Q. 判断所有叶子节点是否在同一层级的程序。

2025年3月17日 | 阅读 7 分钟

说明

在此程序中，我们需要检查给定二叉树的所有叶子节点是否在同一层级。

如果一个节点没有子节点，则称其为叶子节点。在下图中，节点 4、5 和 6 是叶子节点，因为它们没有任何子节点。节点 4、5 和 6 位于同一层级，即第 2 层。

Program to determine whether all leaves are at same level

算法

定义 Node 类，它有三个属性：data、left 和 right。其中，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，将数据传递给节点的 data 属性，并将 left 和 right 都设置为 null。
定义另一个类，该类具有两个属性：root 和 level。
1. Root 表示树的根节点，并将其初始化为 null。
2. level 将用于存储遇到的第一个叶子节点的层级。
isSameLevel() 将检查给定二叉树的所有叶子节点是否在同一层级。
1. 它检查根是否为空，这意味着树是空的。
2. 如果树非空，则遍历树并检查叶子节点，其左右子节点都为 null。
3. CurrentLevel 将跟踪当前遍历的层级。
4. 当遇到第一个叶子节点时，将 currentLevel 的值存储在变量 level 中。
5. 递归地遍历所有层级，检查后续的叶子节点。如果所有叶子节点的 currentLevel 都等于存储在 level 中的值，则所有叶子节点都在同一层级。

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 LeafLevel:
    def __init__(self):
        #Represent the root of binary tree
        self.root = None;
        #It will store level of first encountered leaf 
        self.level = 0;
        
    #isSameLevel() will check whether all leaves of the binary tree is at same level or not
    def isSameLevel(self, temp, currentLevel):
        
        #Check whether tree is empty
        if(self.root == None):
            print("Tree is empty");
            return true;
            
        else:
            #Checks whether node is None
            if(temp == None):
                return True;
                
            if(temp.left == None and temp.right == None):
                #If first leaf is encountered, set level to current level
                if(self.level == 0):
                    self.level = currentLevel;
                    return True;
                    
                #Checks whether the other leaves are at the same level as that of the first leaf
                else:
                    return (self.level == currentLevel);
                    
            #Checks for leaf node in left and right subtree recursively.
            return  (self.isSameLevel(temp.left, currentLevel + 1) and self.isSameLevel(temp.right, currentLevel + 1));
                
bt = LeafLevel();
#Add nodes to the binary tree
bt.root = Node(1);
bt.root.left = Node(2);
bt.root.right = Node(3);
bt.root.left.left = Node(4);
bt.root.right.left = Node(5);
bt.root.right.right = Node(6);
 
#Checks whether all leaves of given binary tree is at same level
if(bt.isSameLevel(bt.root, 1)):
    print("All leaves are at same level");
else:
    print("All leaves are not at same level");

输出

All leaves are at same level

C

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.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;
 
//It will store level of first encountered leaf 
static int level = 0;
    
//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;
}
 
//isSameLevel() will check whether all leaves of the binary tree is at the same level or not
bool isSameLevel(struct node *temp, int currentLevel ) {
    
    //Check whether tree is empty
    if(root == NULL){
        printf("Tree is empty\n");
        return true;
    }
    else {
        //Checks whether node is null
        if(temp == NULL)
            return true;
 
        if(temp->left == NULL && temp->right == NULL) {
            //If first leaf is encountered, set level to current level
            if(level == 0) {
                level = currentLevel ;
                return true;
            }
            //Checks whether the other leaves are at the same level of that of first leaf
            else 
               return (level == currentLevel) ;
         }
        
        //Checks for leaf node in left and right subtree recursively.
        return  (isSameLevel(temp->left, currentLevel + 1) && isSameLevel(temp->right, currentLevel + 1)) ;
     }
}
 
int main()
{
    //Add nodes to the binary tree
    root = createNode(1);
    root->left = createNode(2);
    root->right = createNode(3);
    root->left->left = createNode(4);
    root->right->left = createNode(5);
    root->right->right = createNode(6);
    
    //Checks whether all leaves of given binary tree is at same level
    if(isSameLevel(root, 1)) 
        printf("All leaves are at same level");
    else
        printf("All leaves are not at same level");
 
    return 0;
}

输出

All leaves are at same level

JAVA

public class LeafLevel {
    
    //Represent a 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;
    
    //It will store level of first encountered leaf 
    public static int level = 0;
  
    public LeafLevel(){
        root = null;
    }
  
    //isSameLevel() will check whether all leaves of the binary tree is at same level or not
    public boolean isSameLevel(Node temp, int currentLevel ) {
        
