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   "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: Determine the minimum number of ways to make n cents, given coins of denominations less than n cents.\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",
    "* Do the coins have to reach exactly n cents?\n",
    "    * Yes\n",
    "* Can we assume we have an infinite number of coins to make n cents?\n",
    "    * Yes\n",
    "* Do we need to report the combination(s) of coins that represent the minimum?\n",
    "    * No\n",
    "* Can we assume the coin denominations are given in sorted order?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* coins: None or n: None -> Exception\n",
    "* coins: [] or n: 0 -> 0\n",
    "* coins: [1, 2, 3] or [3, 2, 1] -> 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change_min/coin_change_min_solution.ipynb).  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": {},
   "outputs": [],
   "source": [
    "class CoinChanger(object):\n",
    "\n",
    "    def make_change(self, coins, total):\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": {},
   "outputs": [],
   "source": [
    "# %load test_coin_change_min.py\n",
    "import unittest\n",
    "\n",
    "\n",
    "class TestCoinChange(unittest.TestCase):\n",
    "\n",
    "    def test_coin_change(self):\n",
    "        coin_changer = CoinChanger()\n",
    "        self.assertRaises(TypeError, coin_changer.make_change, None, None)\n",
    "        self.assertEqual(coin_changer.make_change([], 0), 0)\n",
    "        self.assertEqual(coin_changer.make_change([1, 2, 3], 5), 2)\n",
    "        self.assertEqual(coin_changer.make_change([3, 2, 1], 5), 2)\n",
    "        self.assertEqual(coin_changer.make_change([3, 2, 1], 8), 3)\n",
    "        print('Success: test_coin_change')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestCoinChange()\n",
    "    test.test_coin_change()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Notebook\n",
    "\n",
    "Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change_min/coin_change_min_solution.ipynb) for a discussion on algorithms and code solutions."
   ]
  }
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