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   "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: Given an array, find the two indices that sum to a specific value.\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 there exactly one solution?\n",
    "    * Yes\n",
    "* Is there always a solution?\n",
    "    * Yes\n",
    "* Is the array an array of ints?\n",
    "    * Yes\n",
    "* Is the array sorted?\n",
    "    No\n",
    "* Are negative values possible?\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 input -> TypeError\n",
    "* [] -> ValueError\n",
    "* [1, 3, 2, -7, 5], 7 -> [2, 4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "### Brute force\n",
    "\n",
    "* For i in range(len(input)):\n",
    "    * For j in range(i+1, len(input)):\n",
    "        * if i + j == target return True\n",
    "* return False\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n^2)\n",
    "* Space: O(1)\n",
    "\n",
    "### Optimized\n",
    "\n",
    "<pre>\n",
    "* Loop through each num in nums\n",
    "    * Calculate the cache_target = target - num\n",
    "\n",
    "target = 7\n",
    "index  =  0  1  2   3  4\n",
    "nums   = [1, 3, 2, -7, 5]\n",
    "          ^\n",
    "cache_target = 7 - 1 = 6\n",
    "cache\n",
    "6 -> 0\n",
    "\n",
    "1 not in cache\n",
    "\n",
    "index  =  0  1  2   3  4\n",
    "nums   = [1, 3, 2, -7, 5]\n",
    "             ^\n",
    "cache_target = 7 - 3 = 4\n",
    "cache\n",
    "6 -> 0\n",
    "4 -> 1\n",
    "\n",
    "3 not in cache\n",
    "\n",
    "index  =  0  1  2   3  4\n",
    "nums   = [1, 3, 2, -7, 5]\n",
    "                ^\n",
    "cache_target = 7 - 2 = 5\n",
    "cache\n",
    "6 -> 0\n",
    "4 -> 1\n",
    "5 -> 2\n",
    "\n",
    "2 not in cache\n",
    "\n",
    "index  =  0  1  2   3  4\n",
    "nums   = [1, 3, 2, -7, 5]\n",
    "                    ^\n",
    "cache_target = 7 + 7 = 14\n",
    "cache\n",
    "6  -> 0\n",
    "4  -> 1\n",
    "5  -> 2\n",
    "14 -> 3\n",
    "\n",
    "-7 not in cache\n",
    "\n",
    "index  =  0  1  2   3  4\n",
    "nums   = [1, 3, 2, -7, 5]\n",
    "                       ^\n",
    "cache_target = 7 - 5 = 2\n",
    "cache\n",
    "6  -> 0\n",
    "4  -> 1\n",
    "5  -> 2\n",
    "14 -> 3\n",
    "\n",
    "5 in cache, success, output matching indices: cache[num] and current iteration index\n",
    "\n",
    "output = [2, 4]\n",
    "</pre>\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Solution(object):\n",
    "\n",
    "    def two_sum(self, nums, target):\n",
    "        if nums is None or target is None:\n",
    "            raise TypeError('nums or target cannot be None')\n",
    "        if not nums:\n",
    "            raise ValueError('nums cannot be empty')\n",
    "        cache = {}\n",
    "        for index, num in enumerate(nums):\n",
    "            cache_target = target - num\n",
    "            if num in cache:\n",
    "                return [cache[num], index]\n",
    "            else:\n",
    "                cache[cache_target] = index\n",
    "        return None"
   ]
  },
  {
   "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_two_sum.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_two_sum.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestTwoSum(object):\n",
    "\n",
    "    def test_two_sum(self):\n",
    "        solution = Solution()\n",
    "        assert_raises(TypeError, solution.two_sum, None, None)\n",
    "        assert_raises(ValueError, solution.two_sum, [], 0)\n",
    "        target = 7\n",
    "        nums = [1, 3, 2, -7, 5]\n",
    "        expected = [2, 4]\n",
    "        assert_equal(solution.two_sum(nums, target), expected)\n",
    "        print('Success: test_two_sum')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestTwoSum()\n",
    "    test.test_two_sum()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_two_sum\n"
     ]
    }
   ],
   "source": [
    "%run -i test_two_sum.py"
   ]
  }
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