recursive binary search

Author: rasbt

ipython_nbs/search/binary_search.ipynb

@@ -83,6 +83,18 @@
   {
    "cell_type": "code",
    "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "binary_search(array=[],\n",
+    "              value=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -91,19 +103,19 @@
        "0"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
-    "                value=1)"
+    "              value=1)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -112,7 +124,7 @@
        "1"
       ]
      },
-     "execution_count": 4,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -124,7 +136,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -133,7 +145,7 @@
        "2"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 6,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -145,7 +157,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
@@ -154,7 +166,7 @@
        "6"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -166,13 +178,145 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
     "binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
     "                value=99)"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Binary Search using Recursion"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Note that this implementation of recursive binary search deliberately avoid slicing the `array` (e.g., `array[:middle_idx]`), because slicing Python lists is expensive due to the random memory access. E.g., slicing a Python list with as `a_list[:k]` is an O(k) operation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def recursive_binary_search(array, value, start_idx=None, end_idx=None):\n",
+    "    \n",
+    "    len_ary = len(array)\n",
+    "    \n",
+    "    if start_idx is None:\n",
+    "        start_idx = 0\n",
+    "    if end_idx is None:\n",
+    "        end_idx = len(array) - 1\n",
+    "    \n",
+    "    if not len_ary or start_idx >= end_idx:\n",
+    "        return None\n",
+    "    \n",
+    "    middle_idx = (start_idx + end_idx) // 2\n",
+    "    if array[middle_idx] == value:\n",
+    "        return middle_idx\n",
+    "\n",
+    "    elif array[middle_idx] > value:\n",
+    "        return recursive_binary_search(array, \n",
+    "                                       value, \n",
+    "                                       start_idx=start_idx,\n",
+    "                                       end_idx=middle_idx)\n",
+    "    else:\n",
+    "        return recursive_binary_search(array,\n",
+    "                                       value,\n",
+    "                                       start_idx=middle_idx + 1,\n",
+    "                                       end_idx=len_ary)\n",
+    "    return None"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "recursive_binary_search(array=[],\n",
+    "                        value=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "recursive_binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
+    "                        value=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "recursive_binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
+    "                        value=4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "recursive_binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
+    "                        value=11)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "recursive_binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
+    "                        value=99)"
+   ]
   }
  ],
  "metadata": {