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   "source": [
    "# Coding Homework  (DATS-6001)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Your Name: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement the following questions in Python. While efficiency is not our primary concern, your code and solutions must be *correct*, *bug-free*, and *well-documented*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1 (2 + 2 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a positive integer $x$, return $x$ with its digits reversed.\n",
    "\n",
    "Eg:  \n",
    "Input: $x = 123$  \n",
    "Output: $321$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a. Describe the logic of your algorithm. In other words, justify why you think your alogirthm must return the desired output for a given input."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b. Implement your algorithm in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2 (2 + 2 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a square matrix (list of lists), calculate the absolute difference between the sums of its diagonals.\n",
    "\n",
    "Eg:\n",
    "Input: \n",
    "mat =   \n",
    "[[11,2,4],  \n",
    "[4,5,6],  \n",
    "[10,8,-12]]\n",
    "\n",
    "Output: 15  \n",
    "Explanation:  \n",
    "Sum of primary diagonal $= 11 + 5 + (-12) = 4$.  \n",
    "Sum of secondary diagonal $= 4 + 5 + 10 = 19$.  \n",
    "Difference $= |19 - 4| = 15$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a. Describe the logic of your algorithm. In other words, justify why you think your alogirthm must return the desired output for a given input."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b. Implement your algorithm in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3 (2 + 2 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given an unsorted integer array $nums$. return the smallest positive integer that is not present in $nums$. Note: 0 is not the positive integer.\n",
    "\n",
    "Input: arr[] = [2, -3, 4, 1, 1, 7]  \n",
    "Output: 3  \n",
    "Explanation: 3 is the smallest positive number missing from the array.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a. Describe the logic of your algorithm. In other words, justify why you think your alogirthm must return the desired output for a given input."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b. Implement your algorithm in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4 (2 + 2 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given an integer array, find the maximum product of any subarray.\n",
    "\n",
    "Input: arr[] = [-2, 6, -3, -10, 0, 2]  \n",
    "Output: 180  \n",
    "Explanation: The subarray with maximum product is {6, -3, -10} with product = 6 * (-3) * (-10) = 180"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a. Describe the logic of your algorithm. In other words, justify why you think your alogirthm must return the desired output for a given input."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b. Implement your algorithm in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 5 (2 + 2 points)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a Python program to find the [median](https://en.wikipedia.org/wiki/Median) of two *sorted* arrays of different sizes. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a. Describe the logic of your algorithm. In other words, justify why you think your alogirthm must return the desired output for a given input."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b. Implement your algorithm in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
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