📜  二叉树的混序遍历

📅  最后修改于: 2021-09-07 02:06:06             🧑  作者: Mango

给定一个由N 个节点组成的二叉树,任务是打印它的混合顺序遍历。

例子:

方法:
可能的混合顺序遍历如下:

中序-预序混合遍历

inorder() 的步骤将是:

  • 左子树上执行先序遍历。
  • 打印当前节点
  • 右子树上执行先序遍历

preorder() 的步骤将是:

  • 打印当前节点
  • 在左子树(root->left)上执行中序遍历。
  • 右子树执行中序遍历

下面是上述方法的实现:

C++
// C++ Program to implement
// the above approach
#include 
using namespace std;
 
void inOrder(struct node* root);
void preOrder(struct node* root);
 
// Node structure
struct node {
    char data;
    struct node *left, *right;
};
 
// Creates and initialize a new node
struct node* newNode(char ch)
{
    // Allocating memory to a new node
    struct node* n = (struct node*)
        malloc(sizeof(struct node));
    n->data = ch;
    n->left = NULL;
    n->right = NULL;
    return n;
}
 
// Perform Inorder Traversal
void inOrder(struct node* root)
{
    if (root) {
        preOrder(root->left);
        cout << root->data << " ";
        preOrder(root->right);
    }
}
 
// Perform Preorder Traversal
void preOrder(struct node* root)
{
    if (root) {
        cout << root->data << " ";
        inOrder(root->left);
        inOrder(root->right);
    }
}
 
// Driver Code
int main()
{
    // Given tree
    struct node* root = newNode('1');
    root->left = newNode('7');
    root->right = newNode('3');
    root->left->left = newNode('4');
    root->left->right = newNode('5');
    root->right->left = newNode('6');
 
    // Perform Mix order traversal
    inOrder(root);
 
    return 0;
}


Java
// Java program to implement
// the above approach
import java.util.*;
 
class GFG{
 
// Node structure
static class node
{
    char data;
    node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
     
    // Allocating memory to a new node
    node n = new node();
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Inorder Traversal
static void inOrder(node root)
{
    if (root != null)
    {
        preOrder(root.left);
        System.out.print(root.data + " ");
        preOrder(root.right);
    }
}
 
// Perform Preorder Traversal
static void preOrder(node root)
{
    if (root != null)
    {
        System.out.print(root.data + " ");
        inOrder(root.left);
        inOrder(root.right);
    }
}
 
// Driver Code
public static void main(String[] args)
{
     
    // Given tree
    node root = newNode('1');
    root.left = newNode('7');
    root.right = newNode('3');
    root.left.left = newNode('4');
    root.left.right = newNode('5');
    root.right.left = newNode('6');
 
    // Perform Mix order traversal
    inOrder(root);
}
}
 
// This code is contributed by 29AjayKumar


C#
// C# program to implement
// the above approach
using System;
class GFG{
 
// Node structure
class node
{
    public char data;
    public node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
     
    // Allocating memory to a new node
    node n = new node();
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Inorder Traversal
static void inOrder(node root)
{
    if (root != null)
    {
        preOrder(root.left);
        Console.Write(root.data + " ");
        preOrder(root.right);
    }
}
 
// Perform Preorder Traversal
static void preOrder(node root)
{
    if (root != null)
    {
        Console.Write(root.data + " ");
        inOrder(root.left);
        inOrder(root.right);
    }
}
 
// Driver Code
public static void Main(String[] args)
{
     
    // Given tree
    node root = newNode('1');
    root.left = newNode('7');
    root.right = newNode('3');
    root.left.left = newNode('4');
    root.left.right = newNode('5');
    root.right.left = newNode('6');
 
    // Perform Mix order traversal
    inOrder(root);
}
}
 
// This code is contributed by sapnasingh4991


C++
// C++ Program to implement
// the above approach
#include 
using namespace std;
 
void preOrder(struct node* root);
void postOrder(struct node* root);
 
// Node structure
struct node {
    char data;
    struct node *left, *right;
};
 
// Creates and initialize a new node
struct node* newNode(char ch)
{
    // Allocating memory to a new node
    struct node* n = (struct node*)
        malloc(sizeof(struct node));
    n->data = ch;
    n->left = NULL;
    n->right = NULL;
    return n;
}
 
