检查数组中斐波那契元素的总和是否为斐波那契数

给定一个包含N 个元素的数组arr[] ，任务是检查数组的斐波那契元素之和是否为斐波那契数。
例子：

Input: arr[] = {2, 3, 7, 11} 
Output: Yes 
Explanation: 
As there are two Fibonacci numbers in the array i.e. 2 and 3. 
So, the sum of Fibonacci numbers is 2 + 3 = 5 and 5 is also a Fibonacci number. 
Input: arr[] = {1, 2, 3} 
Output: No 
 

方法：这个想法是使用散列来预先计算并存储最大数量的斐波那契节点，以使检查变得容易和高效(在 O(1) 时间内)。
预计算后，迭代数组的所有元素。如果数字是斐波那契数，则将其添加到总和中。最后，检查总和是否为斐波那契数。
下面是上述方法的实现：

C++

// C++ program to check whether the
// sum of fibonacci elements of the
// array is a Fibonacci number or not
 
#include 
#define ll long long int
#define MAX 100005
using namespace std;
 
// Hash to store the Fibonacci
// numbers up to Max
set fibonacci;
 
// Function to create the hash table
// to check Fibonacci numbers
void createHash()
{
    // Inserting the first two Fibonacci
    // numbers into the hash
    int prev = 0, curr = 1;
    fibonacci.insert(prev);
    fibonacci.insert(curr);
 
    // Add the remaining Fibonacci numbers
    // based on the previous two numbers
    while (curr <= MAX) {
        int temp = curr + prev;
        fibonacci.insert(temp);
        prev = curr;
        curr = temp;
    }
}
 
// Function to check if the sum of
// Fibonacci numbers is Fibonacci or not
bool checkArray(int arr[], int n)
{
    // Find the sum of
    // all Fibonacci numbers
    ll sum = 0;
 
    // Iterating through the array
    for (int i = 0; i < n; i++)
        if (fibonacci.find(arr[i])
            != fibonacci.end())
            sum += arr[i];
 
    // If the sum is Fibonacci
    // then return true
    if (fibonacci.find(sum)
        != fibonacci.end())
        return true;
 
    return false;
}
 
// Driver code
int main()
{
    // array of elements
    int arr[] = { 1, 2, 4, 8, 2 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    // Creating a set containing
    // all fibonacci numbers
    createHash();
 
    if (checkArray(arr, n))
        cout << "Yes";
    else
        cout << "No";
 
    return 0;
}

Java

// Java program to check whether the
// sum of fibonacci elements of the
// array is a Fibonacci number or not
import java.util.*;
 
class GFG{
 
static final int MAX = 100005;
 
// Hash to store the Fibonacci
// numbers up to Max
static HashSet fibonacci = new HashSet();
  
// Function to create the hash table
// to check Fibonacci numbers
static void createHash()
{
    // Inserting the first two Fibonacci
    // numbers into the hash
    int prev = 0, curr = 1;
    fibonacci.add(prev);
    fibonacci.add(curr);
  
    // Add the remaining Fibonacci numbers
    // based on the previous two numbers
    while (curr <= MAX) {
        int temp = curr + prev;
        fibonacci.add(temp);
        prev = curr;
        curr = temp;
    }
}
  
// Function to check if the sum of
// Fibonacci numbers is Fibonacci or not
static boolean checkArray(int arr[], int n)
{
    // Find the sum of
    // all Fibonacci numbers
    int sum = 0;
  
    // Iterating through the array
    for (int i = 0; i < n; i++)
        if (fibonacci.contains(arr[i]))
            sum += arr[i];
  
    // If the sum is Fibonacci
    // then return true
    if (fibonacci.contains(sum))
        return true;
  
    return false;
}
  
// Driver code
public static void main(String[] args)
{
    // array of elements
    int arr[] = { 1, 2, 4, 8, 2 };
    int n = arr.length;
  
    // Creating a set containing
    // all fibonacci numbers
    createHash();
  
    if (checkArray(arr, n))
        System.out.print("Yes");
    else
        System.out.print("No");
}
}
 
// This code is contributed by Rajput-Ji

Python3

# Python 3 program to check whether the
# sum of fibonacci elements of the
# array is a Fibonacci number or not
  
MAX = 100005
  
# Hash to store the Fibonacci
# numbers up to Max
fibonacci = set()
  
# Function to create the hash table
# to check Fibonacci numbers
def createHash():
 
    global fibonacci
     
    # Inserting the first two Fibonacci
    # numbers into the hash
    prev , curr = 0, 1
    fibonacci.add(prev)
    fibonacci.add(curr)
  
