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   "source": [
    "<small><i>This notebook was prepared by [mrb00l34n](http://github.com/mrb00l34n). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges).</i></small>"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Challenge Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Counting Ways of Making Change\n",
    "\n",
    "* [Explanation](#Explanation)\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": [
    "## Explanation\n",
    "\n",
    "How many ways are there of making change for n, given k distinct coins? For example:\n",
    "\n",
    "Input: n = 4, k = 2, coins = [1,2]\n",
    "\n",
    "Output: 3. 1+1+1+1, 1+2+1, 2+2, would be the ways of making change.\n",
    "\n",
    "Note that a coin can be used any number of times, and we are counting unique combinations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Input: n = 0, k = 2, coins = [1,2] -> Output: 0\n",
    "* Input: n = 100, k = 3, coins = [1,2,3] -> Output: 884\n",
    "* Input: n = 1000, k = 100, coins = [1,2,3...99,100] -> Output: 15658181104580771094597751280645\n"
   ]
  },
  {
   "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/coinchange_ways/coinchange_ways_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": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def change_ways(n,k,coins):\n",
    "    # TODO: Implement me\n",
    "    return n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test\n",
    "\n",
    "\n",
    "\n",
    "**The following unit test is expected to fail until you solve the challenge.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name":"stdout",
     "text":[],
     "output_type": "stream"
    }
   ],
   "source": [
    "# %load test_coinchange_ways.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class Challenge(object):\n",
    "\n",
    "    def test_coinchange_ways(self,solution):\n",
    "        assert_equal(solution(0,2,[1,2]), 0)\n",
    "        assert_equal(solution(100,3,[1,2,3]), 884)\n",
    "        assert_equal(solution(1000,100,range(1,101)), 15658181104580771094597751280645)\n",
    "        print('Success: test_coinchange_ways')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = Challenge()\n",
    "    test.test_coinchange_ways(change_ways)\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/coinchange_ways/coinchange_ways_solution.ipynb) for a discussion on algorithms and code solutions."
   ]
  }
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