SJU_ACM_Software_Engineering_Interview_Prep_.ipynb

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        "#  <mark> **SJU ACM Software Engineering Interview Prep**\n",
        "\n",
        "# **Understanding the Importance of Time and Space Complexity**\n",
        "\n",
        "### Inspired by: https://www.youtube.com/watch?v=oBt53YbR9Kk\n",
        "\n",
        "<br>\n",
        "\n",
        "### Nowadays, a majority of software engineering interviews focus on two main concepts: **Data Structures & Algorithms**. But why? \n",
        "\n",
        "### Why are these two concepts so essential to understand in order to work in an engineering role? \n",
        "\n",
        "### The short answer is **speed & efficiency**. \n",
        "\n",
        "<br>\n",
        "\n",
        "> ### At major tech companies - Google, Facebook, Microsoft, Amazon, etc., engineers spend most of their time developing optimal algorithms to maximize the speed of their programs while also minimizing use of the company’s resources (servers, computation power, etc).\n",
        "\n",
        "<br>\n",
        "\n",
        "> ### This is the main reason why interviews for these companies are so focused on data structures and algorithms, as they want people who can think outside the box to design algorithms that can save the company valuable resources. Google, YouTube, Facebook, Amazon, and Instagram have the highest number of users in the world. To handle more users on these sites it requires more optimization to be done and that’s why big tech companies hire candidates who can optimize their software and build new and efficient solutions for their problems. \n",
        "\n",
        "<br> \n",
        "\n",
        "---\n",
        "\n",
        "<br>\n",
        "\n",
        "## **To understand why writing fast and efficient algorithms is so important, think about this:**\n",
        "\n",
        "\n",
        "* ## What if it took 30 seconds to load your home and explore page on Instagram, would you still use the app?\n",
        "\n",
        "* ## What if searching for a song on Spotify took 1 minute, would you continue using it?\n",
        "\n",
        "* ## What if Google Maps took 2 minutes to calculate the best route, would you continue using it?\n",
        "\n",
        "<br>\n",
        "\n",
        "---\n",
        "\n",
        "<br>\n",
        "\n",
        "## In order to write fast and efficient algorithms, we have to be able to compare the performance of algorithms to determine which one would be faster. \n",
        "\n",
        "\n",
        "### This is where **time complexity** comes in. \n",
        "\n",
        "#  <mark> **The time complexity of an algorithm measures its performance in relation to the size of its input** </mark>"
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        "### In order to better understand time complexity, we will focus on a problem that everyone is likely familiar with - the **Fibonacci Sequence**. \n",
        "\n",
        "\n",
        "## The Fibonacci Sequence is a series of numbers where the next number is found by adding up the two numbers before it. \n",
        "\n",
        "<br>\n",
        "\n",
        "## The Formula for the Fibonacci Sequence is as follows:\n",
        "    \n",
        "> ## $F(n) = F(n-1) + F(n - 2)$\n",
        "\n",
        "<br>\n",
        "\n",
        "## As such, the first 10 numbers of the Fibonacci Sequence are:\n",
        "\n",
        "> ## 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55"
      ]
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      "source": [
        "### Lets now imagine that we're making a web app that calculates the nth Fibonacci Number such as this:\n",
        "![image](https://user-images.githubusercontent.com/43652410/142350052-57a87712-dd69-4f7f-a2d0-8414dbf520ec.png)\n",
        "### We have to create a function that calculates Fib(n) given n\n",
        "\n",
        "<br>\n",
        "\n",
        "### The functions below show three different algorithms to calculate the Fibonacci numbers, with each set to calculate the 40th Fibonacci number"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZTzCXdUrFyK6"
      },
      "source": [
        "import time\n",
