From 256755a9628b61069426915f78f98449dc8415ab Mon Sep 17 00:00:00 2001
From: Donne Martin <donne.martin@gmail.com>
Date: Mon, 27 Mar 2017 05:14:53 -0400
Subject: [PATCH] Add rotated array search challenge

---
 .../rotated_array_search/__init__.py          |   0
 .../rotated_array_search_challenge.ipynb      | 175 ++++++++++++
 .../rotated_array_search_solution.ipynb       | 268 ++++++++++++++++++
 .../test_search_sorted_array.py               |  24 ++
 4 files changed, 467 insertions(+)
 create mode 100644 sorting_searching/rotated_array_search/__init__.py
 create mode 100644 sorting_searching/rotated_array_search/rotated_array_search_challenge.ipynb
 create mode 100644 sorting_searching/rotated_array_search/rotated_array_search_solution.ipynb
 create mode 100644 sorting_searching/rotated_array_search/test_search_sorted_array.py

diff --git a/sorting_searching/rotated_array_search/__init__.py b/sorting_searching/rotated_array_search/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/sorting_searching/rotated_array_search/rotated_array_search_challenge.ipynb b/sorting_searching/rotated_array_search/rotated_array_search_challenge.ipynb
new file mode 100644
index 0000000..2ea3ae2
--- /dev/null
+++ b/sorting_searching/rotated_array_search/rotated_array_search_challenge.ipynb
@@ -0,0 +1,175 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Challenge Notebook"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Problem: Find an element in a sorted array that has been rotated a number of times.\n",
+    "\n",
+    "* [Constraints](#Constraints)\n",
+    "* [Test Cases](#Test-Cases)\n",
+    "* [Algorithm](#Algorithm)\n",
+    "* [Code](#Code)\n",
+    "* [Unit Test](#Unit-Test)\n",
+    "* [Solution Notebook](#Solution-Notebook)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Constraints\n",
+    "\n",
+    "* Is the input an array of ints?\n",
+    "    * Yes\n",
+    "* Do we know how many times the array was rotated?\n",
+    "    * No\n",
+    "* Was the array originally sorted in increasing or decreasing order?\n",
+    "    * Increasing\n",
+    "* For the output, do we return the index?\n",
+    "    * Yes\n",
+    "* Can we assume the inputs are valid?\n",
+    "    * No\n",
+    "* Can we assume this fits memory?\n",
+    "    * Yes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Test Cases\n",
+    "\n",
+    "* None -> Exception\n",
+    "* [] -> None\n",
+    "* Not found -> None\n",
+    "* General case with duplicates\n",
+    "* General case without duplicates"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Algorithm\n",
+    "\n",
+    "Refer to the [Solution Notebook]().  If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "class Array(object):\n",
+    "\n",
+    "    def search_sorted_array(self, array, val):\n",
+    "        # TODO: Implement me\n",
+    "        pass"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Unit Test"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**The following unit test is expected to fail until you solve the challenge.**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "# %load test_search_sorted_array.py\n",
+    "from nose.tools import assert_equal, assert_raises\n",
+    "\n",
+    "\n",
+    "class TestArray(object):\n",
+    "\n",
+    "    def test_search_sorted_array(self):\n",
+    "        array = Array()\n",
+    "        assert_raises(TypeError, array.search_sorted_array, None)\n",
+    "        assert_equal(array.search_sorted_array([3, 1, 2], 0), None)\n",
+    "        assert_equal(array.search_sorted_array([3, 1, 2], 0), None)\n",
+    "        data = [10, 12, 14,  1,  3,  5,  6,  7,  8,  9]\n",
+    "        assert_equal(array.search_sorted_array(data, val=1), 3)\n",
+    "        data = [ 1,  1,  2,  1,  1,  1,  1,  1,  1,  1]\n",
+    "        assert_equal(array.search_sorted_array(data, val=2), 2)\n",
+    "        print('Success: test_search_sorted_array')\n",
+    "\n",
+    "\n",
+    "def main():\n",
+    "    test = TestArray()\n",
+    "    test.test_search_sorted_array()\n",
+    "\n",
+    "\n",
+    "if __name__ == '__main__':\n",
+    "    main()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Solution Notebook\n",
+    "\n",
