Encuentre dos números de Fibonacci cuya suma se pueda representar como N

Dado un número par N , la tarea es encontrar dos números de Fibonacci cuya suma se pueda representar como N . Puede haber varias combinaciones posibles. Imprima solo el primer par. Si no hay solución, imprima -1 .
Ejemplos: 
 

Entrada: N = 90 
Salida: 1, 89 
Explicación: 
El primer par cuya suma es igual a 90 es {1, 89}
Entrada: N = 74 
Salida: -1 
 

Enfoque: la idea es usar hashing para precalcular y almacenar los números de Fibonacci , y luego verificar si un par es un valor de Fibonacci en tiempo O (1).
A continuación se muestra la implementación del enfoque anterior: 
 

// C++ program to find two
// Fibonacci numbers whose
// sum can be represented as N
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to create hash table
// to check Fibonacci numbers
void createHash(set<int>& hash,
                int maxElement)
{
 
    // Storing the first two numbers
    // in the hash
    int prev = 0, curr = 1;
    hash.insert(prev);
    hash.insert(curr);
 
    // Finding Fibonacci numbers up to N
    // and storing them in the hash
    while (curr < maxElement) {
        int temp = curr + prev;
        hash.insert(temp);
        prev = curr;
        curr = temp;
    }
}
 
// Function to find the Fibonacci pair
// with the given sum
void findFibonacciPair(int n)
{
    // creating a set containing
    // all fibonacci numbers
    set<int> hash;
    createHash(hash, n);
 
    // Traversing all numbers
    // to find first pair
    for (int i = 0; i < n; i++) {
 
        // If both i and (N - i) are Fibonacci
        if (hash.find(i) != hash.end()
            && hash.find(n - i) != hash.end()) {
 
            // Printing the pair because
            // i + (N - i) = N
            cout << i << ", "
                 << (n - i) << endl;
            return;
        }
    }
 
    // If no fibonacci pair is found
    // whose sum is equal to n
    cout << "-1\n";
}
 
// Driven code
int main()
{
    int N = 90;
 
    findFibonacciPair(N);
 
    return 0;
}

// Java program to find two
// Fibonacci numbers whose
// sum can be represented as N
import java.util.*;
 
class GFG{
 
// Function to create hash table
// to check Fibonacci numbers
static void createHash(HashSet<Integer> hash,
                int maxElement)
{
 
    // Storing the first two numbers
    // in the hash
    int prev = 0, curr = 1;
    hash.add(prev);
    hash.add(curr);
 
    // Finding Fibonacci numbers up to N
    // and storing them in the hash
    while (curr < maxElement) {
        int temp = curr + prev;
        hash.add(temp);
        prev = curr;
        curr = temp;
    }
}
 
// Function to find the Fibonacci pair
// with the given sum
static void findFibonacciPair(int n)
{
    // creating a set containing
    // all fibonacci numbers
    HashSet<Integer> hash = new HashSet<Integer>();
    createHash(hash, n);
 
    // Traversing all numbers
    // to find first pair
    for (int i = 0; i < n; i++) {
 
        // If both i and (N - i) are Fibonacci
        if (hash.contains(i)
            && hash.contains(n - i)) {
 
            // Printing the pair because
            // i + (N - i) = N
            System.out.print(i+ ", "
                + (n - i) +"\n");
            return;
        }
    }
 
    // If no fibonacci pair is found
    // whose sum is equal to n
    System.out.print("-1\n");
}
 
// Driven code
public static void main(String[] args)
{
    int N = 90;
 
    findFibonacciPair(N);
}
}
 
// This code is contributed by PrinciRaj1992

# Python3  program to find two
# Fibonacci numbers whose
# sum can be represented as N
 
# Function to create hash table
# to check Fibonacci numbers
def createHash(hash1,maxElement):
 
    # Storing the first two numbers
    # in the hash
    prev , curr = 0 , 1
    hash1.add(prev)
    hash1.add(curr)
 
    # Finding Fibonacci numbers up to N
    # and storing them in the hash
    while (curr < maxElement):
        temp = curr + prev
        hash1.add(temp)
        prev = curr
        curr = temp
 