        "from tqdm import tqdm\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.pyplot import figure\n",
        "import statistics"
      ],
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TsnQgMLZksHX"
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      "source": [
        "FIBONACCI_NUM = 40"
      ],
      "execution_count": 12,
      "outputs": []
    },
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        "id": "bRcStLAZFyK6"
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      "source": [
        "### Brute Force Recursive Approach for the Fibonacci Sequence"
      ]
    },
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      "source": [
        "def bruteforce_fibonacci(n):\n",
        "    \n",
        "    if n <= 2: return 1 \n",
        "    \n",
        "    return bruteforce_fibonacci(n - 1) + bruteforce_fibonacci(n - 2)\n",
        "\n",
        "\n",
        "bf_start = time.time()\n",
        "\n",
        "bf_fib = bruteforce_fibonacci(FIBONACCI_NUM)\n",
        "\n",
        "bf_end = time.time()\n",
        "\n",
        "print(f\"F({FIBONACCI_NUM}) = {bf_fib} \\nExecution Time: {round(bf_end - bf_start, 2)} seconds\")"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "F(40) = 102334155 \n",
            "Execution Time: 29.1 seconds\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lpm9ryZiFyK8"
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      "source": [
        "### Optimized Recursive Approach with Memoization"
      ]
    },
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        "def memoized_fibonacci(n, memo):\n",
        "    \n",
        "    if n in memo: return memo[n]\n",
        "    \n",
        "    if n <= 2: return 1\n",
        "    \n",
        "    memo[n] = memoized_fibonacci(n - 1, memo) + memoized_fibonacci(n - 2, memo)\n",
        "    \n",
        "    return memo[n]\n",
        "\n",
        "\n",
        "mem_start = time.time()\n",
        "\n",
        "mem_fib = memoized_fibonacci(FIBONACCI_NUM, {})\n",
        "\n",
        "mem_end = time.time()\n",
        "\n",
        "print(f\"F({FIBONACCI_NUM}) = {mem_fib} \\nExecution Time: {mem_end - mem_start} seconds\")"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "F(40) = 102334155 \n",
            "Execution Time: 0.00011229515075683594 seconds\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "## Optimized Iterative Approach with Tabulation"
      ]
    },
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        },
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      "source": [
        "def tabulation_fibonacci(n):\n",
        "    \n",
        "    table = [0] * (n + 1)\n",
        "    \n",
        "    table[1] = 1\n",
        "    \n",
        "    for index in range(2, n + 1):\n",
        "        \n",
        "        table[index] += table[index - 1] + table[index - 2]\n",
        "        \n",
        "    return table[n]\n",
        "\n",
        "\n",
        "tab_start = time.time()\n",
        "\n",
        "tab_fib = tabulation_fibonacci(FIBONACCI_NUM)\n",
        "\n",
        "tab_end = time.time()\n",
        "\n",
        "print(f\"F({FIBONACCI_NUM}) = {tab_fib} \\nExecution Time: {tab_end - tab_start} seconds\")"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "F(40) = 102334155 \n",
            "Execution Time: 5.1021575927734375e-05 seconds\n"
          ]
        }
      ]
    },
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        "outputId": "49cba29e-b9df-4a66-896f-2edf6fe88dc5"
      },
      "source": [
        "print(f\"The memoized_fibonacci function is {round((bf_end - bf_start) / (mem_end - mem_start), 2)}x faster than the bruteforce_Fibonacci function\")\n",
        "print(f\"\\nThe tabulation_fibonacci function is {round((bf_end - bf_start) / (tab_end - tab_start), 2)}x faster than the bruteforce_Fibonacci function\")"
      ],
      "execution_count": 16,
      "outputs": [
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          "text": [
            "The memoized_fibonacci function is 259161.68x faster than the bruteforce_Fibonacci function\n",
            "\n",
            "The tabulation_fibonacci function is 359015.15x faster than the bruteforce_Fibonacci function\n"