// Perform Preorder Traversal
void preOrder(struct node* root)
{
    if (root) {
        cout << root->data << " ";
        postOrder(root->left);
        postOrder(root->right);
    }
}
 
// Perform Postorder Traversal
void postOrder(struct node* root)
{
    if (root) {
        preOrder(root->left);
        preOrder(root->right);
        cout << root->data << " ";
    }
}
 
// Driver Code
int main()
{
    // Given tree
    struct node* root = newNode('A');
    root->left = newNode('B');
    root->right = newNode('C');
    root->left->left = newNode('F');
    root->left->right = newNode('D');
    root->right->right = newNode('E');
 
    // Starting Mix order traversal
    preOrder(root);
 
    return 0;
}


Java
// Java Program to implement
// the above approach
class GFG{
 
// Node structure
static class node
{
    char data;
    node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
    // Allocating memory to a new node
    node n = new node();
      
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Preorder Traversal
static void preOrder(node root)
{
    if (root != null)
    {
        System.out.print(root.data + " ");
        postOrder(root.left);
        postOrder(root.right);
    }
}
 
// Perform Postorder Traversal
static void postOrder(node root)
{
    if (root != null)
    {
        preOrder(root.left);
        preOrder(root.right);
        System.out.print(root.data + " ");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    // Given tree
    node root = newNode('A');
    root.left = newNode('B');
    root.right = newNode('C');
    root.left.left = newNode('F');
    root.left.right = newNode('D');
    root.right.right = newNode('E');
 
    // Starting Mix order traversal
    preOrder(root);
}
}
 
// This code is contributed by Rajput-Ji


C#
// C# Program to implement
// the above approach
using System;
class GFG{
 
// Node structure
class node
{
    public char data;
    public node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
    // Allocating memory to a new node
    node n = new node();
      
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Preorder Traversal
static void preOrder(node root)
{
    if (root != null)
    {
        Console.Write(root.data + " ");
        postOrder(root.left);
        postOrder(root.right);
    }
}
 
// Perform Postorder Traversal
static void postOrder(node root)
{
    if (root != null)
    {
        preOrder(root.left);
        preOrder(root.right);
        Console.Write(root.data + " ");
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    // Given tree
    node root = newNode('A');
    root.left = newNode('B');
    root.right = newNode('C');
    root.left.left = newNode('F');
    root.left.right = newNode('D');
    root.right.right = newNode('E');
 
    // Starting Mix order traversal
    preOrder(root);
}
}
 
// This code is contributed by Rohit_ranjan


C++
// C++ Program to implement
// the above approach
#include 
using namespace std;
 
void inOrder(struct node* root);
void postOrder(struct node* root);
 
// Node structure
struct node {
    char data;
    struct node *left, *right;
};
 
// Creates and initialize a new node
struct node* newNode(char ch)
{
 
    // Allocating memory to a new node
    struct node* n = (struct node*)
        malloc(sizeof(struct node));
    n->data = ch;
    n->left = NULL;
    n->right = NULL;
    return n;
}
 
// Perform Inorder Traversal
void inOrder(struct node* root)
{
    if (root) {
        postOrder(root->left);
        cout << root->data << " ";
        postOrder(root->right);
    }
}
 
// Perform Postorder Traversal
void postOrder(struct node* root)
{
    if (root) {
        inOrder(root->left);
        inOrder(root->right);
        cout << root->data << " ";
    }
}
 
// Driver Code
int main()
{
    // Given tree
    struct node* root = newNode('A');
    root->left = newNode('B');
    root->right = newNode('C');
    root->left->left = newNode('F');
    root->left->right = newNode('D');
    root->right->right = newNode('E');
 
    // Starting Mix order traversal
    inOrder(root);
 
    return 0;
}


Java
// Java Program to implement
// the above approach
import java.util.*;
class GFG{
 
// Node structure
static class node
{
    char data;
    node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
 
    // Allocating memory to a new node
    node n = new node();
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Inorder Traversal
static void inOrder(node root)
{
    if (root != null)
    {
        postOrder(root.left);
        System.out.print(root.data + " ");
        postOrder(root.right);
    }
}
 
