diff --git a/recursion_dynamic/magic_index/__init__.py b/recursion_dynamic/magic_index/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/recursion_dynamic/magic_index/magic_index_challenge.ipynb b/recursion_dynamic/magic_index/magic_index_challenge.ipynb
new file mode 100644
index 0000000..3dc9734
--- /dev/null
+++ b/recursion_dynamic/magic_index/magic_index_challenge.ipynb
@@ -0,0 +1,196 @@
+{
+ "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 the magic index in an array, where array[i] = i.\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 array sorted?\n",
+ " * Yes\n",
+ "* Are the elements in the array distinct?\n",
+ " * No\n",
+ "* Does a magic index always exist?\n",
+ " * No\n",
+ "* If there is no magic index, do we just return -1?\n",
+ " * Yes\n",
+ "* Are negative values allowed in the array?\n",
+ " * Yes\n",
+ "* If there are multiple magic values, what do we return?\n",
+ " * Return the left-most one\n",
+ "* Can we assume this fits memory?\n",
+ " * Yes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Test Cases\n",
+ "\n",
+ "* None input -> -1\n",
+ "* Empty array -> -1\n",
+ "\n",
+ "\n",
+ "a[i] -4 -2 2 6 6 6 6 10\n",
+ " i 0 1 2 3 4 5 6 7\n",
+ "
\n",
+ "\n",
+ "Result: 2\n",
+ "\n",
+ "\n",
+ "a[i] -4 -2 1 6 6 6 6 10\n",
+ " i 0 1 2 3 4 5 6 7\n",
+ "
\n",
+ "\n",
+ "Result: 6\n",
+ "\n",
+ "\n",
+ "a[i] -4 -2 1 6 6 6 7 10\n",
+ " i 0 1 2 3 4 5 6 7\n",
+ "
\n",
+ "\n",
+ "Result: -1"
+ ]
+ },
+ {
+ "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 MagicIndex(object):\n",
+ "\n",
+ " def find_magic_index(self, array):\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_find_magic_index.py\n",
+ "from nose.tools import assert_equal\n",
+ "\n",
+ "\n",
+ "class TestFindMagicIndex(object):\n",
+ "\n",
+ " def test_find_magic_index(self):\n",
+ " magic_index = MagicIndex()\n",
+ " assert_equal(magic_index.find_magic_index(None), -1)\n",
+ " assert_equal(magic_index.find_magic_index([]), -1)\n",
+ " array = [-4, -2, 2, 6, 6, 6, 6, 10]\n",
+ " assert_equal(magic_index.find_magic_index(array), 2)\n",
+ " array = [-4, -2, 1, 6, 6, 6, 6, 10]\n",
+ " assert_equal(magic_index.find_magic_index(array), 6)\n",
+ " array = [-4, -2, 1, 6, 6, 6, 7, 10]\n",
+ " assert_equal(magic_index.find_magic_index(array), -1)\n",
+ " print('Success: test_find_magic')\n",
+ "\n",
+ "\n",
+ "def main():\n",
+ " test = TestFindMagicIndex()\n",
+ " test.test_find_magic_index()\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/recursion_dynamic/magic_index/magic_index_solution.ipynb b/recursion_dynamic/magic_index/magic_index_solution.ipynb
new file mode 100644
index 0000000..eade7fc
--- /dev/null
+++ b/recursion_dynamic/magic_index/magic_index_solution.ipynb
@@ -0,0 +1,256 @@
+{
+ "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 the magic index in an array, where array[i] = i.\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 array sorted?\n",
+ " * Yes\n",
+ "* Are the elements in the array distinct?\n",
+ " * No\n",
+ "* Does a magic index always exist?\n",
+ " * No\n",
+ "* If there is no magic index, do we just return -1?\n",
+ " * Yes\n",
+ "* Are negative values allowed in the array?\n",
+ " * Yes\n",
+ "* If there are multiple magic values, what do we return?\n",
+ " * Return the left-most one\n",
+ "* Can we assume this fits memory?\n",
+ " * Yes"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Test Cases\n",
+ "\n",
+ "* None input -> -1\n",
+ "* Empty array -> -1\n",
+ "\n",
+ "\n",
+ "a[i] -4 -2 2 6 6 6 6 10\n",
+ " i 0 1 2 3 4 5 6 7\n",
+ "
\n",
+ "\n",
+ "Result: 2\n",
+ "\n",
+ "\n",
+ "a[i] -4 -2 1 6 6 6 6 10\n",
+ " i 0 1 2 3 4 5 6 7\n",
+ "
\n",
+ "\n",
+ "Result: 6\n",
+ "\n",
+ "\n",
+ "a[i] -4 -2 1 6 6 6 7 10\n",
+ " i 0 1 2 3 4 5 6 7\n",
+ "
\n",
+ "\n",
+ "Result: -1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Algorithm\n",
+ "\n",