          ]
        }
      ]
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      "source": [
        "def compare_execution_times():\n",
        "\n",
        "    bf_times = [] \n",
        "    memo_times = []\n",
        "    tab_times = []\n",
        "\n",
        "    for n in range(5, 40):\n",
        "\n",
        "        bf_start = time.time()\n",
        "        bruteforce_fibonacci(n)\n",
        "        bf_end = time.time()\n",
        "        bf_times.append(bf_end - bf_start)\n",
        "\n",
        "        mem_start = time.time()\n",
        "        memoized_fibonacci(n, {})\n",
        "        mem_end = time.time()\n",
        "        memo_times.append(mem_end - mem_start)\n",
        "\n",
        "        tab_start = time.time()\n",
        "        tabulation_fibonacci(n)\n",
        "        tab_end = time.time()\n",
        "        tab_times.append(tab_end - tab_start)\n",
        "\n",
        "    figure, axis = plt.subplots(2, figsize=(10,10))\n",
        "    axis[0].plot(bf_times, label = 'Brute Force')\n",
        "    axis[0].plot(memo_times, label = 'Memoized')\n",
        "    axis[0].plot(tab_times, label = 'Tabulation')\n",
        "    axis[0].legend(loc=\"upper left\")\n",
        "\n",
        "    axis[1].plot(memo_times, label = 'Memoized')\n",
        "    axis[1].plot(tab_times, label = 'Tabulation')\n",
        "    plt.legend()\n",
        "    plt.show()\n"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RZn1V0V1u3QF"
      },
      "source": [
        "### These graphs show the relationship between the nth Fibonacci number (x-axis) and how long each function takes to compute the number (y-axis)\n",
        "\n",
        "<br>\n",
        "\n",
        "### We can see here that the Brute Force approach is extremely inefficient and slow compared to the memoized and tabulation approach, as for larger fibonacci numbers, the execution time increases **exponentially**"
      ]
    },
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          "height": 592
        },
        "id": "xkRbvRxKGSrj",
        "outputId": "58ef125a-8fa5-4d07-b960-84767e006c1a"
      },
      "source": [
        "compare_execution_times()"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 720x720 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bxZLr7XkuusP"
      },
      "source": [
        "## Why is the Brute Force approach so slow?\n",
        "\n",
        "<br>\n",
        "\n",
        "Lets take a closer look at the Brute Force function:\n",
        "\n",
        "```python\n",
        "def bruteforce_fibonacci(n):\n",
        "    \n",
        "    if n <= 2: return 1 \n",
        "\n",
        "    return bruteforce_fibonacci(n - 1) + bruteforce_fibonacci(n - 2)\n",
        "```\n",
        "\n",
        "<br>\n",
        "\n",
        "With this code, we can draw a tree to show how the 8th Fibonacci number is calculated:\n",
        "\n",
        "<img src=\"https://github.com/SJUACM/Technical-Interview-Prep/blob/gh-pages/img/Practice%20Problems/Fibonacci/fib_tree.png?raw=true\"></img>\n",
        "\n",
        "\n",
        "<br>\n",
        "\n",
        "From the recursive tree, we can see that in order to calculate the 8th Fibonacci number, we would have to calculate\n",
        "\n",
        "\n",
        "> fib(4) 5 separate times (highlighted in green) \n",
        "\n",
        "> fib(3) 7 separate times (highlighted in blue)\n",
        "\n",
        "\n",
        "This is clearly a problem, as each fib(n) number should be calculated only once, if any calculation is repeated, that is wasted computation time.\n",
        "\n",
        "<br>\n",
        "\n",
        "## In total, this function takes 42 recursive calls just to calculate the 8th Fibonacci number!\n",
        "\n",
        "## <mark> **In general, the time complexity of this brute force algorithm is $O(2^n)$** </mark>\n",
        "\n",
        "<br>\n",
        "\n",
        "It is important to note that the time complexity of an algorithm does not indicate exactly how many times the function is called / executed. Rather, it is an approximation based on a pattern that the function follows. It provides an **upper bound** for the amount of time taken.\n",
        "\n",
