Elijas/sprendimu_medis.ipynb

## sprendimu_medis.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "massive-static",
   "metadata": {},
   "source": [
    "Elijas Dapšauskas TSf-17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "provincial-reform",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "occupied-slovenia",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Duomenys is skaidriu pavyzdzio (pasitikrinimui)\n",
    "pvz_duomenys = \"\"\"0 0 0 0\n",
    "0 1 1 0\n",
    "1 1 1 1\n",
    "1 1 0 0\n",
    "1 1 1 1\"\"\"\n",
    "pvz_stulp_pavad = list('SILY')\n",
    "\n",
    "# Duomenys is uzduoties\n",
    "duomenys = \"\"\"1 1 1 1 0\n",
    "0 1 1 0 1\n",
    "0 0 1 1 1\n",
    "1 0 1 0 1\n",
    "0 1 0 0 0\n",
    "1 1 1 1 0\n",
    "0 0 1 1 0\n",
    "0 1 0 0 1\n",
    "1 0 1 0 0\"\"\"\n",
    "stulp_pavad = ['Namuose', 'Lietus', 'PalaikymoKom', 'Lyderiai', 'Pergalė']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "higher-group",
   "metadata": {},
   "source": [
    "Įkeliame duomenis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "later-approach",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Namuose</th>\n",
       "      <th>Lietus</th>\n",
       "      <th>PalaikymoKom</th>\n",
       "      <th>Lyderiai</th>\n",
       "      <th>Pergalė</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Namuose  Lietus  PalaikymoKom  Lyderiai  Pergalė\n",
       "0      1.0     1.0           1.0       1.0      0.0\n",
       "1      0.0     1.0           1.0       0.0      1.0\n",
       "2      0.0     0.0           1.0       1.0      1.0\n",
       "3      1.0     0.0           1.0       0.0      1.0\n",
       "4      0.0     1.0           0.0       0.0      0.0\n",
       "5      1.0     1.0           1.0       1.0      0.0\n",
       "6      0.0     0.0           1.0       1.0      0.0\n",
       "7      0.0     1.0           0.0       0.0      1.0\n",
       "8      1.0     0.0           1.0       0.0      0.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def nuskaityti_duomenis(duomenys, stulp_pavad):\n",
    "    df = pd.DataFrame([k.split() for k in duomenys.split('\\n')],\n",
    "                     columns=stulp_pavad,\n",
    "                     dtype=float)\n",
    "    Y = df.iloc[:,len(df.columns)-1] # pask. stulpelis\n",
    "    X = df.iloc[:,:len(df.columns)-1] # kiti stulpeliai\n",
    "    return df, X, Y\n",
    "\n",
    "# Pavyzdys\n",
    "XY, X, Y = nuskaityti_duomenis(duomenys, stulp_pavad)\n",
    "XY"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "welcome-superior",
   "metadata": {},
   "source": [
    "Apskaičiuojame gini koeficientus ir surikiuojame juos didėjančia tvarka. Pirmoji šaka skiriama pagal ties mažiausią koeficientą turinčiu stulpeliu ir t.t."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dimensional-elimination",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Namuose         0.433333\n",
       "Lyderiai        0.433333\n",
       "Lietus          0.488889\n",
       "PalaikymoKom    0.492063\n",
       "dtype: float64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def apskaiciuoti_gini(x):\n",
    "    Pr_s0 = sum(x==0) / len(x)\n",
    "    Pr_s1 = sum(x==1) / len(x)\n",
    "    Pr_y0_s0 = sum(Y.loc[x==0]==0) / sum(x==0)\n",
    "    Pr_y1_s0 = sum(Y.loc[x==0]==1) / sum(x==0)\n",
    "    Pr_y0_s1 = sum(Y.loc[x==1]==0) / sum(x==1)\n",
    "    Pr_y1_s1 = sum(Y.loc[x==1]==1) / sum(x==1)\n",
    "    gini_impurity_s0 = 1 - Pr_y0_s0**2 - Pr_y1_s0**2\n",
    "    gini_impurity_s1 = 1 - Pr_y0_s1**2 - Pr_y1_s1**2\n",
    "    gini_impurity_s0, gini_impurity_s1\n",
    "    gini_s = Pr_s0 * gini_impurity_s0 + Pr_s1 * gini_impurity_s1\n",
    "    return(gini_s)\n",
    "\n",
    "# Pavyzdys\n",
    "X.apply(apskaiciuoti_gini).sort_values()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "extreme-functionality",
   "metadata": {},
   "source": [
    "Pirmiausia sukursime funkciją kuri keliauja per grafą."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "adult-orlando",
   "metadata": {},
   "outputs": [],
   "source": [
    "def keliauti_per_grafa(stulpeliai, ar_baigti_paieska, _istorija=None):\n",
    "    _istorija = _istorija or []\n",
    "    if ar_baigti_paieska(_istorija) or not len(stulpeliai):\n",
    "        return    \n",
    "    for v in (0, 1):\n",
    "        nauja_istorija = _istorija.copy()\n",
    "        nauja_istorija.append((stulpeliai[0], v))\n",
    "        keliauti_per_grafa(stulpeliai[1:], \n",
    "                           ar_baigti_paieska, \n",
    "                           nauja_istorija)\n",
    "\n",
    "## Pavyzdys\n",
