Finding Fibonacci sequence in an array using JavaScript


Fibonacci Sequence:

A sequence X_1, X_2, ..., X_n is fibonacci if:

  • n >= 3

  • X_i + X_{i+1} = X_{i+2} for all i + 2 <= n

Problem

We are required to write a JavaScript function that takes in an array of numbers, arr, as the first and the only argument. Our function should find and return the length of the longest Fibonacci subsequence that exists in the array arr.

A subsequence is derived from another sequence arr by deleting any number of elements (including none) from arr, without changing the order of the remaining elements.

For example, if the input to the function is

Input

const arr = [1, 3, 7, 11, 14, 25, 39];

Output

const output = 5;

Output Explanation

Because the longest Fibonacci subsequence is [3, 11, 14, 25, 39]

Following is the code:

Example

 Live Demo

const arr = [1, 3, 7, 11, 14, 25, 39];
const longestFibonacci = (arr = []) => {
   const map = arr.reduce((acc, num, index) => {
      acc[num] = index
      return acc
   }, {})
   const memo = arr.map(() => arr.map(() => 0))
   let max = 0
   for(let i = 0; i < arr.length; i++) {
      for(let j = i + 1; j < arr.length; j++) {
         const a = arr[i]
         const b = arr[j]
         const index = map[b - a]
         if(index < i) {
            memo[i][j] = memo[index][i] + 1
         }
         max = Math.max(max, memo[i][j])
      }
   }
   return max > 0 ? max + 2 : 0
};
console.log(longestFibonacci(arr));

Output

5

Updated on: 23-Apr-2021

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