Add Interpolation Search.

Author: trekhleb

README.md

@@ -86,6 +86,7 @@ a set of rules that precisely define a sequence of operations.
   * `B` [Linear Search](src/algorithms/search/linear-search)
   * `B` [Jump Search](src/algorithms/search/jump-search) (or Block Search) - search in sorted array
   * `B` [Binary Search](src/algorithms/search/binary-search) - search in sorted array
+  * `B` [Interpolation Search](src/algorithms/search/interpolation-search) - search in uniformly distributed sorted array
 * **Sorting**
   * `B` [Bubble Sort](src/algorithms/sorting/bubble-sort)
   * `B` [Selection Sort](src/algorithms/sorting/selection-sort)

src/algorithms/search/interpolation-search/README.md

@@ -0,0 +1,40 @@
+# 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 we have a sorted array of `n` uniformly distributed values `arr[]`, 
+and we need to write a function to search for a particular element `x` in the array.
+
+**Linear Search** finds the element in `O(n)` time, **Jump Search** takes `O(√ n)` time 
+and **Binary Search** take `O(Log n)` time.
+
+The **Interpolation Search** is an improvement over Binary Search for instances, 
+where the values in a sorted array are _uniformly_ distributed. Binary Search 
+always goes to the middle element to check. On the other hand, interpolation 
+search may go to different locations according to the value of the key being 
+searched. For example, if the value of the key is closer to the last element, 
+interpolation search is likely to start search toward the end side.
+
+To find the position to be searched, it uses following formula:
+
+```
+// 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]
+pos = lo + ((x - arr[lo]) * (hi - lo) / (arr[hi] - arr[Lo]))
+
+arr[] - Array where elements need to be searched
+x - Element to be searched
+lo - Starting index in arr[]
+hi - Ending index in arr[]
+```
+
+## Complexity
+
+**Time complexity**: `O(log(log(n))`
+
+## References
+
+- [GeeksForGeeks](https://www.geeksforgeeks.org/interpolation-search/)
+- [Wikipedia](https://en.wikipedia.org/wiki/Interpolation_search)

src/algorithms/search/interpolation-search/__test__/interpolationSearch.test.js

@@ -0,0 +1,24 @@
+import interpolationSearch from '../interpolationSearch';
+
+describe('interpolationSearch', () => {
+  it('should search elements in sorted array of numbers', () => {
+    expect(interpolationSearch([], 1)).toBe(-1);
+    expect(interpolationSearch([1], 1)).toBe(0);
+    expect(interpolationSearch([1], 0)).toBe(-1);
+    expect(interpolationSearch([1, 1], 1)).toBe(0);
+    expect(interpolationSearch([1, 2], 1)).toBe(0);
+    expect(interpolationSearch([1, 2], 2)).toBe(1);
+    expect(interpolationSearch([10, 20, 30, 40, 50], 40)).toBe(3);
+    expect(interpolationSearch([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], 14)).toBe(13);
+    expect(interpolationSearch([1, 6, 7, 8, 12, 13, 14, 19, 21, 23, 24, 24, 24, 300], 24)).toBe(10);
+    expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 600)).toBe(-1);
+    expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 1)).toBe(0);
+    expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 2)).toBe(1);
+    expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 3)).toBe(2);
+    expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 700)).toBe(3);
+    expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 800)).toBe(4);
+    expect(interpolationSearch([0, 2, 3, 700, 800, 1200, 1300, 1400, 1900], 1200)).toBe(5);
+    expect(interpolationSearch([1, 2, 3, 700, 800, 1200, 1300, 1400, 19000], 800)).toBe(4);
+    expect(interpolationSearch([0, 10, 11, 12, 13, 14, 15], 10)).toBe(1);
+  });
+});

src/algorithms/search/interpolation-search/interpolationSearch.js

@@ -0,0 +1,52 @@
+/**
+ * Interpolation search implementation.
+ *
+ * @param {*[]} sortedArray - sorted array with uniformly distributed values
+ * @param {*} seekElement
+ * @return {number}
+ */
+export default function interpolationSearch(sortedArray, seekElement) {
+  let leftIndex = 0;
+  let rightIndex = sortedArray.length - 1;
+
+  while (leftIndex <= rightIndex) {
+    const rangeDelta = sortedArray[rightIndex] - sortedArray[leftIndex];
+    const indexDelta = rightIndex - leftIndex;
+    const valueDelta = seekElement - sortedArray[leftIndex];
+
+    // If valueDelta is less then zero it means that there is no seek element
+    // exists in array since the lowest element from the range is already higher
+    // then seek element.
+    if (valueDelta < 0) {
+      return -1;
+    }
+
+    // If range delta is zero then subarray contains all the same numbers
+    // and thus there is nothing to search for unless this range is all
+    // consists of seek number.
+    if (!rangeDelta) {
+      // By doing this we're also avoiding division by zero while
+      // calculating the middleIndex later.
+      return sortedArray[leftIndex] === seekElement ? leftIndex : -1;
+    }
+
+    // Do interpolation of the middle index.
+    const middleIndex = leftIndex + Math.floor(valueDelta * indexDelta / rangeDelta);
+
+    // If we've found the element just return its position.
+    if (sortedArray[middleIndex] === seekElement) {
+      return middleIndex;
+    }
+
+    // Decide which half to choose for seeking next: left or right one.
+    if (sortedArray[middleIndex] < seekElement) {
+      // Go to the right half of the array.
+      leftIndex = middleIndex + 1;
+    } else {
+      // Go to the left half of the array.
+      rightIndex = middleIndex - 1;
+    }
+  }
+
+  return -1;
+}

src/algorithms/search/jump-search/README.md

@@ -23,5 +23,5 @@ minimum when `m = √n`. Therefore, the best step size is `m = √n`.
 
 ## References
 
-- [Wikipedia](https://en.wikipedia.org/wiki/Jump_search)
 - [GeeksForGeeks](https://www.geeksforgeeks.org/jump-search/)
+- [Wikipedia](https://en.wikipedia.org/wiki/Jump_search)

src/algorithms/search/jump-search/jumpSearch.js

@@ -3,7 +3,7 @@ import Comparator from '../../../utils/comparator/Comparator';
 /**
  * Jump (block) search implementation.
  *
- * @param {*[]} sortedArray.
+ * @param {*[]} sortedArray
  * @param {*} seekElement
  * @param {function(a, b)} [comparatorCallback]
  * @return {number}