{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<br><b><center><font size=\"10\">Gyakorló feladatok megoldásai</font></center></b>\n",
    "\n",
    "\n",
    "<p style=\"text-align: right;\">**Ha valaki az igazságot és a törvényszerűséget keresi, nem tehet különbséget kicsiny és nagy problémák között. <br>Aki a kicsiny dolgokban nem veszi komolyan az igazságot, abban az emberben nagy dolgokkal kapcsolatban sem bízhatunk meg.**\n",
    "<br>*Albert Einstein*</p>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "hide_input": false,
    "run_control": {
     "frozen": false,
     "marked": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b><font size=6>Több megoldást is közzéteszünk, mindegyik helyes, és tökéletesen elvégzi a kiadott feladatot.</font></b>\n",
    "<br><br><br><b><font size=4>Először mindig futtasuk le a \"%pylab inline\" parancsot</font></b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generálj egy egész számokból álló 1000 tagú véletlen számsorozatot (0-100-ig vannak elemek). Majd írasd ki a 100.-tól a 200.-ig elmeig 7-sével az értékeket. Ehhez használd a \"randint()\" függvényt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[44, 98, 45, 74, 15, 73, 48, 64, 70, 51, 75, 2, 16, 40, 7]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A=[]   # Létrehozunk egy üres listát, amit majd később lehet növelni\n",
    "for i in range(0,1000):  # Elindítunk egy ciklust, ami 1000-szer fut le\n",
    "    B=randint(0,100)  # randint választ egy számot 0 és 100 között\n",
    "    A.append(B) # hozzáírjuk az A listához a B számot\n",
    "A[100:200:7] # kiírjuk a lista elemeit 100 és 200 között 7-sével"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([40, 89, 22, 18, 45,  7, 30,  8, 71, 52, 20, 43, 68, 72, 88])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B=randint(0,100,1000) # Generálunk egy 1000 tagú listát a randint-tel\n",
    "C=arange(100,200,7) # megalkotjuk azoknak a számoknak a listáját, amilyen indexű elmeet kiíratni szeretnénk\n",
    "B[C] #kiírjuk a megfelelő indexű számokat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([69, 66, 83, 73, 96, 60, 44, 20, 12, 19, 20, 17, 83, 52, 20])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B=randint(0,100,1000) # Generálunk egy 1000 tagú listát a randint-tel\n",
    "B[100:200:7] #Lekérjük a megfelelő elemeket a listából"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás  (D) (1 sorban megoldva)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([38, 54, 68, 29, 17, 71, 53, 70, 35,  1, 14, 47, 41, 71, 58])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "randint(0,100,1000)[100:200:7] #A generált lista megfelelő elemeét hívjuk meg\n",
    "#Magyarázat:  A randint egy listát ad, aminek hívatkozhatunk az elemeire"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Írjunk egy olyan programot, ami egy alsó és egy felső határ között kirajzol egy $log10(a*x)+b$ függvényt. (Itt a és b is a felhasználó által bevitt paraméter)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e910118d0>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e60d43208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mini=1.0 #bekérjük a kezdő értéket\n",
    "maxi=2.0 #bekérjük a végső értéket\n",
    "a=1 # bekérjük az \"a\" értéket\n",
    "b=2 # bekérjük a \"b\" értéket\n",
    "xlim(mini, maxi) # megadjuk az ábrázolási tartományt (x tengelyen)\n",
    "x=arange(mini,maxi, 0.01) # 0,01-s lépésközzel megadom az x tengely értékeit\n",
    "plot(x,(log10(a*x)+b)) # x-et és az egyenletet ábrázoljuk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e61368198>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jdKAkwOipmby5MJ/Le7fjkat66klcEanTFPzHYffeg/z4Hwv5dM127vpOJ0ae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\nX0QkxvwfjA6Es8Hmy+8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5fcdc4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mini=1.0 #bekérjük a kezdő értéket\n",
    "maxi=2.0 #bekérjük a végső értéket\n",
    "a=1 # bekérjük az \"a\" értéket\n",
    "b=2 # bekérjük a \"b\" értéket\n",
    "x=linspace(mini, maxi,1000) # Generálunk 1000 számot a tartományban egyenlő lépésközzel\n",
