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interpolationSearch.js
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58 lines (55 loc) · 2.44 KB
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/**
* @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