        "The time complexity for the brute force algorithm can be derived as shown below:\n",
        "\n",
        "    2^0=1                                     fib(n)\n",
        "    2^1=2                  fib(n-1)                              fib(n-2)\n",
        "    2^2=4         fib(n-2)          fib(n-3)           fib(n-3)            fib(n-4)\n",
        "    2^3=8   fib(n-3) fib(n-4)  fib(n-4) fib(n-5)   fib(n-4) fib(n-5)   fib(n-5) fib(n-6)    ..so on\n",
        "    2^i for ith level\n",
        "\n",
        "\n",
        "Each Fibonacci number increases the depth of the tree by 1, where at each level of the tree, the number of function calls is equal to $2^i$ where $i$ is the current level of the tree.\n",
        "\n",
        "### This implies that each new level of the tree has twice as many function calls as the level above it, leading to the overall time complexity of the brute force algorithm to be $O(2^n)$, where **each new Fibonacci number takes twice as long to compute as the previous number.**\n",
        "\n",
        "<br>\n",
        "\n",
        "## <mark> **This brute force algorithm is so slow that it would take over 2,500,000,000,000,000,000,000,000,000 YEARS to calculate just the 200th Fibonacci number! Whereas the optimized approaches each take less than a second to calculate it!** </mark>\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xrKtLuWMEXrO"
      },
      "source": [
        "## What makes the Memoized and Tabulation approaches so fast?\n",
        "\n",
        "Lets take a look at the memoized function:\n",
        "\n",
        "```python\n",
        "def memoized_fibonacci(n, memo):\n",
        "    \n",
        "    if n in memo: return memo[n]\n",
        "    \n",
        "    if n <= 2: return 1\n",
        "    \n",
        "    memo[n] = memoized_fibonacci(n - 1, memo) + memoized_fibonacci(n - 2, memo)\n",
        "    \n",
        "    return memo[n]\n",
        "```\n",
        "\n",
        "The memoized_fibonacci function is efficient because it does not recompute the value of a Fibonacci number that has been computed previously.\n",
        "\n",
        "We saw with the brute force function that in order to calculate the 8th Fibonacci number, we would have to calculate fib(4) 5 separate times and fib(3) 7 separate times, which is wasted computation time.\n",
        "\n",
        "<br>\n",
        "\n",
        "### A better approach would be to store the result of a Fibonacci number and if we need to access it again, we can just load it from memory. **This is the goal of memoization.**\n",
        "\n",
        "### **By utilizing a dictionary data structure, indicated by the *memo* variable** in the function, we can store the result of each Fibonacci number, so after each recursive call, we can check if we computed that number previously by checking if it is stored inside the memo variable. If it is inside the memo variable, we can simply access the corresponding Fibonacci number from there instead of recomputing the value through more recursive calls.\n",
        "\n",
        "<br>\n",
        "\n",
        "### This process shown in the following diagram:\n",
        "\n",
        "<img src = \"https://github.com/SJUACM/Technical-Interview-Prep/blob/gh-pages/img/Practice%20Problems/Fibonacci/bf_vs_memoized_fib_tree.png?raw=true\"> </img>\n",
        "\n",
        "Note that for the memoized diagram, once fib(4) was calculated once on the left side of the tree, its result was stored and then accessed when fib(4) is called on the right side of the tree. This eliminates the need for any recalculation and makes the algorithm very efficient.\n",
        "\n",
        "<br>\n",
        "\n",
        "In fact, for larger Fibonacci numbers, the recursion tree for the memoized function does not grow exponentially like the brute force function. Instead, only two more nodes are added for each incremental number, as shown in the diagram below. \n",
        "\n",
        "<img src= \"https://github.com/SJUACM/Technical-Interview-Prep/blob/gh-pages/img/Practice%20Problems/Fibonacci/memoized_fib_tree.png?raw=true\"></img>\n",
        "\n",