    "plot(x,log10(a*x)+b) # x-et és az egyenletet ábrázoljuk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e611bd6d8>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jdKAkwOipmby5MJ/Le7fjkat66klcEanTFPzHYffeg/z4Hwv5dM127vpOJ0ae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\nX0QkxvwfjA6Es8Hmy+8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e8c5c97f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mini=1.0 #bekérjük a kezdő értéket\n",
    "maxi=2.0 #bekérjük a végső értéket\n",
    "a=1 # bekérjük az \"a\" értéket\n",
    "b=2 # bekérjük a \"b\" értéket\n",
    "plot(linspace(mini,maxi, 1000),log10(a*x)+b) # Beírható a generálás közvetlen a plot-ba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e5fedec88>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jdKAkwOipmby5MJ/Le7fjkat66klcEanTFPzHYffeg/z4Hwv5dM127vpOJ0ae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\nX0QkxvwfjA6Es8Hmy+8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5fe8f630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mini=1.0 #bekérjük a kezdő értéket\n",
    "maxi=2.0 #bekérjük a végső értéket\n",
    "a=1 # bekérjük az \"a\" értéket\n",
    "b=2 # bekérjük a \"b\" értéket\n",
    "def func(x,a,b): # létrehozok egy függvényt, ami elvégzi a kért műveletet\n",
    "# A függvény megkapja az \"x\", \"a\" és \"b\" értékeket!\n",
    "    y=log10(a*x)+b # kiszámoljuk az y-t\n",
    "    return y # a függvény visszatér az ny értékkel\n",
    "x=linspace(mini,maxi, 1000) \n",
    "plot(x,func(x,a,b)) #ábárolzjuk az x-et és a függvényt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás  (E)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e60d6d2b0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e61366b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mini=1.0 #bekérjük a kezdő értéket\n",
    "maxi=2.0 #bekérjük a végső értéket\n",
    "a=1 # bekérjük az \"a\" értéket\n",
    "b=2 # bekérjük a \"b\" értéket\n",
    "def func(x,a,b):\n",
    "    y=log10(a*x)+b\n",
    "    return y\n",
    "x=linspace(mini,maxi, 1000)\n",
    "adat=(a,b) #létrehozok egy \"tuple\" listát az a,b paraméterekből\n",
    "plot(x,func(x,*adat)) # a paraméterekkel hívjuk mega  függvényt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Írjunk olyan programot, ahol egy 2 dimenziós rácson haladunk előre (0,0-ból indulva). X vagy Y koordináta változhat, 0 vagy +1 értékkel. Hasznájuk a random.choice függvényt a megoldáshoz. Tegyünk meg 100 lépést. Minden lépést mentsünk egy 100 x 2-es tömbbe, és ábrázoljuk a mozgást."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (A)\n",
    "\n",
    "- Létrehozunk egy tömböt, melynek van 100 sor és 2 oszlopa (csupa nullával töltjük fel)\n",
    "- Végigmegyünk a tömb elemein (ciklussal)\n",
    "- Először az adott sorba beírjuk az előző sor értékeit, azaz megmondjuk, hogy honnan fogunk továbblépni (emlékezzünk mindenhova alapból 0 van beírva!) !! Ezért kell 1-től indítani a cilust és nem nullától !!\n",
    "- Kiválasztjuk a lépés irányát és nagyságát\n",
    "- Csinálunk egy elágazást, ahol megadjuk, hogy merre lépünk\n",
    "- Az adott lépést elvégezzük a megadott irányban (itt a 0. oszlop az x irány és az 1. oszlop az y irányt jelenti)\n",
    "- Ábrázoljuk a mozgást"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e5fe3b5c0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e60d7b6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b=zeros((100,2))\n",
    "for i in arange(1,100):\n",
    "    b[i,:]=b[i-1,:]\n",
    "    irany=random.choice(['X','Y'])\n",
    "    lepes=random.choice([0,1])\n",
    "    if irany == \"X\":\n",
    "        b[i,0]=b[i,0]+lepes\n",
    "    else:\n",
    "        b[i,1]=b[i,1]+lepes\n",
    "plot(b[:,0], b[:,1], \"o\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (B)\n",
    "\n",
    "- Létrehozok egy 2 elemű vektort, 0-0 elmekkel\n",
    "- Létrehozunk egy tömböt, melynek van 100 sor és 2 oszlopa (csupa nullával töltjük fel)\n",
    "- Végigmegyünk a tömb elemein (ciklussal)\n",
    "- Kiválasztjuk a lépés irányát\n",
    "- Csinálunk egy elágazást, ahol megadjuk, hogy merre lépünk\n",
    "- A vektor kiválasztott elemének helyére véletlenül választunk lépésnagyságot és ezzel megnöveljük a nagyságát. (itt a 0. oszlop az x irány és az 1. oszlop az y irányt jelenti)\n",
    "- Beírjuk a tömb adott sorába az aktuális kordinétapárost\n",
