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📜  检查数组中斐波那契元素的总和是否为斐波那契数

📅  最后修改于: 2021-05-17 19:09:22             🧑  作者: Mango

给定一个包含N个元素的数组arr [] ,任务是检查数组中斐波那契元素的总和是否为斐波那契数。

例子:

方法:想法是使用散列来预先计算和存储Fibonacci节点到最大数量,以使检查变得容易和高效(在O(1)时间内)。

预计算后,遍历数组的所有元素。如果该数字是斐波那契数字,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


输出:
Yes