给定一个二叉树，任务是计算给定二叉树中斐波那契路径的数量。
Fibonacci Path is a path which contains all nodes in root to leaf path are terms of Fibonacci series.
例子：
Input:
0
/ \
1 1
/ \ / \
1 10 70 1
/ \
81 2
Output: 2
Explanation:
There are 2 Fibonacci path for
the above Binary Tree, for x = 3,
Path 1: 0 1 1
Path 2: 0 1 1 2
Input:
8
/ \
4 81
/ \ / \
3 2 70 243
/ \
81 909
Output: 0方法：想法是使用预排序树遍历。在对给定的二叉树进行遍历时，请执行以下操作：
- 首先计算二叉树的高度。
- 现在创建一个长度等于树的高度的向量，以使其包含斐波那契数。
- 如果第i级节点的当前值不等于斐波那契数列的第i项，或者指针变为NULL，则返回计数。
- 如果当前节点是叶节点，则将计数增加1。
- 递归调用与更新的计左和右子树。
- 在所有递归调用之后，count的值是给定二叉树的斐波那契路径数。
下面是上述方法的实现：
C++
// C++ program to count all of
// Fibonacci paths in a Binary tree
#include
using namespace std;
// Vector to store the fibonacci series
vector fib;
// Binary Tree Node
struct node {
struct node* left;
int data;
struct node* right;
};
// Function to create a new tree node
node* newNode(int data)
{
node* temp = new node;
temp->data = data;
temp->left = NULL;
temp->right = NULL;
return temp;
}
// Function to find the height
// of the given tree
int height(node* root)
{
int ht = 0;
if (root == NULL)
return 0;
return (max(height(root->left),
height(root->right))
+ 1);
}
// Function to make fibonacci series
// upto n terms
void FibonacciSeries(int n)
{
fib.push_back(0);
fib.push_back(1);
for (int i = 2; i < n; i++)
fib.push_back(fib[i - 1]
+ fib[i - 2]);
}
// Preorder Utility function to count
// exponent path in a given Binary tree
int CountPathUtil(node* root,
int i, int count)
{
// Base Condition, when node pointer
// becomes null or node value is not
// a number of pow(x, y )
if (root == NULL
|| !(fib[i] == root->data)) {
return count;
}
// Increment count when
// encounter leaf node
if (!root->left
&& !root->right) {
count++;
}
// Left recursive call
// save the value of count
count = CountPathUtil(
root->left, i + 1, count);
// Right reursive call and
// return value of count
return CountPathUtil(
root->right, i + 1, count);
}
// Function to find whether
// fibonacci path exists or not
void CountPath(node* root)
{
// To find the height
int ht = height(root);
// Making fibonaci series
// upto ht terms
FibonacciSeries(ht);
cout << CountPathUtil(root, 0, 0);
}
// Driver code
int main()
{
// Create binary tree
node* root = newNode(0);
root->left = newNode(1);
root->right = newNode(1);
root->left->left = newNode(1);
root->left->right = newNode(4);
root->right->right = newNode(1);
root->right->right->left = newNode(2);
// Function Call
CountPath(root);
return 0;
} Java
// Java program to count all of
// Fibonacci paths in a Binary tree
import java.util.*;
class GFG{
// Vector to store the fibonacci series
static Vector fib = new Vector();
// Binary Tree Node
static class node {
node left;
int data;
node right;
};
// Function to create a new tree node
static node newNode(int data)
{
node temp = new node();
temp.data = data;
temp.left = null;
temp.right = null;
return temp;
}
// Function to find the height
// of the given tree
static int height(node root)
{
if (root == null)
return 0;
return (Math.max(height(root.left),
height(root.right))
+ 1);
}
// Function to make fibonacci series
// upto n terms
static void FibonacciSeries(int n)
{
fib.add(0);
fib.add(1);
for (int i = 2; i < n; i++)
fib.add(fib.get(i - 1)
+ fib.get(i - 2));
}
// Preorder Utility function to count
// exponent path in a given Binary tree
static int CountPathUtil(node root,
int i, int count)
{
// Base Condition, when node pointer
// becomes null or node value is not
// a number of Math.pow(x, y )
if (root == null
|| !(fib.get(i) == root.data)) {
return count;
}
// Increment count when
// encounter leaf node
if (root.left != null
&& root.right != null) {
count++;
}
// Left recursive call
// save the value of count
count = CountPathUtil(
root.left, i + 1, count);
// Right reursive call and
// return value of count
return CountPathUtil(
root.right, i + 1, count);
}
// Function to find whether
// fibonacci path exists or not
static void CountPath(node root)
{
// To find the height
int ht = height(root);
// Making fibonaci series
// upto ht terms
FibonacciSeries(ht);
System.out.print(CountPathUtil(root, 0, 0));
