fibonacci_search.ts

/**
 * @function fibonacciSearch
 * @description Fibonacci search algorithm for a sorted array.
 *
 * The algorithm searches for a specific value in a sorted array using Fibonacci numbers
 * to divide the array into smaller subarrays. This algorithm is useful for large arrays where
 * the cost of accessing elements is high.
 *
 * @param {number[]} array - sorted list of numbers
 * @param {number} target - target number to search for
 * @return {number | null} - index of the target number in the list, or null if not found
 * @see [FibonacciSearch](https://www.geeksforgeeks.org/fibonacci-search/)
 * @example fibonacciSearch([1,2,3], 2) => 1
 * @example fibonacciSearch([4,5,6], 2) => null
 */

export const fibonacciSearch = (
  array: number[],
  target: number
): number | null => {
  const arrayLength = array.length
  let a = 0;  // (n-2)'th Fibonacci No.
  let b = 1;  // (n-1)'th Fibonacci No.
  let c = a + b;  // n'th Fibonacci

  while (c < arrayLength) {
    a = b;
    b = c;
    c = a + b;
  }

  let offset = -1

  while (c > 1) {
    let i = Math.min(offset + a, arrayLength - 1);

    if (array[i] < target) {
      c = b;
      b = a;
      a = c - b;
      offset = i;
    } else if (array[i] > target) {
      c = a;
      b = b - a;
      a = c - b;
    } else {
      // Element found then return index
      return i;
    }
  }

  if (b && array[offset + 1] === target) {
    return offset + 1;
  }

  // Element not found then return null
  return null;
}