+ "We'll use a binary search to split the search space in half on each iteration. To obtain more efficiency, we can do a little better than a naive left and half split.\n",
+ "\n",
+ "In the example below, we see that i == 5 cannot be the magic index, otherwise a[5] would have to equal 5 (note a[4] == 6).\n",
+ "\n",
+ "\n",
+ "a[i] -4 -2 2 6 6 6 6 10\n",
+ " i 0 1 1 3 4 5 6 7\n",
+ " mid\n",
+ "
\n",
+ "\n",
+ "Similarly, in the example below we can further trim the left search space.\n",
+ "\n",
+ "\n",
+ "a[i] -4 -2 2 2 2 6 6 10\n",
+ " i 0 1 2 3 4 5 6 7\n",
+ " mid\n",
+ "
\n",
+ "\n",
+ "\n",
+ "* Calculate mid\n",
+ "* If mid == array[mid], return mid\n",
+ "* Recurse on the left side of the array\n",
+ " * start: 0\n",
+ " * end: min(mid-1, array[mid]\n",
+ "* Recurse on the right side of the array\n",
+ " * start: max(mid+1, array[mid]\n",
+ " * end: end\n",
+ "\n",
+ "Complexity:\n",
+ "* Time: O(log(n))\n",
+ "* Space: O(log(n))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Code"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ "from __future__ import division\n",
+ "\n",
+ "\n",
+ "class MagicIndex(object):\n",
+ "\n",
+ " def find_magic_index(self, array):\n",
+ " if array is None or not array:\n",
+ " return -1\n",
+ " return self._find_magic_index(array, 0, len(array) - 1)\n",
+ "\n",
+ " def _find_magic_index(self, array, start, end):\n",
+ " if end < start or start < 0 or end >= len(array):\n",
+ " return -1\n",
+ " mid = (start + end) // 2\n",
+ " if mid == array[mid]:\n",
+ " return mid\n",
+ " left_end = min(mid - 1, array[mid])\n",
+ " left_result = self._find_magic_index(array, start, end=left_end)\n",
+ " if left_result != -1:\n",
+ " return left_result\n",
+ " right_start = max(mid + 1, array[mid])\n",
+ " right_result = self._find_magic_index(array, start=right_start, end=end)\n",
+ " if right_result != -1:\n",
+ " return right_result\n",
+ " return -1"
+ ]
+ },
+ {
+ "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_find_magic_index.py\n"
+ ]
+ }
+ ],
+ "source": [
+ "%%writefile test_find_magic_index.py\n",
+ "from nose.tools import assert_equal\n",
+ "\n",
+ "\n",
+ "class TestFindMagicIndex(object):\n",
+ "\n",
+ " def test_find_magic_index(self):\n",
+ " magic_index = MagicIndex()\n",
+ " assert_equal(magic_index.find_magic_index(None), -1)\n",
+ " assert_equal(magic_index.find_magic_index([]), -1)\n",
+ " array = [-4, -2, 2, 6, 6, 6, 6, 10]\n",
+ " assert_equal(magic_index.find_magic_index(array), 2)\n",
+ " array = [-4, -2, 1, 6, 6, 6, 6, 10]\n",
+ " assert_equal(magic_index.find_magic_index(array), 6)\n",
+ " array = [-4, -2, 1, 6, 6, 6, 7, 10]\n",
+ " assert_equal(magic_index.find_magic_index(array), -1)\n",
+ " print('Success: test_find_magic')\n",
+ "\n",
+ "\n",
+ "def main():\n",
+ " test = TestFindMagicIndex()\n",
+ " test.test_find_magic_index()\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_find_magic\n"
+ ]
+ }
+ ],
+ "source": [
+ "%run -i test_find_magic_index.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/recursion_dynamic/magic_index/test_find_magic_index.py b/recursion_dynamic/magic_index/test_find_magic_index.py
new file mode 100644
index 0000000..d6b1bb2
--- /dev/null
+++ b/recursion_dynamic/magic_index/test_find_magic_index.py
@@ -0,0 +1,25 @@
+from nose.tools import assert_equal
+
+
+class TestFindMagicIndex(object):
+
+ def test_find_magic_index(self):
+ magic_index = MagicIndex()
+ assert_equal(magic_index.find_magic_index(None), -1)
+ assert_equal(magic_index.find_magic_index([]), -1)
+ array = [-4, -2, 2, 6, 6, 6, 6, 10]
+ assert_equal(magic_index.find_magic_index(array), 2)
+ array = [-4, -2, 1, 6, 6, 6, 6, 10]
+ assert_equal(magic_index.find_magic_index(array), 6)
+ array = [-4, -2, 1, 6, 6, 6, 7, 10]
+ assert_equal(magic_index.find_magic_index(array), -1)
+ print('Success: test_find_magic')
+
+
+def main():
+ test = TestFindMagicIndex()
+ test.test_find_magic_index()
+
+
+if __name__ == '__main__':
+ main()
\ No newline at end of file