Find two Fibonacci numbers whose sum can be represented as N

Last Updated : 22 Nov, 2021

Given an even number N, the task is to find two Fibonacci numbers whose sum can be represented as N. There may be several combinations possible. Print only first such pair. If there is no solution then print -1.
Examples:

Input: N = 90
Output: 1, 89
Explanation:
The first pair with whose sum is equal to 90 is {1, 89}
Input: N = 74
Output: -1

Approach: The idea is to use hashing to precompute and store the Fibonacci numbers, and then check if a pair is a Fibonacci value in O(1) time.
Below is the implementation of the above approach:

CPP

// 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

// 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

# 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

JavaScript

<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>

Output:

1, 89

Time Complexity: O(N)

Auxiliary Space: O(N)

Count of ways in which N can be represented as sum of Fibonacci numbers without repetition

muskan_garg

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Find two Fibonacci numbers whose sum can be represented as N

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