Add Ternary search (knaxus#76)

* implamenting ternary search

* adding complexity

* changed `ternarySearch` to be more like recursive, fixed recursive, tests now correct

* fixing recursive search, removing unnecessary if

Author: Kyle-Ski

src/_Searching_/TernarySearch/TernarySearch.test.js

@@ -0,0 +1,41 @@
+const { ternarySearch, ternarySearchRecursive } = require('.');
+
+describe('Ternary Search', () => {
+  const array = [1, 2, 3, 4, 5, 6, 7, 8];
+  const low = 0;
+  const high = array.length - 1;
+
+  describe('When element to find is at 1st position ', () => {
+    it('Ternary search with Loop', () => {
+      expect(ternarySearch(array, 1)).toEqual(0);
+    });
+    it('Ternary serach with recursion', () => {
+      expect(ternarySearchRecursive(array, low, high, 1)).toEqual(0);
+    });
+  });
+  describe('When element to find is at last position ', () => {
+    it('Ternary search with Loop', () => {
+      expect(ternarySearch(array, 8)).toEqual(7);
+    });
+    it('Ternary serach with recursion', () => {
+      expect(ternarySearchRecursive(array, low, high, 8)).toEqual(7);
+    });
+  });
+  describe('When element to find is at random position ', () => {
+    it('Ternary search with Loop', () => {
+      expect(ternarySearch(array, 3)).toEqual(2);
+    });
+    it('Ternary serach with recursion', () => {
+      expect(ternarySearchRecursive(array, low, high, 4)).toEqual(3);
+    });
+  });
+  describe('When element to find is no present in array ', () => {
+    it('Ternary search with Loop', () => {
+      expect(ternarySearch(array, 10)).toEqual(null);
+    });
+    it('Ternary serach with recursion', () => {
+      expect(ternarySearchRecursive(array, low, high, 10)).toEqual(null);
+    });
+  });
+  
+});

src/_Searching_/TernarySearch/index.js

@@ -0,0 +1,53 @@
+/**
+ * Note: Array must be sorted for ternary search
+ * Complexity: 
+ * Worst case time complexity: O(log N)
+ * Average case time complexity: O(log N)
+ * Best case time complexity: O(1)
+ * Space complexity: O(1)
+*/
+function ternarySearch(arr, key){
+    let low = 0;
+    let high = arr.length - 1;
+    while(low <= high){
+        let lowMiddle = low + Math.floor((high - low) / 3);
+        let highMiddle = low + 2 * Math.floor((high - low) / 3);
+        if(key == arr[low]){
+            return low;
+        } else if(key  == arr[high]){
+            return high;
+        } else if(key <= arr[lowMiddle]){
+            high = lowMiddle;
+        } else if(key > arr[lowMiddle] && key <= arr[highMiddle]){
+            low = lowMiddle + 1;
+            high = highMiddle;
+        } else {
+            low = highMiddle + 1;
+        }
+    }
+    return null;
+}
+
+function ternarySearchRecursive(arr, low, high, key){
+    if(high >= low){
+        let highMiddle = low + 2 * Math.floor((high - low) / 3);
+        let lowMiddle = low + Math.floor((high - low) / 3);
+        if(key === arr[lowMiddle]){
+            return lowMiddle;
+        } else if(key === arr[highMiddle]){
+            return highMiddle;
+        } else if(key < arr[lowMiddle]){
+            return ternarySearchRecursive(arr, low, lowMiddle - 1, key);
+        } else if(key > arr[lowMiddle] && key < arr[highMiddle]){
+            return ternarySearchRecursive(arr, lowMiddle + 1, highMiddle - 1, key);
+        } else {
+            return ternarySearchRecursive(arr, highMiddle + 1, high, key);
+        } 
+    } 
+    return null;
+}
+
+module.exports = {
+    ternarySearch,
+    ternarySearchRecursive
+};