{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Asymptotics - Perspective\n"
      ],
      "metadata": {
        "id": "CrUe37fCnoJL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Consider a task that can be solved by two algorithms - one with run time $n^{2}$ and another with run time $1000n + 277$ on inputs of size $n$. Which one would you prefer to use?\n",
        "\n"
      ],
      "metadata": {
        "id": "L-vn3EMcn2Ck"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 1. Generate x values using numpy.linspace() for a smooth curve\n",
        "x = np.linspace(0, 10, 10) # 1000 evenly spaced points from 0 to 1000\n",
        "\n",
        "# 2. Define the function and calculate y values (vectorization is efficient)\n",
        "def square_function(x):\n",
        "  return x**2\n",
        "\n",
        "def linear_function(x):\n",
        "  return (1000*x + 277)\n",
        "\n",
        "y = square_function(x)\n",
        "z = linear_function(x)\n",
        "\n",
        "# 3. Plot the data\n",
        "plt.plot(x, y, label='f(x) = x^2', color='red') # Customize the line\n",
        "plt.plot(x, z, label='g(x) = 1000x + 277', color='blue') # Customize the line\n",
        "\n",
        "# 4. Add labels and a title\n",
        "plt.xlabel(\"X-axis\")\n",
        "plt.ylabel(\"Y-axis\")\n",
        "plt.title(\"Plot of two Functions f(x) and g(x)\")\n",
        "plt.legend()\n",
        "\n",
        "# 5. Display the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "VkWrk_HHn7TO",
        "outputId": "dd0eda94-58d0-44b2-887c-1f37b1558b0c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 1. Generate x values using numpy.linspace() for a smooth curve\n",
        "x = np.linspace(0, 100, 100) # 1000 evenly spaced points from 0 to 1000\n",
        "\n",
        "# 2. Define the function and calculate y values (vectorization is efficient)\n",
        "def square_function(x):\n",
        "  return x**2\n",
        "\n",
        "def linear_function(x):\n",
        "  return (1000*x + 277)\n",
        "\n",
        "y = square_function(x)\n",
        "z = linear_function(x)\n",
        "\n",
        "# 3. Plot the data\n",
        "plt.plot(x, y, label='f(x) = x^2', color='red') # Customize the line\n",
        "plt.plot(x, z, label='g(x) = 1000x + 277', color='blue') # Customize the line\n",
        "\n",
        "# 4. Add labels and a title\n",
        "plt.xlabel(\"X-axis\")\n",
        "plt.ylabel(\"Y-axis\")\n",
        "plt.title(\"Plot of two Functions y(x) and z(x)\")\n",
        "plt.legend()\n",
        "\n",
        "# 5. Display the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "mDCv_Jleow32",
        "outputId": "95b71944-7471-4492-cc0e-4a90fee17830"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 1. Generate x values using numpy.linspace() for a smooth curve\n",
        "x = np.linspace(0, 1000, 1000) # 1000 evenly spaced points from 0 to 1000\n",
        "\n",
        "# 2. Define the function and calculate y values (vectorization is efficient)\n",
        "def square_function(x):\n",
        "  return x**2\n",
        "\n",
        "def linear_function(x):\n",
        "  return (1000*x + 277)\n",
        "\n",
        "y = square_function(x)\n",
        "z = linear_function(x)\n",
        "\n",
        "# 3. Plot the data\n",
        "plt.plot(x, y, label='f(x) = x^2', color='red') # Customize the line\n",
        "plt.plot(x, z, label='g(x) = 1000x + 277', color='blue') # Customize the line\n",
        "\n",
        "# 4. Add labels and a title\n",
        "plt.xlabel(\"X-axis\")\n",
        "plt.ylabel(\"Y-axis\")\n",
        "plt.title(\"Plot of two Functions y(x) and z(x)\")\n",
        "plt.legend()\n",
        "\n",
        "# 5. Display the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "GMtR40b1pRdy",
        "outputId": "7793c170-a110-4baf-f242-3506c0d188c1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "# 1. Generate x values using numpy.linspace() for a smooth curve\n",
        "x = np.linspace(0, 10000, 10000) # 10000 evenly spaced points from 0 to 10000\n",
        "\n",
        "# 2. Define the function and calculate y values (vectorization is efficient)\n",
        "def square_function(x):\n",
        "  return x**2\n",
        "\n",
        "def linear_function(x):\n",
        "  return (1000*x + 277)\n",
        "\n",
        "y = square_function(x)\n",
        "z = linear_function(x)\n",
        "\n",
        "# 3. Plot the data\n",
        "plt.plot(x, y, label='f(x) = x^2', color='red') # Customize the line\n",
        "plt.plot(x, z, label='g(x) = 1000x + 277', color='blue') # Customize the line\n",
        "\n",
        "# 4. Add labels and a title\n",
        "plt.xlabel(\"X-axis\")\n",
        "plt.ylabel(\"Y-axis\")\n",
        "plt.title(\"Plot of two Functions y(x) and z(x)\")\n",
        "plt.legend()\n",
        "\n",
        "# 5. Display the plot\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "iKzbD_kSpqzr",
        "outputId": "b4b2b6a0-78c8-4c9f-9d96-b20f77f823e7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Observe that while the function plot for $x^{2}$ (red) is significantly below the function plot for $1000x + 277$ (blue) for small values of $x$ ($x \\leq 1000$), eventually, $x^{2}$ (red) dominates $1000x + 277$ (blue) after a certain value of $x$ (in this case, $x = 1001)$.\n",
        "\n",
        "While it may be tempting to think of $x^{2}$ as the more efficient run time for the given task (for small values of $x$), it is definitely much slower than $1000x + 277$ as $x$ takes on larger values. That is, for large input sizes, $1000x + 277$ is *by far the better run time*.\n",
        "\n",
        "**Important point**\n",
        "\n",
        "Functions that grow slower take less time on large inputs, and so these are more desirable. In the case above, $1000x + 277$ is more efficient than $x^{2}$."
