added interpolation search

Author: webcoderspeed

Algorithms/interpolationSearch.js

@@ -0,0 +1,58 @@
+/**
+ * @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