# Interpolation Search in JavaScript

## Interpolation Search

Interpolation search is an algorithm for searching for a key in an array that has been ordered by numerical values assigned to the keys (key values).

For example

Suppose, we have a sorted array of n uniformly distributed values arr[], and we need to write a function to search for a particular element target in the array.

It does the following operations to find the position −

// The idea of the formula is to return a higher value of pos

// when element to be searched is closer to arr[hi]. And

// smaller value when closer to arr[lo]

pos = lo + ((x - arr[lo]) * (hi - lo) / (arr[hi] - arr[Lo]))

Keys −

• arr[] - Array where elements need to be searched

• x - Element to be searched

• lo - Starting index in arr[]

• hi - Ending index in arr[]

We are required to write a JavaScript function that takes in an array of numbers as the first argument and a search target as the second argument.

The function should make use of the Interpolation search algorithm to search for the target in the array.

## Example

Following is the code −

const arr = [1, 4, 6, 7, 9, 12, 15, 16, 17, 23, 25, 26, 27, 31];
const target = 25;
const interpolationSearch = (arr = [], target) => {
let left = 0;
let right = arr.length - 1;
while (left <= right) {
const rangeDelta = arr[right] - arr[left];
const indexDelta = right - left;
const valueDelta = target - arr[left];
if (valueDelta < 0) {
return -1;
}
if (!rangeDelta) {
return arr[left] === target ? left : -1;
}
const middleIndex = left + Math.floor((valueDelta * indexDelta) / rangeDelta);
if (arr[middleIndex] === target) {
return middleIndex;
}
if (arr[middleIndex] < target) {
left = middleIndex + 1;
} else {
right = middleIndex - 1;
}
};
return -1;
};
console.log(interpolationSearch(arr, target));

## Output

Following is the output on console −

10