      ],
      "metadata": {
        "id": "vmiStGqKuLx3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Main point - Asymptotics**\n",
        "\n",
        "We care about behavior of functions for large values of $n$ : think **$n \\rightarrow \\infty$**"
      ],
      "metadata": {
        "id": "sJsEqN2-pxfA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Motivation\n",
        "\n",
        "Algorithms are typically designed for large data sets - so it is important that they **scale** well. The test for how well algorithms scale is what asymptotic analysis of run time, space (in some cases) tells us."
      ],
      "metadata": {
        "id": "Wtqxas1NqSS9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Working with functions - asymptotics"
      ],
      "metadata": {
        "id": "N76uXn61qzz2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "At a high level, we care mainly about the asymptotic growth of functions. So, an algorithm with runtime of $n^2$  is essentially as good as another algorithm with a run time of $100 n^2$ despite the original algorithm being 100 times more efficient. In asymptotic analysis, this is relatively small.\n",
        "\n",
        "\n",
        "Indeed, consider the difference between $n^2$ and $n^3$ - these functions are a factor of $n$ apart - and as we know, we think of $n \\rightarrow \\infty$. The multiplcative factor in this case is significantly higher.\n",
        "\n",
        "\n",
        "The takeaway for us is when we talk about efficiency of algorithms, we are concerned about the asymptotics of running time rather than the exact running time.\n"
      ],
      "metadata": {
        "id": "8AA430ygq5-2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Working with big O:\n",
        "\n",
        " $f(n) = O(g(n))$ : $ \\lim_{n\\to \\infty} \\frac{f(n)}{g(n)}$ $\\leq k$ for some positive constant $k$.\n",
        "\n",
        " Examples\n",
        "\n",
        "*   $f(n) = n$, $g(n) = n^2$\n",
        " $$\\displaystyle \\lim_{n\\to \\infty} \\frac{f(n)}{g(n)} = \\lim_{n\\to \\infty}\\frac{n}{n^2} = \\lim_{n\\to \\infty} \\frac{1}{n} = 0 $$ so, $n = O(n^2)$\n",
        "\n",
        "\n",
        "*    $f(n) = n + 10$, $g(n) = 5n - 223$\n",
        " $$\\displaystyle \\lim_{n\\to \\infty} \\frac{f(n)}{g(n)} = \\lim_{n\\to \\infty}\\frac{n + 10}{5n - 223} = \\frac{1}{5} = 0.2 $$\n",
        "so, $n + 10 = O(5n - 223)$. Both these functions are essentially $O(n)$ - which is the asymptotic upper bound for these functions (as it is for any linear function).\n",
        "*    $f(n) = \\log_{2}{n}$, $g(n) = 7n$\n",
        " $$\\displaystyle \\lim_{n\\to \\infty} \\frac{f(n)}{g(n)} = \\lim_{n\\to \\infty}\\frac{\\log_{2}{n}}{7n} = 0 $$\n",
        "so, $\\log_{2}{n} = O(7n)$\n",
        "*   $f(n) = n + \\sqrt{n}$, $g(n) = 2^n$\n",
        " $$\\displaystyle \\lim_{n\\to \\infty} \\frac{f(n)}{g(n)} = \\lim_{n\\to \\infty}\\frac{n + \\sqrt{n}}{2^n} = \\lim_{n\\to \\infty} \\frac{1}{2^{n}{\\log_{e}{2}}} = 0 $$\n",
        "so, $n + \\sqrt{n} = O(2^{n})$"
      ],
      "metadata": {
        "id": "KwHrkat7r3z0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Some more worked out examples:\n",
        "\n",
        "*   $f(n) = n + 10$, $g(n) = 3n - 25$\n",
        "\n",
        "$$\\displaystyle \\lim_{n \\rightarrow \\infty}\\frac{f(n)}{g(n)} = \\lim_{n \\rightarrow \\infty}\\frac{n + 10}{3n - 25} = \\frac{1}{3}$$ So, we have $f(n) = O(g(n))$.\n",
        "\n",
        "Notice also that:\n",
        "$$\\lim_{n \\rightarrow \\infty}\\frac{g(n)}{f(n)} = \\lim_{n \\rightarrow \\infty}\\frac{3n - 25}{n + 10} = 3$$ So, we also have $g(n) = O(f(n))$.\n",
        "\n",
        "In particular, when $f(n) = O(g(n))$ and $g(n) = O(f(n))$, we say that $f(n) = \\Theta(g(n))$. In such cases, $f$ and $g$ are within a constant factor of each other in the asymptotic sense.\n",
        "\n",
        "*   $f(n) = n\\log_{2}n$, $g(n) = n$\n",
