duducosmos/Aula03.ipynb

## Aula03.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Análise de Algoritmos\n",
    "\n",
    "## Recorrência.\n",
    "\n",
    "Função recursiva, aquela que chama a si mesmo:\n",
    "\n",
    "Exemplo, cálculo fatorial em Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]\n"
     ]
    }
   ],
   "source": [
    "fatorial = lambda n: 1 if n == 0 or n == 1 else n * fatorial(n-1)\n",
    "\n",
    "print([fatorial(i) for  i in range(10)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Expansão Telescópica\n",
    "\n",
    "Considere a relação de Recorrência:\n",
    "\n",
    "$ T(n) = T(\\frac{n}{2})+1$\n",
    "\n",
    "Para resolver essa equação, aplicamos $T(\\frac{n}{2})$ na fórmula de $T(n)$ e obtemos:\n",
    "\n",
    "$T(\\frac{n}{2}) = T(\\frac{n}{4})+1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$ T(n) = T(\\frac{n}{2})+1$\n",
    "$ T(n) = (T(\\frac{n}{4})+1)+1$\n",
    "$ T(n) = ((T(\\frac{n}{8})+1)+1)+1$\n",
    "...\n",
    "$ T(n) = (...((((T(\\frac{n}{2^k})+1+1)+1)+...+1)$\n",
    "\n",
    "Vamos assumir que $n$ é uma potência de 2, logo $n=2^k$. Também consideramos que $T(n/2^k)=T(1) = 1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Logo:\n",
    "\n",
    "$ T(n) = (...((((T(\\frac{n}{2^k})+1+1)+1)+...+1)$\n",
    "$ T(n) = \\sum_{i=1}^{k}{1}$\n",
    "$ T(n) = k$\n",
    "\n",
    "Mas: $n=2^k$. Fazendo o $\\log_{2}$ nos dois lados da equação:\n",
    "\n",
    "$\\log_{2}(n) = \\log_{2}{2^k}$\n",
    "\n",
    "$\\log_{2}(n) = k\\log_{2}{2}$\n",
    "\n",
    "$\\log_{2}(n) = k$.\n",
    "Ou seja:\n",
    "\n",
    "$ T(n) = \\log_{2}(n)$\n",
    "\n",
    "Assim, a complexidade do algoritmo é $O(\\log_{2}(n))$.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Asssumir $T(1) =1 $ é a chamada condição de parada, sendo 1 o valor base da recorrência, ou seja, o valor para o qual a recorrência é interrompida"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "E para o caso em que temos:\n",
    "\n",
    "$T(n) = T(n/2) + n$, com $T(1)=$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Expandimos a relação:\n",
    "\n",
    "$T(n) = T(n/2) + n$\n",
    "$T(n) = (T(n/4)+ n/2) + n$\n",
    "$T(n) = ((T(n/8) + n/4)+n/2)+n$\n",
    "...\n",
    "$T(n) = (...((T(n/2^k) + n/2^{k-1})+n/2^{k-2})+...+n/2)+n$\n",
    "\n",
    "Com $n = 2^{k}$\n",
    "$T(n) = T(1) + 2+ 4 +8+16+...+2^{k}$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "A partir da expansão anterior, podemos ver que um bom valor para $T(1)$ é 1, pois isso facilita o fechamento do somatório. Assim:\n",
    "$T(n) = 1 + 2+ 4 +8+16+...+2^{k}$\n",
    "\n",
    "$T(n) = \\sum_{i=0}^{k}2^{i}$\n",
    "\n",
    "Isso é uma Progressão Geométrica de Ordem 2, com termo geral sendo $a_{k} = a_{1}q^{k-1}$.\n",
    "\n",
    "A somatóra dos termos da PG é:\n",
    "\n",
    "$S_{n} = \\frac{a_{1}(q^{k}-1)}{q-1}$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Levando em conta a seguinte propriedade de somatório:\n",
    "\n",
    "$\\sum_{i=0}^{k}2^{i} = 2^{k}-1$\n",
    "\n",
    "Lembrando que $n=2^{k}$ implica em $k = \\log_{2}(n)$, ou seja:\n",
    "\n",
    "$T(n) = \\sum_{i=0}^{k}2^{i} = 2^{\\log_{2}(n)}-1$\n",
    "\n",
    "$T(n) = 2n-1$\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Em princípio, toda relação de recorrência pode ser resolvida por expansão telescópia. Mas nesse caso é preciso achar a somatória conveniente para encontrar uma solução."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Podemos visualizar a recorrência através de uma árvore de recorrência. Vamos considerar a equação de recorrência para o algoritmo MergeSort:\n",
    "\n",
    "$T(n) = 2T(n/2) + n$\n",
    "\n",
    "$T(1)=$?\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./imagens/arvoreRecorrenciaA.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='./imagens/arvoreRecorrenciaB.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Com isso, basta achar a altura da árvore. Veja que a altura da árvore é $log_{n}$, mas o número de folhas é $n$, ou seja, o passo total será o número de folhas multiplicado pela altura da árvore.\n",
    "\n",
    "Assim, a complexidade do algoritmos será: $O(n\\log_{2}(n))$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}