add recursive binary search implementation

recursion/recursive_binary_search.ipynb

@@ -0,0 +1,105 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Binary search recursive approach"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def binary_search(A, value):\n",
+    "    if len(A) == 0:\n",
+    "        return -1\n",
+    "    return binary_search_helper(A, 0, len(A) - 1, value)\n",
+    "\n",
+    "def binary_search_helper(A, left, right, value):\n",
+    "    # base case\n",
+    "    if left > right:\n",
+    "        return -1\n",
+    "    mid = (right + left) // 2\n",
+    "    if A[mid] == value:\n",
+    "        return mid\n",
+    "    elif A[mid] > value:\n",
+    "        return binary_search_helper(A, left, mid, value)\n",
+    "    elif A[mid] < value:\n",
+    "        return binary_search_helper(A, mid + 1, right, value)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-1"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "A = [1, 2, 3]\n",
+    "binary_search(A, 13)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "4"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "array = [1, 2, 3, 5, 7, 13, 14, 16]\n",
+    "binary_search(array, 7)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}