给定一个整数数组，任务是使用递归以级别顺序方式构造一个二叉树。
例子
Given an array arr[] = {15, 10, 20, 8, 12, 16, 25}
方法：
想法是跟踪左子树和右子树中子节点的数量，然后根据这些计数做出决定。
- 当左子树和右子树中的子节点数相等时，则必须通过在二叉树中创建新级别将节点插入左子树。
- 当左子树中的子节点数大于右子树中的子节点数时，有两种情况。
- 当左子树是完美二叉树时，则将节点插入到右子树中。
- 当左子树不是完美二叉树时，将节点插入到左子树中。
具有 n 级的完美二叉树有 2 (n-1) 个节点，所有叶节点都在同一级别。
下面是上述方法的实现
C++
// C++ implementation to construct
// Binary Tree in level order fashion
#include
using namespace std;
// Structure of the Node of Binary tree
// with count of Children nodes in
// left sub-tree and right sub-tree.
struct Node {
int data;
int rcount;
int lcount;
struct Node* left;
struct Node* right;
};
// Function to check whether the given
// Binary tree is a perfect binary tree
// using the no. of nodes in tree.
bool isPBT(int count)
{
count = count + 1;
// Loop to check the count is in
// the form of 2^(n-1)
while (count % 2 == 0)
count = count / 2;
if (count == 1)
return true;
else
return false;
}
// Function to create a new Node
struct Node* newNode(int data)
{
struct Node* temp =
(struct Node*)malloc(
sizeof(struct Node)
);
temp->data = data;
temp->right = NULL;
temp->left = NULL;
temp->rcount = 0;
temp->lcount = 0;
}
// Recursive function to insert
// elements in a binary tree
struct Node* insert(struct Node* root,
int data)
{
// Condition when root is NULL
if (root == NULL) {
struct Node* n = newNode(data);
return n;
}
// Condition when count of left sub-tree
// nodes is equal to the count
// of right sub-tree nodes
if (root->rcount == root->lcount) {
root->left = insert(root->left, data);
root->lcount += 1;
}
// Condition when count of left sub-tree
// nodes is greater than
// the right sub-tree nodes
else if (root->rcount < root->lcount) {
// Condition when left Sub-tree is
// Perfect Binary Tree then Insert
// in right sub-tree.
if (isPBT(root->lcount)) {
root->right = insert(root->right, data);
root->rcount += 1;
}
// If Left Sub-tree is not Perfect
// Binary Tree then Insert in left sub-tree
else {
root->left = insert(root->left, data);
root->lcount += 1;
}
}
return root;
}
// Function for inorder Traversal of tree.
void inorder(struct Node* root)
{
if (root != NULL) {
inorder(root->left);
cout << root->data << " ";
inorder(root->right);
}
}
// Driver Code
int main()
{
int arr[] = { 8, 6, 7, 12, 5, 1, 9 };
int size = sizeof(arr) / sizeof(int);
struct Node* root = NULL;
// Loop to insert nodes in
// Binary Tree in level order
for (int i = 0; i < size; i++)
root = insert(root, arr[i]);
inorder(root);
return 0;
} Java
// Java implementation to construct
// Binary Tree in level order fashion
class Node {
int data;
int rcount;
int lcount;
Node left;
Node right;
Node(int data)
{
this.data = data;
this.rcount = this.lcount = 0;
this.left = this.right = null;
}
// Function for inorder Traversal of tree.
static void inorder(Node root)
{
if (root != null) {
inorder(root.left);
System.out.print(root.data + " ");
inorder(root.right);
}
}
// Function to check whether the given
// Binary tree is a perfect binary tree
// using the no. of nodes in tree.
static boolean isPBT(int count)
{
count = count + 1;
// Loop to check the count is in
// the form of 2^(n-1)
while (count % 2 == 0)
count = count / 2;
if (count == 1)
return true;
else
return false;
}
// Recursive function to insert
// elements in a binary tree
static Node insert(Node root, int data)
{
// Condition when root is NULL
if (root == null) {
Node n = new Node(data);
return n;
}
// Condition when count of left sub-tree
// nodes is equal to the count
// of right sub-tree nodes
if (root.rcount == root.lcount) {
root.left = insert(root.left, data);
root.lcount += 1;
}
// Condition when count of left sub-tree
// nodes is greater than
// the right sub-tree nodes
else if (root.rcount < root.lcount) {
// Condition when left Sub-tree is
// Perfect Binary Tree then Insert
// in right sub-tree.
