S10_OrdenacionBusqueda.ipynb

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   "source": [
    "<h1 align=\"center\">Estructura de Datos y Algoritmos I</h1>\n",
    "<h1 align=\"center\">Algoritmos de Ordenación y Búsqueda</h1>\n",
    "<h1 align=\"center\">2024</h1>\n",
    "<h1 align=\"center\">MEDELLÍN - COLOMBIA </h1>"
   ]
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    "*** \n",
    "|[![Outlook](https://img.shields.io/badge/Microsoft_Outlook-0078D4?style=plastic&logo=microsoft-outlook&logoColor=white)](mailto:calvar52@eafit.edu.co)||[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/carlosalvarezh/EstructuraDatosAlgoritmos1/blob/main/S10_OrdenacionBusqueda.ipynb)\n",
    "|-:|:-|--:|\n",
    "|[![LinkedIn](https://img.shields.io/badge/linkedin-%230077B5.svg?style=plastic&logo=linkedin&logoColor=white)](https://www.linkedin.com/in/carlosalvarez5/)|[![@alvarezhenao](https://img.shields.io/twitter/url/https/twitter.com/alvarezhenao.svg?style=social&label=Follow%20%40alvarezhenao)](https://twitter.com/alvarezhenao)|[![@carlosalvarezh](https://img.shields.io/badge/github-%23121011.svg?style=plastic&logo=github&logoColor=white)](https://github.com/carlosalvarezh)|\n",
    "\n",
    "<table>\n",
    " <tr align=left><td><img align=left src=\"https://github.com/carlosalvarezh/Curso_CEC_EAFIT/blob/main/images/CCLogoColorPop1.gif?raw=true\" width=\"25\">\n",
    " <td>Text provided under a Creative Commons Attribution license, CC-BY. All code is made available under the FSF-approved MIT license.(c) Carlos Alberto Alvarez Henao</td>\n",
    "</table>\n",
    "\n",
    "***"
   ]
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   "metadata": {},
   "source": [
    "<a id='TOC'></a>"
   ]
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  {
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     "slide_type": "slide"
    }
   },
   "source": [
    "## Introducción"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Sorting01.PNG?raw=true\" width=\"500\" />\n",
    "</p>"
   ]
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   "source": [
    "**Ordenación o Clasificación de datos ($sort$, en inglés):** Operación consistente en disponer un conjunto —estructura— de datos en algún determinado orden con respecto a uno de los campos de elementos del conjunto. Una colección de datos (Estructura) puede ser almacenada en un archivo, un arreglo (lista, tupla, diccionario) u otra estructura especial.\n",
    "\n",
    "\n",
    "**Ejemplo:** cada elemento del conjunto de datos de una guía telefónica tiene un campo nombre, un campo dirección y un campo número de teléfono; la guía telefónica está dispuesta en orden alfabético de nombres; los elementos numéricos se pueden ordenar en orden creciente o decreciente de acuerdo al valor numérico del elemento. \n",
    "\n",
    "En terminología de ordenación, el elemento por el cual está ordenado un conjunto de datos (o se está buscando) se denomina clave. Un arreglo se dice que está ordenado por la clave $k$ si está en orden ascendente o descendente con respecto a la clave.\n",
    " \n",
    "  - El arreglo se dice que está en orden ascendente si: \n",
    "$𝑖<𝑗$, esto implica que $𝑘_𝑖 \\leq 𝑘_j$\n",
    "\n",
    "  - y se dice que está en orden descendente si:\n",
    "$𝑖>𝑗$, esto implica que $𝑘_𝑖 \\geq 𝑘_j$\n",
    " "
   ]
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   },
   "source": [
    "## Algoritmos de Ordenamiento"
   ]
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   "source": [
    "Existen muchos algoritmos de ordenamiento, cuál es el “mejor”? \n",
    "\n",
    "***Eficiencia:*** factor que mide la calidad y rendimiento de un algoritmo. El más eficiente es el que:\n",
    "    - Resuelve en menor tiempo de ejecución en computador;\n",
    "    - Menor número de instrucciones.\n",
    "\n",
    "\n",
    "- A veces no se cuenta con un mecanismo que permita cuantificar la *eficiencia*.\n",
    "\n",
    "\n",
    "- El mejor criterio para medirla es aislar una operación específica clave en la ordenación.\n",
    "\n",
    "\n",
    "- Se empleará como medida de $eficiencia$ el número de comparaciones efectuada entre elementos.\n",
    "\n",
    "  - $A$ será más eficiente que $B$ si se requiere un menor número de comparaciones."
