# Find two Fibonacci numbers whose sum can be represented as N

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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 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 hash = ``new` `HashSet();  ` `    ``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#

 `// 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 `

Output:

```1, 89
```

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