if (isPBT(root.lcount)) {
root.right = insert(root.right, data);
root.rcount += 1;
}
// If Left Sub-tree is not Perfect
// Binary Tree then Insert in left sub-tree
else {
root.left = insert(root.left, data);
root.lcount += 1;
}
}
return root;
}
// Driver Code
public static void main(String args[])
{
int arr[] = { 8, 6, 7, 12, 5, 1, 9 };
int size = 7;
Node root = null;
// Loop to insert nodes in
// Binary Tree in level order Traversal
for (int i = 0; i < size; i++)
root = insert(root, arr[i]);
inorder(root);
}
}Python3
# Python3 implementation to construct
# Binary Tree in level order fashion
# Structure of the Node of Binary tree
# with count of Children nodes in
# left sub-tree and right sub-tree.
class Node:
def __init__(self, data):
self.data = data
self.rcount = 0
self.lcount = 0
self.left = None
self.right = None
# Function to check whether the given
# Binary tree is a perfect binary tree
# using the no. of nodes in tree.
def isPBT(count: int) -> bool:
count = count + 1
# Loop to check the count is in
# the form of 2^(n-1)
while (count % 2 == 0):
count = count / 2
if (count == 1):
return True
else:
return False
# Recursive function to insert
# elements in a binary tree
def insert(root: Node, data: int) -> Node:
# Condition when root is NULL
if (root is None):
n = Node(data)
return n
# Condition when count of left sub-tree
# nodes is equal to the count
# of right sub-tree nodes
if (root.rcount == root.lcount):
root.left = insert(root.left, data)
root.lcount += 1
# Condition when count of left sub-tree
# nodes is greater than
# the right sub-tree nodes
elif (root.rcount < root.lcount):
# Condition when left Sub-tree is
# Perfect Binary Tree then Insert
# in right sub-tree.
if (isPBT(root.lcount)):
root.right = insert(root.right, data)
root.rcount += 1
# If Left Sub-tree is not Perfect
# Binary Tree then Insert in left sub-tree
else:
root.left = insert(root.left, data)
root.lcount += 1
return root
# Function for inorder Traversal of tree.
def inorder(root: Node) -> None:
if root != None:
inorder(root.left)
print(root.data, end = " ")
inorder(root.right)
# Driver Code
if __name__ == "__main__":
arr = [ 8, 6, 7, 12, 5, 1, 9 ]
size = len(arr)
root = None
# Loop to insert nodes in
# Binary Tree in level order
for i in range(size):
root = insert(root, arr[i])
inorder(root)
# This code is contributed by sanjeev2552C#
// C# implementation to construct
// Binary Tree in level order fashion
using System;
class Node {
public int data;
public int rcount;
public int lcount;
public Node left;
public Node right;
public Node(int data)
{
this.data = data;
this.rcount = this.lcount = 0;
this.left = this.right = null;
}
// Function for inorder Traversal of tree.
static void inorder(Node root)
{
if (root != null) {
inorder(root.left);
Console.Write(root.data + " ");
inorder(root.right);
}
}
// Function to check whether the given
// Binary tree is a perfect binary tree
// using the no. of nodes in tree.
static bool isPBT(int count)
{
count = count + 1;
// Loop to check the count is in
// the form of 2^(n-1)
while (count % 2 == 0)
count = count / 2;
if (count == 1)
return true;
else
return false;
}
// Recursive function to insert
// elements in a binary tree
static Node insert(Node root, int data)
{
// Condition when root is NULL
if (root == null) {
Node n = new Node(data);
return n;
}
// Condition when count of left sub-tree
// nodes is equal to the count
// of right sub-tree nodes
if (root.rcount == root.lcount) {
root.left = insert(root.left, data);
root.lcount += 1;
}
// Condition when count of left sub-tree
// nodes is greater than
// the right sub-tree nodes
else if (root.rcount < root.lcount) {
// Condition when left Sub-tree is
// Perfect Binary Tree then Insert
// in right sub-tree.
if (isPBT(root.lcount)) {
root.right = insert(root.right, data);
root.rcount += 1;
}
// If Left Sub-tree is not Perfect
// Binary Tree then Insert in left sub-tree
else {
root.left = insert(root.left, data);
root.lcount += 1;
}
}
return root;
}
// Driver Code
public static void Main(String []args)
{
int []arr = { 8, 6, 7, 12, 5, 1, 9 };
int size = 7;
Node root = null;
// Loop to insert nodes in
// Binary Tree in level order Traversal
for (int i = 0; i < size; i++)
root = insert(root, arr[i]);
inorder(root);
}
}
// This code is contributed by 29AjayKumar输出：
12 6 5 8 1 7 9
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