873. Length of Longest Fibonacci Subsequence

Description

A sequence x1, x2, ..., xn is Fibonacci-like if:

• n >= 3
• xi + xi+1 == xi+2 for all i + 2 <= n

Given a strictly increasing array arr of positive integers forming a sequence, return the length of the longest Fibonacci-like subsequence of arr. If one does not exist, return 0.

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, [3, 5, 8] is a subsequence of [3, 4, 5, 6, 7, 8].

 

Example 1:

Input: arr = [1,2,3,4,5,6,7,8]
Output: 5
Explanation: The longest subsequence that is fibonacci-like: [1,2,3,5,8].

Example 2:

Input: arr = [1,3,7,11,12,14,18]
Output: 3
Explanation: The longest subsequence that is fibonacci-like: [1,11,12], [3,11,14] or [7,11,18].

 

Constraints:

• 3 <= arr.length <= 1000
• 1 <= arr[i] < arr[i + 1] <= 109

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(n²)
• Space complexity: O(n²)

 

JavaScript

/**
 * @param {number[]} arr
 * @return {number}
 */
const lenLongestFibSubseq = function (arr) {
  const n = arr.length;
  const valueMap = new Map();
  const dp = new Map();
  let result = 0;

  for (let index = 0; index < n; index++) {
    valueMap.set(arr[index], index);
  }

  for (let a = 1; a < n; a++) {
    for (let b = 0; b < a; b++) {
      const target = arr[a] - arr[b];

      if (target >= arr[b] || !valueMap.has(target)) continue;
      const c = valueMap.get(target);
      const len = dp.get(`${c},${b}`) ?? 0;

      dp.set(`${b},${a}`, len + 1);
      result = Math.max(len + 1, result);
    }
  }

  return result ? result + 2 : 0;
};