recursive binary search

Author: rasbt

ipython_nbs/essentials/recursion-examples.ipynb

@@ -131,27 +131,87 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Array Sum"
+    "## Length of an array"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def array_len(x):\n",
+    "    if x == []:\n",
+    "        return 0\n",
+    "    else:\n",
+    "        return 1 + array_len(x[1:])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "array_len([])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "array_len([1, 2, 3])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Sum of the elements in an array"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
    "source": [
     "def array_sum(x):\n",
-    "    if not len(x):\n",
+    "    if x == []:\n",
     "        return 0\n",
     "    else:\n",
     "        return x[0] + array_sum(x[1:])"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -160,7 +220,7 @@
        "0"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -171,7 +231,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -180,7 +240,7 @@
        "5"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -191,7 +251,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
@@ -200,14 +260,144 @@
        "15"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "array_sum([1, 2, 3, 4, 5])"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Binary search using recursion"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def binary_search(array, value, min_idx=0, max_idx=None):\n",
+    "    \n",
+    "    if min_idx == max_idx:\n",
+    "        return None\n",
+    "    elif max_idx is None:\n",
+    "        max_idx = len(array)\n",
+    "    else:\n",
+    "        pass\n",
+    "\n",
+    "    middle_idx = min_idx + (max_idx - min_idx) // 2\n",
+    "\n",
+    "    if array[middle_idx] == value:\n",
+    "        return middle_idx\n",
+    "    elif array[middle_idx] < value:\n",
+    "        min_idx = middle_idx + 1\n",
+    "    else:\n",
+    "        max_idx = middle_idx\n",
+    "        \n",
+    "    return binary_search(array, value, min_idx, max_idx)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
+    "                value=1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
+    "                value=2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
+    "                value=4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
+    "                value=11)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "binary_search(array=[1, 2, 4, 7, 8, 10, 11],\n",
+    "                value=99)"
+   ]
   }
  ],
  "metadata": {