    # Add the remaining Fibonacci numbers
    # based on the previous two numbers
    while (curr <= MAX):
        temp = curr + prev
        if temp <= MAX:
            fibonacci.add(temp)
        prev = curr
        curr = temp
  
# Function to check if the sum of
# Fibonacci numbers is Fibonacci or not
def checkArray(arr, n):
 
    # Find the sum of
    # all Fibonacci numbers
    sum = 0
     
    # Iterating through the array
    for i in range( n ):
        if (arr[i] in fibonacci):
            sum += arr[i]
  
    # If the sum is Fibonacci
    # then return true
    if (sum in fibonacci):
        return True
  
    return False
  
# Driver code
if __name__ == "__main__":
     
    # array of elements
    arr = [ 1, 2, 4, 8, 2 ]
    n = len(arr)
  
    # Creating a set containing
    # all fibonacci numbers
    createHash()
  
    if (checkArray(arr, n)):
        print("Yes")
    else:
        print("No")
  
# This code is contributed by chitranayal

C#

// C# program to check whether the
// sum of fibonacci elements of the
// array is a Fibonacci number or not
using System;
using System.Collections.Generic;
 
class GFG{
  
static readonly int MAX = 100005;
  
// Hash to store the Fibonacci
// numbers up to Max
static HashSet fibonacci = new HashSet();
   
// Function to create the hash table
// to check Fibonacci numbers
static void createHash()
{
    // Inserting the first two Fibonacci
    // numbers into the hash
    int prev = 0, curr = 1;
    fibonacci.Add(prev);
    fibonacci.Add(curr);
   
    // Add the remaining Fibonacci numbers
    // based on the previous two numbers
    while (curr <= MAX) {
        int temp = curr + prev;
        fibonacci.Add(temp);
        prev = curr;
        curr = temp;
    }
}
   
// Function to check if the sum of
// Fibonacci numbers is Fibonacci or not
static bool checkArray(int []arr, int n)
{
    // Find the sum of
    // all Fibonacci numbers
    int sum = 0;
   
    // Iterating through the array
    for (int i = 0; i < n; i++)
        if (fibonacci.Contains(arr[i]))
            sum += arr[i];
   
    // If the sum is Fibonacci
    // then return true
    if (fibonacci.Contains(sum))
        return true;
   
    return false;
}
   
// Driver code
public static void Main(String[] args)
{
    // array of elements
    int []arr = { 1, 2, 4, 8, 2 };
    int n = arr.Length;
   
    // Creating a set containing
    // all fibonacci numbers
    createHash();
   
    if (checkArray(arr, n))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}
  
// This code is contributed by sapnasingh4991

Javascript

 
// Javascript program to check whether the
// sum of fibonacci elements of the
// array is a Fibonacci number or not
 
let MAX = 100005;
   
// Hash to store the Fibonacci
// numbers up to Max
let fibonacci = new Set();
    
// Function to create the hash table
// to check Fibonacci numbers
function createHash()
{
    // Inserting the first two Fibonacci
    // numbers leto the hash
    let prev = 0, curr = 1;
    fibonacci.add(prev);
    fibonacci.add(curr);
    
    // Add the remaining Fibonacci numbers
    // based on the previous two numbers
    while (curr <= MAX) {
        let temp = curr + prev;
        fibonacci.add(temp);
        prev = curr;
        curr = temp;
    }
}
    
// Function to check if the sum of
// Fibonacci numbers is Fibonacci or not
function checkArray(arr, n)
{
    // Find the sum of
    // all Fibonacci numbers
    let sum = 0;
    
    // Iterating through the array
    for (let i = 0; i < n; i++)
        if (fibonacci.has(arr[i]))
            sum += arr[i];
    
    // If the sum is Fibonacci
    // then return true
    if (fibonacci.has(sum))
        return true;
    
    return false;
}
 
// Driver code
     
      // array of elements
    let arr = [ 1, 2, 4, 8, 2 ];
    let n = arr.length;
    
    // Creating a set containing
    // all fibonacci numbers
    createHash();
    
    if (checkArray(arr, n))
        document.write("Yes");
    else
        document.write("No");
 
 // This code is contributed by sanjoy_62.                                                                              

输出：

Yes

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