    "# def ar_baigti_paieska(istorija):\n",
    "#     if len(istorija) == 3:\n",
    "#         print(istorija)\n",
    "#         return True\n",
    "#     return False\n",
    "#keliauti_per_grafa(['A', 'B', 'C'], ar_baigti_paieska)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "complicated-particle",
   "metadata": {},
   "source": [
    "Tada sukursime funkciją, kuri tikrina, ar tam tikras eilučių filtravimas leidžia pasiekti homogenišką Y stulpelį (t.y. atfiltravus visi Y=1 arba visi Y=0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "spanish-alignment",
   "metadata": {},
   "outputs": [],
   "source": [
    "def spausdinti_atsakyma(filtrai, y0, tikimybe=None):\n",
    "    salyga = ' ir '.join(\n",
    "        f'[{k} = {\"Taip\" if v else \"Ne\"}]' for k, v in filtrai)\n",
    "    txt = (\n",
    "        f'Jei {salyga}:\\n  '\n",
    "        f'tada Y = {int(y0) if tikimybe != 0.5 else \"0 arba 1\"}'\n",
    "    )\n",
    "    if tikimybe:\n",
    "        txt = f\"{txt}\\n  (tikimybė: {100*tikimybe:.2f}%)\"\n",
    "    print(f'{txt}\\n')\n",
    "\n",
    "def filtruoti(df, filtrai):\n",
    "    for stulp, reiksme in filtrai:\n",
    "        df = df.loc[df[stulp] == reiksme]\n",
    "    return df\n",
    "\n",
    "def trumpiausia_filtru_israiska(XY, filtrai):\n",
    "    for i in reversed(range(len(filtrai))):\n",
    "        if (filtruoti(XY, filtrai[:i]).shape[0] \n",
    "            != filtruoti(XY, filtrai[:i+1]).shape[0]):\n",
    "            return filtrai[:i+1]\n",
    "\n",
    "def ar_Y_homogeniskas(XY, filtrai, viso_stulpeliu):\n",
    "    Y = filtruoti(XY, filtrai).iloc[:,-1]\n",
    "    if not len(Y):\n",
    "        return False\n",
    "    y0 = Y.iloc[0]\n",
    "    if not (y0 == Y).all():\n",
    "        if len(filtrai) == viso_stulpeliu:\n",
    "            spausdinti_atsakyma(\n",
    "                trumpiausia_filtru_israiska(XY, filtrai), \n",
    "                y0, np.mean(y0 == Y)\n",
    "            )\n",
    "        return False\n",
    "    spausdinti_atsakyma(trumpiausia_filtru_israiska(XY, filtrai), y0)\n",
    "    return True\n",
    "\n",
    "## Pavyzdys\n",
    "#filtrai = [('S', 1), (('I'), 1)]\n",
    "#filtruoti(XY, filtrai), ar_Y_homogeniskas(XY, filtrai)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "christian-dutch",
   "metadata": {},
   "source": [
    "Apjungiame praeitas dvi funkcijas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "featured-worcester",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Jei [Namuose = Ne] ir [Lyderiai = Ne] ir [Lietus = Taip] ir [PalaikymoKom = Ne]:\n",
      "  tada Y = 0 arba 1\n",
      "  (tikimybė: 50.00%)\n",
      "\n",
      "Jei [Namuose = Ne] ir [Lyderiai = Ne] ir [Lietus = Taip] ir [PalaikymoKom = Taip]:\n",
      "  tada Y = 1\n",
      "\n",
      "Jei [Namuose = Ne] ir [Lyderiai = Taip]:\n",
      "  tada Y = 0 arba 1\n",
      "  (tikimybė: 50.00%)\n",
      "\n",
      "Jei [Namuose = Taip] ir [Lyderiai = Ne]:\n",
      "  tada Y = 0 arba 1\n",
      "  (tikimybė: 50.00%)\n",
      "\n",
      "Jei [Namuose = Taip] ir [Lyderiai = Taip]:\n",
      "  tada Y = 0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "XY, X, Y = nuskaityti_duomenis(duomenys, stulp_pavad)\n",
    "stulpeliu_pav = X.apply(apskaiciuoti_gini).sort_values().index\n",
    "keliauti_per_grafa(\n",
    "    stulpeliu_pav, \n",
    "     lambda istorija: ar_Y_homogeniskas(XY, istorija, len(stulpeliu_pav))\n",
    ")"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "ordinary-spoke",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "extreme-logan",
   "metadata": {},
   "source": [
    "Įsitikiname, kad kodas veikia teisingai išspręsdami pavyzdinį uždavinį:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "narrative-right",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Jei [S = Ne]:\n",
      "  tada Y = 0\n",
      "\n",
      "Jei [S = Taip] ir [L = Ne]:\n",
      "  tada Y = 0\n",
      "\n",
      "Jei [S = Taip] ir [L = Taip]:\n",
      "  tada Y = 1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "XY, X, Y = nuskaityti_duomenis(pvz_duomenys, pvz_stulp_pavad)\n",
    "stulpeliu_pav = X.apply(apskaiciuoti_gini).sort_values().index\n",
    "keliauti_per_grafa(\n",
    "    stulpeliu_pav, \n",
    "    lambda istorija: ar_Y_homogeniskas(XY, istorija, len(stulpeliu_pav))\n",
    ")"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "spread-greece",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  }
 ],
 "metadata": {
  "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": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}