    "- Ábrázoljuk a mozgást"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e5fe22a90>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5hBYMUVgEoF7bLejaQQs6AEgvtAUdt1wAIBIEOgBEgnvoBdq6/4gOnzw/93rD6qU6sGN9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5fe5ba90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a=[0,0]\n",
    "b=zeros((100,2))\n",
    "for i in arange(0,100):\n",
    "    irany=random.choice(['X','Y'])\n",
    "    if irany == \"X\":\n",
    "        a[0]=a[0]+random.choice([0,1])\n",
    "    else:\n",
    "        a[1]=a[1]+random.choice([0,1])\n",
    "    b[i,:]=a[:]\n",
    "plot(b[:,0], b[:,1], \"o\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (C)\n",
    "\n",
    "- Létrehozunk egy tömböt, melynek van 100 sor és 2 oszlopa (csupa nullával töltjük fel)\n",
    "- Végigmegyünk a tömb elemein (ciklussal)\n",
    "- Először az adott sorba beírjuk az előző sor értékeit, azaz megmondjuk, hogy honnan fogunk továbblépni (emlékezzünk mindenhova alapból 0 van beírva!) !! Ezért kell 1-től indítani a cilust és nem nullától !!\n",
    "- Kiválasztjuk a lépés irányát\n",
    "- Csinálunk egy elágazást, ahol megadjuk, hogy merre lépünk\n",
    "- A megadott irányban választunk egy lépést, és el is végezzük (itt a 0. oszlop az x irány és az 1. oszlop az y irányt jelenti)\n",
    "- Ábrázoljuk a mozgást"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e5e556be0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5e608c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "b=zeros((100,2))\n",
    "for i in arange(1,100):\n",
    "    b[i,:]=b[i-1,:]\n",
    "    irany=random.choice(['X','Y'])\n",
    "    if irany == \"X\":\n",
    "        b[i,0]=b[i,0]+random.choice([0,1])\n",
    "    else:\n",
    "        b[i,1]=b[i,1]+random.choice([0,1])\n",
    "plot(b[:,0], b[:,1], \"o\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (D)\n",
    "\n",
    "- Létrehozunk egy tömböt, melynek van 100 sor és 2 oszlopa (csupa nullával töltjük fel)\n",
    "- Végigmegyünk a tömb elemein (ciklussal)\n",
    "- Először az adott sorba beírjuk az előző sor értékeit, azaz megmondjuk, hogy honnan fogunk továbblépni (emlékezzünk mindenhova alapból 0 van beírva!) !! Ezért kell 1-től indítani a cilust és nem nullától !!\n",
    "- Kiválasztjuk a lépés irányát, és nagysagat egyben, úgy hogy felismerjük, hogy az irány is lehet 0-1, és így 2-szer kell ugyanaból választani (itt a 0. oszlop az x irány és az 1. oszlop az y irányt jelenti)\n",
    "- A mátrix megadott eleméhez hozzáadjuk a választott lépés nagyságát (itt szintén a 0. oszlop az x irány és az 1. oszlop az y irányt jelenti)\n",
    "- Ábrázoljuk a mozgást"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e5bfa9160>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e611ec710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xy=zeros((100,2))\n",
    "for i in range(1,100):\n",
    "    xy[i]=xy[i-1]\n",
    "    irany,lepes=random.choice([0,1],2)\n",
    "    xy[i,irany]+=lepes\n",
    "plot(xy[:,0], xy[:,1], \"o\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (E)\n",
    "\n",
    "- Létrehozok egy 2 elemű vektort, 0-0 elmekkel\n",
    "- Létrehozunk egy tömböt, melynek van 100 sor és 2 oszlopa (csupa nullával töltjük fel)\n",
    "- Végigmegyünk a tömb elemein (ciklussal)\n",
    "- Módósítjuk a \"a\" vektor elemét a választott helyen a választott mértékben\n",
    "- A mátrix megadott sorába beírjuk az előző sor plusz az \"a\" vektor értékét\n",
    "- Ábrázoljuk a mozgást"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e5bf89828>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Vwxs0c1hbciip+aqscgngc8BzmfkH6556GNhd3N8NPDT+8jSKsvNWerlSRWqPKpHLtcC/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\nQ5eklrChS1JL2NAlqSX+PypOMLvNG4cNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5bfbd3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a=[0,0]\n",
    "xy=zeros((100,2))\n",
    "for i in range(1,100):\n",
    "    a[random.choice([0,1])]=random.choice([0,1])\n",
    "    xy[i,:]=xy[i-1,:]+a\n",
    "plot(xy[:,0], xy[:,1], \"o\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e5beeccf8>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e60d81240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x,y=cumsum(list(map(eval,random.choice(('[0,0]','[0,1]','[1,0]'),100))),axis=0).T\n",