# Function to find the Fibonacci pair
# with the given sum
def findFibonacciPair( n):
 
    # creating a set containing
    # all fibonacci numbers
    hash1 = set()
    createHash(hash1, n)
 
    # Traversing all numbers
    # to find first pair
    for i in range(n):
 
        # If both i and (N - i) are Fibonacci
        if (i in hash1 and (n - i) in hash1):
 
            # Printing the pair because
            # i + (N - i) = N
            print(i , ", ", (n - i))
            return
 
    # If no fibonacci pair is found
    # whose sum is equal to n
    print("-1")
     
# Driven code
if __name__ == "__main__":
    N = 90
    findFibonacciPair(N)
 
# This code is contributed by chitranayal

// C# program to find two
// Fibonacci numbers whose
// sum can be represented as N
using System;
using System.Collections.Generic;
 
class GFG{
  
// Function to create hash table
// to check Fibonacci numbers
static void createHash(HashSet<int> hash,
                int maxElement)
{
  
    // Storing the first two numbers
    // in the hash
    int prev = 0, curr = 1;
    hash.Add(prev);
    hash.Add(curr);
  
    // Finding Fibonacci numbers up to N
    // and storing them in the hash
    while (curr < maxElement) {
        int temp = curr + prev;
        hash.Add(temp);
        prev = curr;
        curr = temp;
    }
}
  
// Function to find the Fibonacci pair
// with the given sum
static void findFibonacciPair(int n)
{
    // creating a set containing
    // all fibonacci numbers
    HashSet<int> hash = new HashSet<int>();
    createHash(hash, n);
  
    // Traversing all numbers
    // to find first pair
    for (int i = 0; i < n; i++) {
  
        // If both i and (N - i) are Fibonacci
        if (hash.Contains(i)
            && hash.Contains(n - i)) {
  
            // Printing the pair because
            // i + (N - i) = N
            Console.Write(i+ ", "
                + (n - i) +"\n");
            return;
        }
    }
  
    // If no fibonacci pair is found
    // whose sum is equal to n
    Console.Write("-1\n");
}
  
// Driven code
public static void Main(String[] args)
{
    int N = 90;
  
    findFibonacciPair(N);
}
}
  
// This code is contributed by Princi Singh

<script>
 
// Javascript program to find two
// Fibonacci numbers whose
// sum can be represented as N
 
// Function to create hash table
// to check Fibonacci numbers
function createHash(hash, maxElement)
{
  
    // Storing the first two numbers
    // in the hash
    let prev = 0, curr = 1;
    hash.add(prev);
    hash.add(curr);
  
    // Finding Fibonacci numbers up to N
    // and storing them in the hash
    while (curr < maxElement) {
        let temp = curr + prev;
        hash.add(temp);
        prev = curr;
        curr = temp;
    }
}
  
// Function to find the Fibonacci pair
// with the given sum
function findFibonacciPair(n)
{
    // creating a set containing
    // all fibonacci numbers
    let hash = new Set();
    createHash(hash, n);
  
    // Traversing all numbers
    // to find first pair
    for (let i = 0; i < n; i++) {
  
        // If both i and (N - i) are Fibonacci
        if (hash.has(i)
            && hash.has(n - i)) {
  
            // Printing the pair because
            // i + (N - i) = N
            document.write(i+ ", "
                + (n - i) + "<br/>");
            return;
        }
    }
  
    // If no fibonacci pair is found
    // whose sum is equal to n
    document.write("-1" + "<br/>");
}
 
// Driver code
     
      let N = 90;
  
    findFibonacciPair(N);
 
// This code is contributed by sanjoy_62.
</script>

1, 89

Complejidad de tiempo: O(N)

Espacio Auxiliar: O(N)