree: %d", calculateSum(root));
    return 0;
}

输出

Sum of all nodes of binary tree: 31

JAVA

public class SumOfNodes {
      
      //Represent the node of binary tree
        public static class Node{
        int data;
        Node left;
        Node right;
        
        public Node(int data){
            //Assign data to the new node, set left and right children to null
            this.data = data;
            this.left = null;
            this.right = null;
        }
      }
      
      //Represent the root of binary tree
      public Node root;
      
      public SumOfNodes(){
        root = null;
      }
      
      //calculateSum() will calculate the sum of all the nodes present in the binary tree
      public int calculateSum(Node temp){
        int sum, sumLeft, sumRight;
        sum = sumRight = sumLeft = 0;
        
        //Check whether tree is empty
        if(root == null) {
            System.out.println("Tree is empty");
            return 0;
        }
        else {
            //Calculate the sum of nodes present in left subtree
            if(temp.left != null)
                sumLeft = calculateSum(temp.left);
            
            //Calculate the sum of nodes present in right subtree
            if(temp.right != null)
                sumRight = calculateSum(temp.right);
            
            //Calculate the sum of all nodes by adding sumLeft, sumRight and root node's data
            sum = temp.data + sumLeft + sumRight; 
            return sum;
        }    
      }
      
      public static void main(String[] args) {
        
        SumOfNodes bt = new SumOfNodes();
        //Add nodes to the binary tree
        bt.root = new Node(5);
        bt.root.left = new Node(2);
        bt.root.right = new Node(9);
        bt.root.left.left = new Node(1);
        bt.root.right.left = new Node(8);
        bt.root.right.right = new Node(6);
        
        //Display the sum of all the nodes in the given binary tree
        System.out.println("Sum of all nodes of binary tree: " + bt.calculateSum(bt.root));
      }
    }

输出

Sum of all nodes of binary tree: 31

C#

using System;
namespace Tree 
{                     
    public class Program
    {
        //Represent a node of binary tree
        public class Node<T>{
            public T data;
            public Node<T> left;
            public Node<T> right;
            
            public Node(T data) {
                //Assign data to the new node, set left and right children to null
                this.data = data;
                this.left = null;
                this.right = null;
            }
        }
        
        public class SumOfNodes<T>{
            //Represent the root of binary tree
            public Node<T> root;
 
            public static Boolean flag = false;
 
            public SumOfNodes(){
                root = null;
            }
        
        //calculateSum() will calculate the sum of all the nodes present in the binary tree
          public int calculateSum(Node<T> temp){
            int sum, sumLeft, sumRight;
            sum = sumRight = sumLeft = 0;
            
            //Check whether tree is empty
            if(root == null) {
                Console.WriteLine("Tree is empty");
                return 0;
            }
            else {
                //Calculate the sum of nodes present in left subtree
                if(temp.left != null)
                    sumLeft = calculateSum(temp.left);
                
                //Calculate the sum of nodes present in right subtree
                if(temp.right != null)
                    sumRight = calculateSum(temp.right);
                
                //Calculate the sum of all nodes by adding sumLeft, sumRight and root node's data
                sum = (int)(object)temp.data + sumLeft + sumRight; 
                return sum;
            }    
          }
    }    
        public static void Main()
        {
            SumOfNodes<int> bt = new SumOfNodes<int>();
            //Add nodes to the binary tree
            bt.root = new Node<int>(5);
            bt.root.left = new Node<int>(2);
            bt.root.right = new Node<int>(9);
            bt.root.left.left = new Node<int>(1);
            bt.root.right.left = new Node<int>(8);
            bt.root.right.right = new Node<int>(6);
            
            //Display the sum of all the nodes in the given binary tree
            Console.WriteLine("Sum of all nodes of binary tree: " + bt.calculateSum(bt.root));            
        }    
    }
}

输出

Sum of all nodes of binary tree: 31

PHP

<!DOCTYPE html>
<html>
<body>
<?php
//Represent a node of binary tree
class Node{
    public $data;
    public $left;
    public $right;
    
    function __construct($data){
        //Assign data to the new node, set left and right children to NULL
        $this->data = $data;
        $this->left = NULL;
        $this->right = NULL;
    }
}
class SumOfNodes{
    //Represent the root of binary tree
    public $root;
    function __construct(){
        $this->root = NULL;
    }
    
    //calculateSum() will calculate the sum of all the nodes present in the binary tree
    function calculateSum($temp){
        $sum = 0;
        $sumLeft = 0;
        $sumRight = 0;
      
        //Check whether tree is empty
        if($this->root == NULL) {
            print "Tree is empty <br>";
            return 0;
        }
        else {
             //Calculate the sum of nodes present in left subtree
            if($temp->left != NULL)
                $sumLeft = $this->calculateSum($temp->left);
 
             //Calculate the sum of nodes present in right subtree
            if($temp->right != NULL)
                $sumRight = $this->calculateSum($temp->right);
 
             //Calculate the sum of all nodes by adding sumLeft, sumRight and root node's data
             $sum = $temp->data + $sumLeft + $sumRight; 
             return $sum;
      }    
    }
}
$bt = new SumOfNodes();
//Add nodes to the binary tree
$bt->root = new Node(5);
$bt->root->left = new Node(2);
$bt->root->right = new Node(9);
$bt->root->left->left = new Node(1);
$bt->root->right->left = new Node(8);
$bt->root->right->right = new Node(6);
 
//Display the sum of all the nodes in the given binary tree
print "Sum of all nodes of binary tree: " . $bt->calculateSum($bt->root);
?>
</body>
</html>

输出

Sum of all nodes of binary tree: 31

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