// Perform Postorder Traversal
static void postOrder(node root)
{
    if (root != null)
    {
        inOrder(root.left);
        inOrder(root.right);
        System.out.print(root.data + " ");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    // Given tree
    node root = newNode('A');
    root.left = newNode('B');
    root.right = newNode('C');
    root.left.left = newNode('F');
    root.left.right = newNode('D');
    root.right.right = newNode('E');
 
    // Starting Mix order traversal
    inOrder(root);
}
}
 
// This code is contributed by sapnasingh4991


C#
// C# Program to implement
// the above approach
using System;
class GFG{
 
// Node structure
class node
{
    public char data;
    public node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
 
    // Allocating memory to a new node
    node n = new node();
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Inorder Traversal
static void inOrder(node root)
{
    if (root != null)
    {
        postOrder(root.left);
        Console.Write(root.data + " ");
        postOrder(root.right);
    }
}
 
// Perform Postorder Traversal
static void postOrder(node root)
{
    if (root != null)
    {
        inOrder(root.left);
        inOrder(root.right);
        Console.Write(root.data + " ");
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    // Given tree
    node root = newNode('A');
    root.left = newNode('B');
    root.right = newNode('C');
    root.left.left = newNode('F');
    root.left.right = newNode('D');
    root.right.right = newNode('E');
 
    // Starting Mix order traversal
    inOrder(root);
}
}
 
// This code is contributed by sapnasingh4991


输出:
7 4 5 1 3 6

前序-后序混合遍历

preorder() 的步骤如下:

  • 打印当前节点
  • 左子树执行后序遍历。
  • 右子树上执行后序遍历

postorder() 的步骤如下:

  • 左子树执行前序遍历。
  • 右子树执行前序遍历。
  • 打印当前节点。

下面是上述方法的实现:

C++

// C++ Program to implement
// the above approach
#include 
using namespace std;
 
void preOrder(struct node* root);
void postOrder(struct node* root);
 
// Node structure
struct node {
    char data;
    struct node *left, *right;
};
 
// Creates and initialize a new node
struct node* newNode(char ch)
{
    // Allocating memory to a new node
    struct node* n = (struct node*)
        malloc(sizeof(struct node));
    n->data = ch;
    n->left = NULL;
    n->right = NULL;
    return n;
}
 
// Perform Preorder Traversal
void preOrder(struct node* root)
{
    if (root) {
        cout << root->data << " ";
        postOrder(root->left);
        postOrder(root->right);
    }
}
 
// Perform Postorder Traversal
void postOrder(struct node* root)
{
    if (root) {
        preOrder(root->left);
        preOrder(root->right);
        cout << root->data << " ";
    }
}
 
// Driver Code
int main()
{
    // Given tree
    struct node* root = newNode('A');
    root->left = newNode('B');
    root->right = newNode('C');
    root->left->left = newNode('F');
    root->left->right = newNode('D');
    root->right->right = newNode('E');
 
    // Starting Mix order traversal
    preOrder(root);
 
    return 0;
}

Java

// Java Program to implement
// the above approach
class GFG{
 
// Node structure
static class node
{
    char data;
    node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
    // Allocating memory to a new node
    node n = new node();
      
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Preorder Traversal
static void preOrder(node root)
{
    if (root != null)
    {
        System.out.print(root.data + " ");
        postOrder(root.left);
        postOrder(root.right);
    }
}
 
// Perform Postorder Traversal
static void postOrder(node root)
{
    if (root != null)
    {
        preOrder(root.left);
        preOrder(root.right);
        System.out.print(root.data + " ");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    // Given tree
    node root = newNode('A');
    root.left = newNode('B');
    root.right = newNode('C');
    root.left.left = newNode('F');
    root.left.right = newNode('D');
    root.right.right = newNode('E');
 
    // Starting Mix order traversal
    preOrder(root);
}
}
 
// This code is contributed by Rajput-Ji

C#

// C# Program to implement
// the above approach
using System;
class GFG{
 
// Node structure
class node
{
    public char data;
    public node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
    // Allocating memory to a new node
    node n = new node();
      
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Preorder Traversal
static void preOrder(node root)
{
    if (root != null)
    {
        Console.Write(root.data + " ");
        postOrder(root.left);
        postOrder(root.right);
    }
}
 