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    "- En el caso de ordenar elementos de un arreglo vectorial, el número de comparaciones será función del número de elementos, $n$, del arreglo: $n+4$, $n^2$, etc.\n",
    "\n",
    "- Los métodos de ordenación se suelen dividir en dos grandes grupos:\n",
    "\n",
    "  - **Directos:** `Burbuja, Selección, Inserción`.\n",
    "  \n",
    "  - **Indirectos:** `Shell, Ordenación Rápida, Ordenación por Mezcla, Radixsort`."
   ]
  },
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   },
   "source": [
    "### Ordenamiento por intercambio (Bubble sort)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Sort_Bubble01.gif?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
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   "source": [
    "- Basado en la lectura sucesiva de la lista a ordenar, comparando el elemento inferior de la lista con los restantes y efectuando el intercambio de posiciones cuando el orden de la comparación no sea el correcto."
   ]
  },
  {
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   "source": [
    "#### Ejemplo"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Ordenar el arreglo $[8, 4, 6, 2]$"
   ]
  },
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   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Ordena_Intercambio0.PNG?raw=true\" width=\"600\" />\n",
    "</p>\n"
   ]
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    "- El elemento de índice $0$ se compara con cada elemento posterior del arreglo de índices $1$, $2$ y $3$.\n",
    "\n",
    "\n",
    "- En cada comparación se comprueba si el elemento siguiente es menor que el del índice $0$, en este caso se intercambian.\n",
    "\n",
    "\n",
    "- Después de terminar todas las comparaciones, el elemento menor se localiza en el índice $0$.\n"
   ]
  },
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   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Ordena_Intercambio1.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
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   "source": [
    "- El algoritmo continua comparando el elemento de índice $1$ con los elementos posteriores de índices $2$ y $3$. En cada comparación, si el elemento mayor está en el índice $1$ se intercambian los elementos.\n",
    "\n",
    "\n",
    "- Después de hacer todas las comparaciones, el segundo elemento de menor valor del arreglo se almacena en el índice $1$.\n"
   ]
  },
  {
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   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Ordena_Intercambio2.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
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     "slide_type": "subslide"
    }
   },
   "source": [
    "La sublista a considerar es $8$, $6$. Una única comparación produce el arreglo ordenado."
   ]
  },
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   "source": [
    "- El método utiliza dos bucles anidados.\n",
    "\n",
    "\n",
    "- Suponiendo que el arreglo es de tamaño $n$, el rango del ciclo externo irá desde el índice $0$ hasta $n-2$.\n",
    "\n",
    "\n",
    "- Por cada índice $i$, se comparan los elementos posteriores de índices $j=i+1, i+2, \\ldots, n-1$."
   ]
  },
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   "source": [
    "El intercambio ($swap$) de los elementos $a_i$, $a_j$ se realiza en un bloque:\n",
    "\n",
    "$$aux = a_i$$\n",
    "$$a_i = a_j$$\n",
    "$$a_j = aux$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Seudocódigo"
   ]
  },
  {
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   "metadata": {
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     "slide_type": "subslide"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Ordena_Burbuja.PNG?raw=true\" width=\"400\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# CODIFIQUE AQUÍ EL ALGORITMO ...\n"
   ]
  },
  {
   "cell_type": "markdown",
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     "slide_type": "slide"
    }
   },
   "source": [
    "### Ordenamiento por Selección (Selection)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Sort_Selection01.gif?raw=true\" width=\"500\" />\n",
    "</p>"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Algoritmo"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "Los pasos del algoritmo son:\n",
    "\n",
    "1. Seleccionar el elemento de menor valor del arreglo, intercambiarlo con el primer elemento, $a_0$. Con esto, la entrada de menor valor está en la primera posición del arreglo.\n",
    "\n",
    "2. Considerar las posiciones del arreglo $a_1, a_2, \\ldots$, seleccionar el elemento de menor valor e intercambiarlo con $a_1$. Las dos primeras entradas están en orden.\n",
    "\n",
    "3. Continuar este proceso encontrando o seleccionando el elemento de menor valor de los restantes elementos del arreglo, intercambiándolos adecuadamente.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejemplo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Ordenar el arreglo $[51,  21,  39,  80,  36]$"
   ]
  },
  {
   "attachments": {
    "Ordena_Seleccion3.PNG": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![Ordena_Seleccion3.PNG](attachment:Ordena_Seleccion3.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Seudocódigo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Ordena_Seleccion_Seudocodigo.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# CODIFIQUE AQUÍ EL ALGORITMO ...\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Ordenamiento por Insersión (Insertion)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Sort_Insertion01.gif?raw=true\" width=\"400\" />\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Algoritmo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Los pasos del algoritmo son:\n",
