/** * @description - This function implements the interpolation search algorithm * @param {Array} arr - The array to be searched * @param {Number} x - The element to be searched * @returns {Number} - The index of the element if found, else -1 * @example * interpolationSearch([1, 2, 3, 4, 5], 3) // returns 2 * interpolationSearch([1, 2, 3, 4, 5], 6) // returns -1 * interpolationSearch([1, 2, 3, 4, 5], 1) // returns 0 * * ### Time Complexity * Best Case: O(1) * Average Case: O(log(log(n))) * Worst Case: O(n) * * ### Space Complexity * O(1) * ### Explanation of the algorithm * The interpolation search algorithm is an improvement over the binary search algorithm. * The interpolation search algorithm works on the probing position of the required value. * For this algorithm to work properly, the data collection should be in a sorted form and equally distributed. * The idea of formula is to return higher value of pos when element to be searched is closer to arr[hi]. And smaller value when closer to arr[lo] * * ### Pseudocode * 1. Find the position to be searched * 2. If it is a match, return the index of the item, and exit. * 3. If the item is less than arr[pos], calculate the probe position of the left sub-array. Otherwise calculate the same in the right sub-array. * 4. Repeat until a match is found or the sub-array reduces to zero. */ const interpolationSearch = (arr, x) => { let lo = 0; // lower bound let hi = arr.length - 1; // upper bound while (lo <= hi && x >= arr[lo] && x <= arr[hi]) { // check if x is in range of the array if (lo === hi) { // if lower bound is equal to upper bound if (arr[lo] === x) return lo; // if the element is found, return the index return -1; // else return -1 } let pos = lo + Math.floor(((hi - lo) / (arr[hi] - arr[lo])) * (x - arr[lo])); // calculate the probe position if (arr[pos] === x) return pos; // if the element is found, return the index if (arr[pos] < x) lo = pos + 1; // if the element is less than the element at pos, update the lower bound else hi = pos - 1; // else update the upper bound } return -1; // if the element is not found, return -1 }; module.exports = interpolationSearch; console.log(interpolationSearch([1, 2, 3, 4, 5], 3)); // returns 2 console.log(interpolationSearch([1, 2, 3, 4, 5], 6)); // returns -1 console.log(interpolationSearch([1, 2, 3, 4, 5], 1)); // returns 0