+    "Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
+   ]
+  }
+ ],
+ "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": "3.5.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/sorting_searching/rotated_array_search/rotated_array_search_solution.ipynb b/sorting_searching/rotated_array_search/rotated_array_search_solution.ipynb
new file mode 100644
index 0000000..6167b72
--- /dev/null
+++ b/sorting_searching/rotated_array_search/rotated_array_search_solution.ipynb
@@ -0,0 +1,268 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Solution Notebook"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Problem: Find an element in a sorted array that has been rotated a number of times.\n",
+    "\n",
+    "* [Constraints](#Constraints)\n",
+    "* [Test Cases](#Test-Cases)\n",
+    "* [Algorithm](#Algorithm)\n",
+    "* [Code](#Code)\n",
+    "* [Unit Test](#Unit-Test)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Constraints\n",
+    "\n",
+    "* Is the input an array of ints?\n",
+    "    * Yes\n",
+    "* Can the input have duplicates?\n",
+    "    * Yes\n",
+    "* Do we know how many times the array was rotated?\n",
+    "    * No\n",
+    "* Was the array originally sorted in increasing or decreasing order?\n",
+    "    * Increasing\n",
+    "* For the output, do we return the index?\n",
+    "    * Yes\n",
+    "* Can we assume the inputs are valid?\n",
+    "    * No\n",
+    "* Can we assume this fits memory?\n",
+    "    * Yes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Test Cases\n",
+    "\n",
+    "* None -> Exception\n",
+    "* [] -> None\n",
+    "* Not found -> None\n",
+    "* General case with duplicates\n",
+    "* General case without duplicates"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Algorithm\n",
+    "\n",
+    "### General case without dupes\n",
+    "\n",
+    "<pre>\n",
+    "\n",
+    "index                   0   1   2   3   4   5   6   7   8   9\n",
+    "input                 [ 1,  3,  5,  6,  7,  8,  9, 10, 12, 14]\n",
+    "input rotated 1x      [10, 12, 14,  1,  3,  5,  6,  7,  8,  9]\n",
+    "input rotated 2x      [ 5,  6,  7,  8,  9, 10, 12, 14,  1,  3]\n",
+    "input rotated 3x      [10, 12, 14,  1,  3,  5,  6,  7,  8,  9]\n",
+    "\n",
+    "find 1\n",
+    "len = 10\n",
+    "mid = 10 // 2 = 5\n",
+    "                        s                   m               e\n",
+    "index                   0   1   2   3   4   5   6   7   8   9\n",
+    "input                 [10, 12, 14,  1,  3,  5,  6,  7,  8,  9]\n",
+    "\n",
+    "input[start] > input[mid]: Left half is rotated\n",
+    "input[end] >= input[mid]: Right half is sorted\n",
+    "1 is not within input[mid+1] to input[end] on the right side, go left\n",
+    "\n",
+    "                        s       m       e\n",
+    "index                   0   1   2   3   4   5   6   7   8   9\n",
+    "input                 [10, 12, 14,  1,  3,  5,  6,  7,  8,  9]\n",
+    "\n",
+    "input[start] <= input[mid]: Right half is rotated\n",
+    "input[end] >= input[mid]: Left half is sorted\n",
+    "1 is not within input[left] to input[mid-1] on the left side, go right\n",
+    "\n",
+    "</pre>\n",
+    "\n",
+    "### General case with dupes\n",
+    "\n",
+    "<pre>\n",
+    "\n",
+    "                        s                   m               e\n",
+    "index                   0   1   2   3   4   5   6   7   8   9\n",
+    "input                 [ 1,  1,  1,  1,  1,  1,  1,  1,  1,  2]\n",
+    "\n",
+    "input[start] == input[mid], input[mid] != input[end], go right\n",
+    "\n",
+    "input rotated 1x      [ 1,  1,  2,  1,  1,  1,  1,  1,  1,  1]\n",
+    "\n",
+    "input[start] == input[mid] == input[end], search both sides\n",
+    "\n",
+    "</pre>\n",
+    "\n",
+    "Complexity:\n",
+    "* Time: O(log n) if there are no duplicates, else O(n)\n",
+    "* Space: O(m), where m is the recursion depth"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "class Array(object):\n",
+    "\n",
+    "    def search_sorted_array(self, array, val):\n",
+    "        if array is None or val is None:\n",
+    "            raise TypeError('array or val cannot be None')\n",
+    "        if not array:\n",