        "Because we are storing the result of each Fibonacci number in the memo variable, there is no need to compute any number twice, which is why once all the Fibonacci numbers are calculated from the input number ***n*** down to 1, all the other recursive calls utilize the memo variable to get the corresponding Fibonacci number.\n",
        "\n",
        "\n",
        "## <mark> **This results in a time complexity of $O(n)$, also known as linear time** </mark>\n",
        "\n",
        "Although there are 2 nodes added for each incremental number, which would make the time complexity $O(2n)$, big O-notation does not include any coefficients, so the time complexity simplifies to $O(n)$.\n",
        "\n",
        "<br>\n",
        "\n",
        "---\n",
        "\n",
        "<br>\n",
        "\n",
        "\n",
        "# **Tabulation Approach** \n",
        "\n",
        "Lets take a closer look at the tabulation function: \n",
        "\n",
        "```python\n",
        "def tabulation_fibonacci(n):\n",
        "    \n",
        "    table = [0] * (n + 1)\n",
        "    \n",
        "    table[1] = 1\n",
        "    \n",
        "    for index in range(2, n + 1):\n",
        "        \n",
        "        table[index] += table[index - 1] + table[index - 2]\n",
        "        \n",
        "    return table[n]\n",
        "```\n",
        "\n",
        "The tabulation_fibonacci function is differs from the brute force and memoized function because it is iterative and not recursive. \n",
        "\n",
        "The first line of the function creates a list called table of length n + 1, with all the elements initialized to 0. Setting the length of the list is important for the next steps, as we modify each element in the table to correspond to the Fibonacci numbers.\n",
        "\n",
        "<br>\n",
        "\n",
        "The second line of the function sets the second element (index 1) of table equal to 1, as that is representative of the 2nd Fibonacci number.\n",
        "\n",
        "Then, we create a for loop where we iterate from index 2 to index n + 1 and we set the value of each corresponding element in table equal to the sum of the previous two elements in table, indicated by this line -> ```table[index] += table[index - 1] + table[index - 2]```\n",
        "\n",
        "<br>\n",
        "\n",
        "## Each element of table is populated with the corresponding Fibonacci number for its index. \n",
        "# Check out the diagram below for an example of what table would look like with an input of 7:\n",
        "\n",
        "<img src=\"https://github.com/SJUACM/Technical-Interview-Prep/blob/gh-pages/img/Practice%20Problems/Fibonacci/tabulation_fib.png?raw=true\"> </img>\n",
        "\n",
        "In this example, with an input of 7, table becomes equal to ```[0, 1, 1, 2, 3, 5, 8, 13]``` and then the function returns ```table[n]```, where n is 7, so it would return 13.\n",
        "\n",
        "## <mark> **Because the for loop runs only n times, the time complexity of this algorithm is $O(n)$** </mark>\n",
        "\n",
        "\n",
        "<br>\n",
        "\n",
        "## In general, going with the tabular approach is a better option than memoization, mainly because for large numbers (even just 1000), you will reach the **maximum recursion depth** and not be able to compute larger numbers. Tabulation is also generally a bit faster than memoization, so it is your best option for a fast algorithm.\n",
        "\n",
        "<br>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9I8crhvMWNxZ"
      },
      "source": [
        "---\n",
        "\n",
        "<br>\n",
        "\n",
        "## Although the tabulation approach is fast, it does have one main drawback: **memory usage**\n",
        "\n",
        "### The algorithm requires a list of size n to be created in order to compute the nth Fibonacci number\n",
        "### If we used the tabulation_fibonacci function to calculate the 1000th Fibonacci number, a list of size 1000 would have to be created and stored in memory\n",
        "### We can visualize this with the code below:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J9wsTUlBXgRV",
        "outputId": "6832f06b-f67d-4b01-de24-74b66d688508"
      },
      "source": [
        "def tabulation_fibonacci_2(n):\n",
        "    \n",
        "    table = [0] * (n + 1)\n",