// Perform Postorder Traversal
static void postOrder(node root)
{
    if (root != null)
    {
        preOrder(root.left);
        preOrder(root.right);
        Console.Write(root.data + " ");
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    // Given tree
    node root = newNode('A');
    root.left = newNode('B');
    root.right = newNode('C');
    root.left.left = newNode('F');
    root.left.right = newNode('D');
    root.right.right = newNode('E');
 
    // Starting Mix order traversal
    preOrder(root);
}
}
 
// This code is contributed by Rohit_ranjan
输出:
A F D B E C

中序-后序混合遍历

inorder() 的步骤如下:

  • 左子树上执行后序遍历
  • 打印当前节点
  • 在右子树上执行后序遍历

postorder() 的步骤将是:

  • 左子树上执行中序遍历
  • 右子树执行中序遍历
  • 打印当前节点

下面是上述方法的实现:

C++

// C++ Program to implement
// the above approach
#include 
using namespace std;
 
void inOrder(struct node* root);
void postOrder(struct node* root);
 
// Node structure
struct node {
    char data;
    struct node *left, *right;
};
 
// Creates and initialize a new node
struct node* newNode(char ch)
{
 
    // Allocating memory to a new node
    struct node* n = (struct node*)
        malloc(sizeof(struct node));
    n->data = ch;
    n->left = NULL;
    n->right = NULL;
    return n;
}
 
// Perform Inorder Traversal
void inOrder(struct node* root)
{
    if (root) {
        postOrder(root->left);
        cout << root->data << " ";
        postOrder(root->right);
    }
}
 
// Perform Postorder Traversal
void postOrder(struct node* root)
{
    if (root) {
        inOrder(root->left);
        inOrder(root->right);
        cout << root->data << " ";
    }
}
 
// Driver Code
int main()
{
    // Given tree
    struct node* root = newNode('A');
    root->left = newNode('B');
    root->right = newNode('C');
    root->left->left = newNode('F');
    root->left->right = newNode('D');
    root->right->right = newNode('E');
 
    // Starting Mix order traversal
    inOrder(root);
 
    return 0;
}

Java

// Java Program to implement
// the above approach
import java.util.*;
class GFG{
 
// Node structure
static class node
{
    char data;
    node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
 
    // Allocating memory to a new node
    node n = new node();
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Inorder Traversal
static void inOrder(node root)
{
    if (root != null)
    {
        postOrder(root.left);
        System.out.print(root.data + " ");
        postOrder(root.right);
    }
}
 
// Perform Postorder Traversal
static void postOrder(node root)
{
    if (root != null)
    {
        inOrder(root.left);
        inOrder(root.right);
        System.out.print(root.data + " ");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    // Given tree
    node root = newNode('A');
    root.left = newNode('B');
    root.right = newNode('C');
    root.left.left = newNode('F');
    root.left.right = newNode('D');
    root.right.right = newNode('E');
 
    // Starting Mix order traversal
    inOrder(root);
}
}
 
// This code is contributed by sapnasingh4991

C#

// C# Program to implement
// the above approach
using System;
class GFG{
 
// Node structure
class node
{
    public char data;
    public node left, right;
};
 
// Creates and initialize a new node
static node newNode(char ch)
{
 
    // Allocating memory to a new node
    node n = new node();
    n.data = ch;
    n.left = null;
    n.right = null;
    return n;
}
 
// Perform Inorder Traversal
static void inOrder(node root)
{
    if (root != null)
    {
        postOrder(root.left);
        Console.Write(root.data + " ");
        postOrder(root.right);
    }
}
 
// Perform Postorder Traversal
static void postOrder(node root)
{
    if (root != null)
    {
        inOrder(root.left);
        inOrder(root.right);
        Console.Write(root.data + " ");
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    // Given tree
    node root = newNode('A');
    root.left = newNode('B');
    root.right = newNode('C');
    root.left.left = newNode('F');
    root.left.right = newNode('D');
    root.right.right = newNode('E');
 
    // Starting Mix order traversal
    inOrder(root);
}
}
 
// This code is contributed by sapnasingh4991
输出:
F D B A E C

时间复杂度: O(N)
辅助空间: O(N)

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