    "plot(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Aranymetszés aránya (aranyarány) előállítása Fibonacci-számokkal. A Fibonacci-sorozat egymást követő tagjainak hányadosából képzett sorozat (1/1, 2/1, 3/2, 5/3, …) határértéke éppen az aranymetszés arány. Határozzuk meg, hanyadik tagtól vállik a különbség 1e16-nál kisebbé (azaz 0.00000000e+00-at ír a python). Az aranymetszés pontos értéke: $\\frac{1+\\sqrt {5}}{2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 -0.61803398875\n",
      "3 0.38196601125\n",
      "4 -0.11803398875\n",
      "5 0.0486326779168\n",
      "6 -0.0180339887499\n",
      "7 0.00696601125011\n",
      "8 -0.00264937336528\n",
      "9 0.00101363029772\n",
      "10 -0.000386929926365\n",
      "11 0.000147829431923\n",
      "12 -5.64606600073e-05\n",
      "13 2.15668056607e-05\n",
      "14 -8.23767693348e-06\n",
      "15 3.14652861966e-06\n",
      "16 -1.20186464891e-06\n",
      "17 4.59071787029e-07\n",
      "18 -1.75349769593e-07\n",
      "19 6.69776591966e-08\n",
      "20 -2.55831884566e-08\n",
      "21 9.77190839357e-09\n",
      "22 -3.73253694619e-09\n",
      "23 1.42570222295e-09\n",
      "24 -5.44569944694e-10\n",
      "25 2.08007167046e-10\n",
      "26 -7.94517784897e-11\n",
      "27 3.03477243335e-11\n",
      "28 -1.15918386001e-11\n",
      "29 4.42756942221e-12\n",
      "30 -1.69131375571e-12\n",
      "31 6.45927755727e-13\n",
      "32 -2.46691556072e-13\n",
      "33 9.41469124882e-14\n",
      "34 -3.59712259979e-14\n",
      "35 1.37667655054e-14\n",
      "36 -5.3290705182e-15\n",
      "37 1.99840144433e-15\n",
      "38 -8.881784197e-16\n",
      "39 2.22044604925e-16\n",
      "40 -2.22044604925e-16\n",
      "41 0.0\n",
      "42 0.0\n",
      "43 0.0\n",
      "44 0.0\n",
      "45 0.0\n",
      "46 0.0\n",
      "47 0.0\n",
      "48 0.0\n",
      "49 0.0\n",
      "50 0.0\n",
      "51 0.0\n"
     ]
    }
   ],
   "source": [
    "fiblist = [0,1] # Megadjuk a sorozat első kettő elemét\n",
    "for i in range(50):  # létrehozunk egy ciklust, ami kiszámolja a sorozatot\n",
    "    #a sorozathoz hozzáírjuk az előző két tag összegét:\n",
    "    fiblist.append(fiblist[i] + fiblist[i+1]) \n",
    "\n",
    "hanyados=[] # létrehozok egy üres listát\n",
    "for i in range(2,len(fiblist)):\n",
    "    # az arány listába beírom a sorozat tagjainak hányadoását\n",
    "    hanyados.append((fiblist[i]) / (fiblist[i-1]))\n",
    "    print(i,hanyados[i-2]-(1+sqrt(5))/2) #kiíratom a hanyados és az aranymetszés különbségét\n",
    "# Vegyük észre, hogy a ciklus 2-től indul (így nincs zéróval való osztás), de a\n",
    "# hányadost ugyanúgy nullától kell indexelni, ezért van az \"i-2\" benne"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás (B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "it: 41\n"
     ]
    }
   ],
   "source": [
    "fiblist = [0,1] # megadjuk az első 2 tagot\n",
    "for i in range(2,100):\n",
    "    #a sorozathoz hozzáírjuk az előző két tag összegét:\n",
    "    fiblist.append(fiblist[-1] + fiblist[-2]) \n",
    "    hanyados = (fiblist[-1]) / (fiblist[-2]) # kiszámoljuk a hányadost\n",
    "    if hanyados == (1+sqrt(5))/2: # Megvizsgáljuk mikor egyezik meg a hányados az aranymetszéssel\n",
    "        print('it:',i) \n",
    "        break # Megállítjuk a program futását"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Teszteljük a random.choice() függvény eloszlását véletlenszerűségét. Készíts programot, ami rendre 20, 50, 100, 200, 500, 1000 elmet választ az [1,2,3,4] tömbből."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás: 5 külön kódcellában"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.,  0.,  0.,  7.,  0.,  0.,  5.,  0.,  0.,  7.]),\n",
       " array([ 1. ,  1.3,  1.6,  1.9,  2.2,  2.5,  2.8,  3.1,  3.4,  3.7,  4. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBoBiCDcAFPNfQxwfM3IntjwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5e57d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(random.choice([1,2,3,4],20)) # generálok egy 20 elemű véletlen listát, és hisztogrammal ábrázolom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 18.,   0.,   0.,   9.,   0.,   0.,  16.,   0.,   0.,   7.]),\n",
