Add Interpolation search (#199)

* Add Interpolation search

* Add new algorithm to directory

---------

Co-authored-by: IcarusTheFly <[email protected]>

Author: IcarusTheFly

DIRECTORY.md

@@ -139,6 +139,7 @@
 
 ## Search
   * [Binary Search](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/search/binary_search.ts)
+  * [Interpolation Search](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/search/interpolation_search.ts)
   * [Jump Search](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/search/jump_search.ts)
   * [Linear Search](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/search/linear_search.ts)
   * [Sentinel Search](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/search/sentinel_search.ts)

search/interpolation_search.ts

@@ -0,0 +1,49 @@
+/**
+ * @function interpolationSearch
+ * @description 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)
+ * @param {number[]} array - list of numbers
+ * @param {number} target - target number to search for
+ * @return {number} - index of the target number in the list, or -1 if not found
+ * @see https://en.wikipedia.org/wiki/Interpolation_search
+ * @example interpolationSearch([1, 3, 5, 7, 9, 11], 1) => 0
+ */
+export const interpolationSearch = (array: number[], target: number): number => {
+  let lowIndex: number = 0;
+  let highIndex: number = array.length - 1;
+  let currentValue: number = array[lowIndex];
+  let pos: number = 0;
+
+  while (lowIndex <= highIndex) {
+    const lowValue: number = array[lowIndex];
+    const highValue: number = array[highIndex];
+
+    if (lowValue === highValue) {
+      if (array[lowIndex] === target) {
+        return lowIndex;
+      }
+      break;
+    }
+
+    pos = Math.round(lowIndex + (target-lowValue)*(highIndex-lowIndex) / (highValue-lowValue));
+
+    if (pos < 0 || pos >= array.length) {
+      break;
+    }
+
+    currentValue = array[pos];
+
+    if (target === currentValue) {
+      return pos;
+    }
+
+    if (target > currentValue) {
+      lowIndex = pos + 1;
+    } else {
+      highIndex = pos - 1;
+    }
+  }
+
+  return -1;
+}

search/test/interpolation_search.test.ts

@@ -0,0 +1,15 @@
+import { interpolationSearch } from "../interpolation_search";
+
+describe("Interpolation search", () => {
+  test.each([
+    [[1, 3, 5, 7, 9, 11], 1, 0],
+    [[1, 3, 7, 10, 14, 15, 16, 18, 20, 21, 22, 23, 25, 33, 35, 42, 45, 47, 50, 52], 33, 13],
+    [[0, 45, 67, 70, 89, 129, 150, 308], 308, 7],
+    [[0, 45, 67, 70, 89, 129, 150, 308], 190, -1]
+  ])(
+    "of %o, searching for %o, expected %i",
+    (array: any[], target: any, index: number) => {
+      expect(interpolationSearch(array, target)).toStrictEqual(index)
+    },
+  );
+});