        "\n",
        "$$\\lim_{n \\rightarrow \\infty}\\frac{f(n)}{g(n)} = \\lim_{n \\rightarrow \\infty}\\frac{n\\log_{2}{n}}{n} = \\lim_{n \\rightarrow \\infty} \\frac{\\log_{2}n}{1} = \\infty$$ So, we have $f(n) \\neq O(g(n))$\n",
        "\n",
        "In this case, observe that $$\\lim_{n \\rightarrow \\infty}\\frac{g(n)}{f(n)} = \\lim_{n \\rightarrow \\infty}\\frac{n}{n\\log_{2}{n}} = \\lim_{n \\rightarrow \\infty} \\frac{1}{\\log_{2}n} = 0$$\n",
        "\n",
        "giving us $g(n) =O(f(n))$.\n",
        "\n"
      ],
      "metadata": {
        "id": "z0WstcrwhFPt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Try out the following examples:\n",
        "\n",
        "\n",
        "*   $f(n) = 3n + 5000 n^{0.99}$, $g(n) = n \\log_{2}n$\n",
        "*   $f(n) = n^3 - 10000 n^2$, $g(n) = 33 n$\n",
        "*   $f(n) = (\\frac{n}{2})^{1.5} + 10n$, $g(n) = n\\log_{2}{n}$\n",
        "*   $f(n) = n \\log_{2}{n}$, $g(n) = 5n^{2}$\n",
        "*   $f(n) = \\log_{2}{n}$, $g(n) = \\log_{10}n$\n",
        "\n",
        "\n",
        "The exact limit computation isn't as important as understanding whether $f(n) = O(g(n))$ or not. But, at this stage, it may be easiest for you to establish this by computing the limit. With some experience, you will be able to declare the asymptotic relations without limit computation in most cases.\n",
        "\n"
      ],
      "metadata": {
        "id": "kP5Y1xSdvzgJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Important facts**\n",
        "\n",
        "The standard functions that we will encounter obey the following asymptotic relations :\n",
        "\n",
        "\n",
        "\n",
        "* Polynomials are much larger than logarithms  \n",
        "\n",
        " $$\\log_{2}{n} = O(n^{a}) \\quad \\quad \\text{ for any } a > 0$$\n",
        "\n",
        "*  Larger polynomial is much larger than smaller polynomial\n",
        "\n",
        "$$n^{a} = O(n^{b}) \\quad \\quad\\text{ for any } 0 < a < b$$\n",
        "\n",
        "*   Exponentials are much larger than polynomials\n",
        "\n",
        "$$n^{a} = O(2^{n}) \\quad \\quad \\text{ for any } a > 0$$\n",
        "\n",
        "where $0 < a \\leq b$ are any two positive constants.\n",
        "\n",
        "You can verify these by applying limits.\n",
        "\n",
        "Comments :\n",
        "\n",
        "\n",
        "1. $\\log_{2}n$ is significantly smaller than functions in the polynomial class and is often the best run time we can hope for. Examples including searching through structured data using Binary search, Fast multiplication of integers that we saw in lecture 2 etc.\n",
        "\n",
        "2. In general,  the polynomial class of running times such as $\\sqrt{n},n,n \\log_{2}{n}, n^{2}, n^{3},...n^{100}$ etc. are common run times for a wide variety of problems such as searching through unstructured data, sorting, distance computations etc.\n",
        "\n",
        "\n",
        "3. The exponential run time $2^{n}$ is signifiantly larger than all polynomial functions and is an indicator of lack of efficiency in computation. However, there are problems such as finding the largest clique in a graph, finding if a list has *any* subset that sums up to a target value etc. for which we have only exponential time algorithms.\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "1QdnOBnBleRf"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Learning objectives for Asymptotics -\n",
        "\n",
        "\n",
        "\n",
        "1. Given a function $f(n)$, finding its asymptotic upper bound.\n",
        "\n",
        "2. Given a function $f(n)$ (representing the runtime of some algorithm), comparing the runtimes on inputs of different sizes.\n",
        "\n",
        "3. Given two functions $f(n)$ and $g(n)$, establish whether $f(n) = O(g(n))$ or $g(n) = O(f(n))$.\n",
        "\n"
      ],
      "metadata": {
        "id": "hdTd6235fA4P"
      }
    }
  ]
}