        //Check whether tree is empty
        if(root == null){
          System.out.println("Tree is empty");
          return true;
        }
        else {
            //Checks whether node is null
            if(temp==null)
                return true;
 
            if(temp.left == null && temp.right == null) {
                //If first leaf is encountered, set level to current level
                if(level == 0) {
                    level = currentLevel ;
                    return true;
                }
                //Checks whether the other leaves are at same level of that of first leaf
                else 
                   return (level == currentLevel) ;
             }
            
            //Checks for leaf node in left and right subtree recursively.
            return  (isSameLevel(temp.left, currentLevel + 1) && isSameLevel(temp.right, currentLevel + 1)) ;
         }
    }
  
    public static void main (String[] args) {
        
        LeafLevel bt = new LeafLevel();
        //Add nodes to the binary tree
        bt.root = new Node(1);
        bt.root.left = new Node(2);
        bt.root.right = new Node(3);
        bt.root.left.left = new Node(4);
        bt.root.right.left = new Node(5);
        bt.root.right.right = new Node(6);
    
        //Checks whether all leaves of given binary tree is at same level
        if(bt.isSameLevel(bt.root, 1)) 
            System.out.println("All leaves are at same level");
        else
            System.out.println("All leaves are not at same level");
  }
}

输出

All leaves are at same level

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 LeafLevel<T>{
            //Represent the root of binary tree
            public Node<T> root;
            
            //It will store level of first encountered leaf 
            public static int level = 0;
            
            public LeafLevel(){
                root = null;
            }
        
            //isSameLevel() will check whether all leaves of the binary tree is at same level or not
            public Boolean isSameLevel(Node<int> temp, int currentLevel ) {
 
                //Check whether tree is empty
                if(root == null){
                  Console.WriteLine("Tree is empty");
                  return true;
                }
                else {
                    //Checks whether node is null
                    if(temp==null)
                        return true;
 
                    if(temp.left == null && temp.right == null) {
                        //If first leaf is encountered, set level to current level
                        if(level == 0) {
                            level = currentLevel ;
                            return true;
                        }
                        //Checks whether the other leaves are at same level of that of first leaf
                        else 
                           return (level == currentLevel) ;
                     }
 
                    //Checks for leaf node in left and right subtree recursively.
                    return  (isSameLevel(temp.left, currentLevel + 1) && isSameLevel(temp.right, currentLevel + 1)) ;
                 }
            }
        }
        
        public static void Main()
        {
            LeafLevel<int> bt = new LeafLevel<int>();
            //Add nodes to the binary tree
            bt.root = new Node<int>(1);
            bt.root.left = new Node<int>(2);
            bt.root.right = new Node<int>(3);
            bt.root.left.left = new Node<int>(4);
            bt.root.right.left = new Node<int>(5);
            bt.root.right.right = new Node<int>(6);
 
            //Checks whether all leaves of given binary tree is at same level
            if(bt.isSameLevel(bt.root, 1)) 
                Console.WriteLine("All leaves are at same level");
            else
                Console.WriteLine("All leaves are not at same level");                
            }    
    }
}

输出

All leaves are at same level

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 LeafLevel{
    //Represent the root of binary tree
    public $root;
    //It will store level of first encountered leaf 
    public $level = 0;
    
    function __construct(){
        $this->root = NULL;
        $this->level = 0;
    }
    
    //isSameLevel() will check whether all leaves of the binary tree is at same level or not
    function isSameLevel($temp, $currentLevel ) {
        
        //Check whether tree is empty
        if($this->root == NULL){
            print("Tree is empty <br>");
              return true;
        }
        else {
            //Checks whether node is null
            if($temp == NULL)
                return true;
 
            if($temp->left == NULL && $temp->right == NULL) {
                //If first leaf is encountered, set level to current level
                if($this->level == 0) {
                    $this->level = $currentLevel ;
                    return true;
                }
                //Checks whether the other leaves are at same level of that of first leaf
                else 
                   return ($this->level == $currentLevel) ;
             }
            
            //Checks for leaf node in left and right subtree recursively.
            return  ($this->isSameLevel($temp->left, $currentLevel + 1) && $this->isSameLevel($temp->right, $currentLevel + 1)) ;
         }
    }
}
$bt = new LeafLevel();
//Add nodes to the binary tree
$bt->root= new Node(1);
$bt->root->left = new Node(2);
$bt->root->right = new Node(3);
$bt->root->left->left = new Node(4);
$bt->root->right->left = new Node(5);
$bt->root->right->right = new Node(6);
 
//Checks whether all leaves of given binary tree is at same level
if($bt->isSameLevel($bt->root, 1)) 
    print("All leaves are at same level");
else
    print("All leaves are not at same level");  
?>
</body>
</html>

输出

All leaves are at same level

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Q. 判断所有叶子节点是否在同一层级的程序。

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