}
// Driver code
public static void main(String[] args)
{
// Create binary tree
node root = newNode(0);
root.left = newNode(1);
root.right = newNode(1);
root.left.left = newNode(1);
root.left.right = newNode(4);
root.right.right = newNode(1);
root.right.right.left = newNode(2);
// Function Call
CountPath(root);
}
}
// This code is contributed by 29AjayKumar Python3
# Python3 program to count all of
# Fibonacci paths in a Binary tree
# Vector to store the fibonacci series
fib = []
# Binary Tree Node
class node:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# Function to create a new tree node
def newNode(data):
temp = node(data)
return temp
# Function to find the height
# of the given tree
def height(root):
ht = 0
if (root == None):
return 0
return (max(height(root.left),
height(root.right)) + 1)
# Function to make fibonacci series
# upto n terms
def FibonacciSeries(n):
fib.append(0)
fib.append(1)
for i in range(2, n):
fib.append(fib[i - 1] + fib[i - 2])
# Preorder Utility function to count
# exponent path in a given Binary tree
def CountPathUtil(root, i, count):
# Base Condition, when node pointer
# becomes null or node value is not
# a number of pow(x, y )
if (root == None or not (fib[i] == root.data)):
return count
# Increment count when
# encounter leaf node
if (not root.left and not root.right):
count += 1
# Left recursive call
# save the value of count
count = CountPathUtil(root.left, i + 1, count)
# Right reursive call and
# return value of count
return CountPathUtil(root.right, i + 1, count)
# Function to find whether
# fibonacci path exists or not
def CountPath(root):
# To find the height
ht = height(root)
# Making fibonaci series
# upto ht terms
FibonacciSeries(ht)
print(CountPathUtil(root, 0, 0))
# Driver code
if __name__=='__main__':
# Create binary tree
root = newNode(0)
root.left = newNode(1)
root.right = newNode(1)
root.left.left = newNode(1)
root.left.right = newNode(4)
root.right.right = newNode(1)
root.right.right.left = newNode(2)
# Function Call
CountPath(root)
# This code is contributed by rutvik_56C#
// C# program to count all of
// Fibonacci paths in a Binary tree
using System;
using System.Collections.Generic;
class GFG{
// List to store the fibonacci series
static List fib = new List();
// Binary Tree Node
class node {
public node left;
public int data;
public node right;
};
// Function to create a new tree node
static node newNode(int data)
{
node temp = new node();
temp.data = data;
temp.left = null;
temp.right = null;
return temp;
}
// Function to find the height
// of the given tree
static int height(node root)
{
if (root == null)
return 0;
return (Math.Max(height(root.left),
height(root.right))
+ 1);
}
// Function to make fibonacci series
// upto n terms
static void FibonacciSeries(int n)
{
fib.Add(0);
fib.Add(1);
for (int i = 2; i < n; i++)
fib.Add(fib[i - 1]
+ fib[i - 2]);
}
// Preorder Utility function to count
// exponent path in a given Binary tree
static int CountPathUtil(node root,
int i, int count)
{
// Base Condition, when node pointer
// becomes null or node value is not
// a number of Math.Pow(x, y)
if (root == null
|| !(fib[i] == root.data)) {
return count;
}
// Increment count when
// encounter leaf node
if (root.left != null
&& root.right != null) {
count++;
}
// Left recursive call
// save the value of count
count = CountPathUtil(
root.left, i + 1, count);
// Right reursive call and
// return value of count
return CountPathUtil(
root.right, i + 1, count);
}
// Function to find whether
// fibonacci path exists or not
static void CountPath(node root)
{
// To find the height
int ht = height(root);
// Making fibonaci series
// upto ht terms
FibonacciSeries(ht);
Console.Write(CountPathUtil(root, 0, 0));
}
// Driver code
public static void Main(String[] args)
{
// Create binary tree
node root = newNode(0);
root.left = newNode(1);
root.right = newNode(1);
root.left.left = newNode(1);
root.left.right = newNode(4);
root.right.right = newNode(1);
root.right.right.left = newNode(2);
// Function Call
CountPath(root);
}
}
// This code is contributed by Princi Singh 输出：
2