+    "            return None\n",
+    "        return self._search_sorted_array(array, val, start=0, end=len(array) - 1)\n",
+    "\n",
+    "    def _search_sorted_array(self, array, val, start, end):\n",
+    "        if end < start:\n",
+    "            return None\n",
+    "        mid = (start + end) // 2\n",
+    "        if array[mid] == val:\n",
+    "            return mid\n",
+    "        # Left side is sorted\n",
+    "        if array[start] < array[mid]:\n",
+    "            if array[start] <= val < array[mid]:\n",
+    "                return self._search_sorted_array(array, val, start, mid - 1)\n",
+    "            else:\n",
+    "                return self._search_sorted_array(array, val, mid + 1, end)\n",
+    "        # Right side is sorted\n",
+    "        elif array[start] > array[mid]:\n",
+    "            if array[mid] < val <= array[end]:\n",
+    "                return self._search_sorted_array(array, val, mid + 1, end)\n",
+    "            else:\n",
+    "                return self._search_sorted_array(array, val, start, mid - 1)\n",
+    "        # Duplicates\n",
+    "        else:\n",
+    "            if array[mid] != array[end]:\n",
+    "                return self._search_sorted_array(array, val, mid + 1, end)\n",
+    "            else:\n",
+    "                result = self._search_sorted_array(array, val, start, mid - 1)\n",
+    "                if result != None:\n",
+    "                    return result\n",
+    "                else:\n",
+    "                    return self._search_sorted_array(array, val, mid + 1, end)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Unit Test"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Overwriting test_search_sorted_array.py\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%writefile test_search_sorted_array.py\n",
+    "from nose.tools import assert_equal, assert_raises\n",
+    "\n",
+    "\n",
+    "class TestArray(object):\n",
+    "\n",
+    "    def test_search_sorted_array(self):\n",
+    "        array = Array()\n",
+    "        assert_raises(TypeError, array.search_sorted_array, None)\n",
+    "        assert_equal(array.search_sorted_array([3, 1, 2], 0), None)\n",
+    "        assert_equal(array.search_sorted_array([3, 1, 2], 0), None)\n",
+    "        data = [10, 12, 14,  1,  3,  5,  6,  7,  8,  9]\n",
+    "        assert_equal(array.search_sorted_array(data, val=1), 3)\n",
+    "        data = [ 1,  1,  2,  1,  1,  1,  1,  1,  1,  1]\n",
+    "        assert_equal(array.search_sorted_array(data, val=2), 2)\n",
+    "        print('Success: test_search_sorted_array')\n",
+    "\n",
+    "\n",
+    "def main():\n",
+    "    test = TestArray()\n",
+    "    test.test_search_sorted_array()\n",
+    "\n",
+    "\n",
+    "if __name__ == '__main__':\n",
+    "    main()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Success: test_search_sorted_array\n"
+     ]
+    }
+   ],
+   "source": [
+    "%run -i test_search_sorted_array.py"
+   ]
+  }
+ ],
+ "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": "3.4.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/sorting_searching/rotated_array_search/test_search_sorted_array.py b/sorting_searching/rotated_array_search/test_search_sorted_array.py
new file mode 100644
index 0000000..cf5229a
--- /dev/null
+++ b/sorting_searching/rotated_array_search/test_search_sorted_array.py
@@ -0,0 +1,24 @@
+from nose.tools import assert_equal, assert_raises
+
+
+class TestArray(object):
+
+    def test_search_sorted_array(self):
+        array = Array()
+        assert_raises(TypeError, array.search_sorted_array, None)
+        assert_equal(array.search_sorted_array([3, 1, 2], 0), None)
+        assert_equal(array.search_sorted_array([3, 1, 2], 0), None)
+        data = [10, 12, 14,  1,  3,  5,  6,  7,  8,  9]
+        assert_equal(array.search_sorted_array(data, val=1), 3)
+        data = [ 1,  1,  2,  1,  1,  1,  1,  1,  1,  1]
+        assert_equal(array.search_sorted_array(data, val=2), 2)
+        print('Success: test_search_sorted_array')
+
+
+def main():
+    test = TestArray()
+    test.test_search_sorted_array()
+
+
+if __name__ == '__main__':
+    main()
\ No newline at end of file