    "\n",
    "1. El primer elemento, $a_0$ se considera ordenado; es decir el arreglo inicial consta de un elemento.\n",
    "\n",
    "2. Se inserta $a_1$ en la posición correcta, delante o detrás de $a_0$, dependiendo de que sea mayor o menor.\n",
    "\n",
    "3. Por cada ciclo o iteración $i$ (𝑑𝑒𝑠𝑑𝑒 $i = 1$ hasta $n-1$) se explora la sublista $a_{i-1} \\ldots, a_{0}$ buscando la posición correcta de inserción; a la vez se mueve hacia la derecha en la sublista una posición todos los elementos mayores que el elemento a insertar $a_i$, para dejar vacía esa posición.\n",
    "\n",
    "4. Insertar el elemento en la posición correcta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejemplo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Ordenar el arreglo $[50,  20,  40,  80,  30]$"
   ]
  },
  {
   "attachments": {
    "Ordena_Insersion.PNG": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "![Ordena_Insersion.PNG](attachment:Ordena_Insersion.PNG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Seudocódigo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Ordena_Insersion_Seudocodigo.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# CODIFIQUE AQUÍ EL ALGORITMO ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Ordenamiento Shell"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Inserción directa:** Cada elemento se compara con los elementos contiguos a su izquierda, uno tras otro.\n",
    "\n",
    "- Si el elemento a insertar es el menor hay qué realizar muchas comparaciones antes de colocar en su lugar definitivo.\n",
    "\n",
    "**Shell:** modifica los saltos contiguos resultantes de las comparaciones por saltos de mayor tamaño.\n",
    "\n",
    "- Generalmente se toma como salto inicial $n/2$ ($n$, número de elementos), luego se reduce el salto a la mitad en cada repetición hasta que le salto es de tamaño $1$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ejemplo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "ordenar el arreglo $[6, 1, 5, 2, 3, 4, 0]$\n",
    "- $n = 7$, salto inicial $n/2 \\approx 3$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Ordena_Shell.PNG?raw=true\" width=\"500\" />\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Seudocódigo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Ordena_Shell_Seudocodigo.PNG?raw=true\" width=\"750\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# CODIFIQUE AQUÍ EL ALGORITMO ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ordenamiento por mezcla (Merge sort)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Sort_Merge01.gif?raw=true\" width=\"400\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ordenamiento rápido (Quick sort)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Sort_Quick01.gif?raw=true\" width=\"400\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparación entre algoritmos de ordenamiento"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/SortComparisson.gif?raw=true\" width=\"600\" />\n",
    "</p>\n",
    "\n",
    "\n",
    "<div style=\"text-align: right\"> Fuente: <a href=\"https://www.toptal.com/developers/sorting-algorithms\">Toptal</a> </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Complejidad en algoritmos de ordenamiento"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/ComplexitySortingAlgorithms.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n",
    "\n",
    "\n",
    "<div style=\"text-align: right\"> Fuente: <a href=\"https://www.bigocheatsheet.com/\">Bigocheatsheet</a> </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Búsqueda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Cuando se trabaja con grandes cantidades de datos es necesario determinar si una estructura contiene un valor que coincida con un cierto valor clave. El proceso de encontrar un elemento específico se denomina búsqueda. \n",
    "\n",
    " Se analizarán dos técnicas de búsqueda:\n",
    " \n",
    " - Lineal o secuencial: más sencilla, \n",
    " \n",
    " - Binaria o dicotómica: más eficiente.\n",
    "\n",
    "**Ejemplo:** encontrar un nombre en una guía telefónica para consultar su teléfono."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Búsqueda Secuencial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- El algoritmo de búsqueda secuencial compara cada elemento del conjunto de datos con la clave de búsqueda. \n",
    "\n",
    "\n",
    "- Dado que el conjunto no está en un orden particular, es probable que el elemento a buscar sea el primer elemento, el último o cualquier otro. \n",
    "\n",
    "\n",
    "- En promedio, el algoritmo tendrá que comparar la clave de búsqueda con al menos la mitad de los elementos. \n",
    "\n",
    "\n",
    "- Este método funciona bien con conjuntos pequeños o no ordenados. La eficiencia de la búsqueda secuencial o lineal es pobre."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "**Ejemplo:** Buscar el elemento `u`:\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Busqueda01.PNG?raw=true\" width=\"500\" />\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Seudocódigo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Busqueda03.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# CODIFIQUE AQUÍ EL ALGORITMO ...\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Busqueda04.PNG?raw=true\" width=\"400\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# CODIFIQUE AQUÍ EL ALGORITMO ...\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Eficiencia y Complejidad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Considerando la cantidad de comparaciones\n",