        "    \n",
        "    table[1] = 1\n",
        "    \n",
        "    for index in range(2, n + 1):\n",
        "        \n",
        "        table[index] += table[index - 1] + table[index - 2]\n",
        "    \n",
        "    print(table)\n",
        "    return table[n]\n",
        "\n",
        "tabulation_fibonacci_2(1000)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C4NSzsdgXvh8"
      },
      "source": [
        "## The list that is created takes up a significant amount of memory, especially considering how large the Fibonacci numbers get, with latter ones being over 60 digits long\n",
        "\n",
        "<br>\n",
        "\n",
        "### We can easily create another function that calculates Fib(n) without creating a list and just iteratively adding numbers to reach the nth Fibonacci number\n",
        "\n",
        "### The function is shown below:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y_MQoWBAGSuB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1f9bbdc5-2d8f-4d13-d5cb-e68b7a5d19ac"
      },
      "source": [
        "def space_optimized_fib(n):\n",
        "\n",
        "    prev_num = 0\n",
        "    curr_num = 1\n",
        "    fib_n = prev_num + curr_num\n",
        "\n",
        "    for x in range(2, n + 1):\n",
        "        fib_n = prev_num + curr_num\n",
        "        prev_num = curr_num\n",
        "        curr_num = fib_n\n",
        "\n",
        "    return fib_n\n",
        "\n",
        "space_optimized_fib(100)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "354224848179261915075"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VTFXhk1KbWPD"
      },
      "source": [
        "## This function has a space complexity of `O(1)` because no matter how large the input `n` is, we only store 3 variables in memory, the number of variables we use does not change with larger Fibonacci numbers. The memory usage remains constant.\n",
        "\n",
        "<br>\n",
        "\n",
        "---\n",
        "\n",
        "<br>\n",
        "\n",
        "#### This `space_optimized_fib` function is also slightly faster than the `tabulation_fibonacci` function\n",
        "#### We can see this with the plot below "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZLvF4MDtYfHY"
      },
      "source": [
        "def compare_execution_times2():\n",
        "\n",
        "    tab_avg_times = [] \n",
        "    opt_avg_times = []\n",
        "\n",
        "    for n in tqdm(range(50, 2000)):\n",
        "\n",
        "        tab_times = []\n",
        "        for _ in range(5):\n",
        "            tab_start = time.time()\n",
        "            tabulation_fibonacci(n)\n",
        "            tab_end = time.time()\n",
        "            tab_times.append(tab_end - tab_start)\n",
        "\n",
        "        tab_avg_times.append(statistics.mean(tab_times))\n",
        "\n",
        "        opt_times = []\n",
        "        for _ in range(5):\n",
        "            opt_start = time.time()\n",
        "            space_optimized_fib(n)\n",
        "            opt_end = time.time()\n",
        "            opt_times.append(opt_end - opt_start)\n",
        "\n",
        "        opt_avg_times.append(statistics.mean(opt_times))\n",
        "\n",
        "    plt.figure(figsize=(10, 6))\n",
        "    plt.plot(tab_avg_times, label = 'Tabulation')\n",
        "    plt.plot(opt_avg_times, label = 'Space Optimized')\n",
        "\n",
        "    plt.legend()\n",
        "    plt.show()"
      ],
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "id": "rIW5u8BYdZTH",
        "outputId": "b018b986-8650-4179-c618-441ea52b8a98"
      },
      "source": [
        "compare_execution_times2()"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 1950/1950 [00:05<00:00, 381.41it/s]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SMZbj29nfyrr"
      },
      "source": [
        "### Because the `space_optimized_fib` function's execution times grow slower than the `tabulation_fibonacci` function, we can conclude that the `space_optimized_fib` function is faster"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "McqJEvdqegdT"
      },
      "source": [
        ""
      ],
      "execution_count": 39,
      "outputs": []
    }
  ]
}