/*
 * Interpolation Search
 *  
 * Time Complexity:
 * -Best case: O(1)
 * -Worst case: O(n)
 * -O((log(log(n))) If the data are uniformly distributed
 *
 *  
 */

function interpolationSearch(arr, key) {

    let length = arr.length - 1;
    let low = 0;
    let high = length;
    let position = -1;
    let delta = -1;

    //Because the array is sorted the key must be between low and high
    while (low <= high && key >= arr[low] && key <= arr[high]) {

        delta = (key - arr[low]) / (arr[high] - arr[low]);
        position = low + Math.floor((high - low) * delta);

        //Target found return its position
        if (arr[position] === key) {
            return position;
        }

        //If the key is larger then it is in the upper part of the array
        if (arr[position] < key) {
            low = position + 1;
            //If the key is smaller then it is in the lower part of the array    
        } else {
            high = position - 1;
        }
    }

    return -1;
}


let arr = [2, 6, 8, 10, 12, 14, 16, 18, 20, 22, 26, 34, 39];

console.log("Found at position :" + interpolationSearch(arr, 2));
console.log("Found at position :" + interpolationSearch(arr, 12));
console.log("Found at position :" + interpolationSearch(arr, 1000));
console.log("Found at position :" + interpolationSearch(arr, 39));