       " array([ 1. ,  1.3,  1.6,  1.9,  2.2,  2.5,  2.8,  3.1,  3.4,  3.7,  4. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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t7ZlYlxHncsrr/p2f6k7P6F4rf6k3K2syylxmRpILgauATwxpsqbrMpPBP4L19qiIl3T/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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5be783c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(random.choice([1,2,3,4],50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 23.,   0.,   0.,  26.,   0.,   0.,  24.,   0.,   0.,  27.]),\n",
       " array([ 1. ,  1.3,  1.6,  1.9,  2.2,  2.5,  2.8,  3.1,  3.4,  3.7,  4. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMOiS1IRBl6Qm/hczJy0HUAGC6wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5bdac748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(random.choice([1,2,3,4],100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 47.,   0.,   0.,  52.,   0.,   0.,  43.,   0.,   0.,  58.]),\n",
       " array([ 1. ,  1.3,  1.6,  1.9,  2.2,  2.5,  2.8,  3.1,  3.4,  3.7,  4. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAD8CAYAAABn919SAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nge4hLo0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5bd2fdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(random.choice([1,2,3,4],200))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 256.,    0.,    0.,  246.,    0.,    0.,  273.,    0.,    0.,  225.]),\n",
       " array([ 1. ,  1.3,  1.6,  1.9,  2.2,  2.5,  2.8,  3.1,  3.4,  3.7,  4. ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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QS1JzBr0kNWfQS1JzBr0kNWfQS1JzBr0kNWfQS1Jz/wvrP/jZyJtc6QAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5bcb7828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(random.choice([1,2,3,4],1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Megoldás több ciklussal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XWBIRPfWcq/boXnYV46++NQOfOHOKvr5pk/Zz9lXqPPUE/35gfURcExFLgduAPdUDIuLq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\nvyQVxuCXpML8J7GJGH7BvSLEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5bcd51d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "j=1 # legyen j változó 1\n",
    "for n in [20,50,100,200,1000]: # menjen egy ciklus végig a az elemszámok listáján\n",
    "    a=[] # legyen \"a\" egy üres vektor\n",
    "    for i in range(n): # egy ciklus végigmegy az adott elemszámig\n",
    "        a.append(random.choice([1, 2, 3, 4])) # folyamatosan hozzáírok az \"a\" vektorhoz\n",
    "    subplot(2,3,j) # suboplotban beállítom, hogy hanyadik részképet ábrázolom\n",
    "    hist(a,normed=1) # elkészítem a hisztogramot\n",
    "    j=j+1 # megnövelem j-t, hogy másik részképet válasszak"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás 1 ciklussal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PJdmd5LfbqVzSoAz3CXLUUUfxqU99il27dvHwww/z2c9+ll27dgGsonebxHXAgzTX6E+y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\nDHdJ6iDDXZI6yHCXpA4y3CWpg/4/ZyCNUFJMXpwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5b9a7c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n=[20,50,100,200,1000] # létrehozom az elemszámok listáját\n",
    "a=random.choice([1,2,3,4],1000) # generálok egy 1000 elemű véletlen listát\n",
    "for j in range(0,len(n)): # egy ciklus anyiszor ismétlődik, aminnyi elemt tartalmaz az \"n\" lista\n",
    "    subplot(2,3,j+1) # használjuk a subplot parancsot, és mindig új részegységben rajzolunk\n",
    "    hist(a[0:n[j]]) # az adott darabszámú részlistáról csinálunk hisztogramot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Megoldás elegánsan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5bb28668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5bb3b320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5b936fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5b8ad710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0e5b898dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for n in [20,50,100,500,1000]: # egy ciklus végigmegy az elemszámok listáján\n",
    "    figure() #mindig új ábrát fog nyitni\n",
    "    # hasonlóan működik, mint a subplot, de itt nem egy képet osztok fel kis részekre,\n",
    "    # hanem magát egy teljesen új képet használok (mintha egy új cellát használnék az ábrázolásra)\n",
    "    hist(random.choice([1, 2, 3, 4],n) ,normed=True) #hisztogram készítése"
   ]
  }
 ],
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