    "\n",
    "**- Mejor caso: 1.** El elemento buscado está en la primera posición, es decir, se hace una sola comparación.\n",
    "\n",
    "**- Peor caso: $n$.** El elemento buscado está en la última posición, necesitando igual número de comparaciones que la cantidad total de elementos en el arreglo.\n",
    "\n",
    "**- Caso promedio: $n/2$.** El elemento buscado estará cerca de la mitad, necesitando, en promedio, la mitad de comparaciones.\n",
    "\n",
    "La velocidad de ejecución depende linealmente del tamaño del arreglo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Búsqueda Binaria"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- La búsqueda secuencial se aplica a cualquier lista. \n",
    "\n",
    "\n",
    "- Si la lista está ordenada, la búsqueda binaria proporciona una técnica de búsqueda mejorada. \n",
    "\n",
    "\n",
    "- Una búsqueda binaria típica es la búsqueda de una palabra en un diccionario. \n",
    "\n",
    "\n",
    "- Una idea similar se aplica en la búsqueda en una lista ordenada. \n",
    "\n",
    "  - Se sitúa la lectura en el centro de la lista y se comprueba si la clave coincide con el valor del elemento central. Si no se encuentra el valor de la clave, se sigue la búsqueda uno en la mitad inferior o superior del elemento central de la lista. \n",
    " \n",
    "  - En general, si los datos de la lista están ordenados se puede utilizar esa información para acortar el tiempo de búsqueda.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Algoritmo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Suponiendo la lista almacenada en un arreglo, los índices de la lista son: `bajo=0` y `alto=n-1`, y `n` es el número de elementos en el arreglo.\n",
    "\n",
    "1. Calcular el índice del punto central del arreglo: `central = mod((bajo+alto)/2)` (división entera)\n",
    "\n",
    "2. Comparar el valor de este elemento central con la clave:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Binaria01.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
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   "source": [
    "- Si `a[central]<clave`, la nueva sublista de búsqueda tiene por valores extremos de su rango `bajo = central+1 … alto`.\n",
    "\n",
    "\n",
    "- Si `a[central]>clave`, la nueva sublista de búsqueda tiene por valores extremos de su rango `bajo … central-1 = alto`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Binaria02.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "El algoritmo termina o porque se ha encontrado la clave, o porque el valor `bajo` excede a `alto`, y el algoritmo devuelve el indicador de fallo `-1` (búsqueda no encontrada)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "***Ejemplo:*** Buscar la clave `40` en el siguiente arreglo:\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Binaria03.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Binaria04.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Buscar en la sublista derecha de Central:\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Binaria05.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Buscar en la sublista derecha de Central:\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Binaria06.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "El algoritmo ha requerido 3 comparaciones frente a 8 comparaciones que se hubieran requerido con la búsqueda secuencial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Seudocódigo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/Binaria07.PNG?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# CODIFIQUE AQUÍ EL ALGORITMO ...\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Eficiencia y Complejidad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Considerando la cantidad de comparaciones\n",
    "\n",
    "**- Mejor caso: $1$.** El elemento buscado está en el centro, por lo tanto se hace una sola comparación.\n",
    "\n",
    "\n",
    "**- Peor caso: $log(n)$.** El elemento buscado está en una esquina.\n",
    "\n",
    "\n",
    "**- Caso promedio: $log(n/2)$.**\n",
    "\n",
    "\n",
    "La velocidad de ejecución depende logarítmicamente del tamaño del arreglo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparación: Búsqueda Binaria y Secuencial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p float=\"center\">\n",
    "  <img src=\"https://github.com/carlosalvarezh/Analisis_de_Algoritmos/blob/master/images/ComparacionBinariaSecuencial.png?raw=true\" width=\"500\" />\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Complejidad en algoritmos de búsqueda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|  Algoritmo  | Mejor caso | Caso medio | Peor caso |\n",
    "|:------------|:----------:|:----------:|:---------:|\n",
    "|Secuencial   | O(1)       |  O(n)      |  O(n)     |\n",
    "|Binaria      | O(1)       |  O(log(n)) |  O(log(n))|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Desafío de clase"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "En la literatura se encuentran muchos otros algoritmos de ordenammiento. Seleccione uno de ellos (diferente a los vistos aquí) e impleméntelo en un lenguaje de programación. Realice un análisis de complejidad del algoritmo seleccionado y compárelo con los restantes algoritmos vistos en clase. Realice un breve documento para el análisis."
   ]
  }
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