Ćwiczenia/6. Ćwiczenia/Zadanie 7. (sklejanie odcinków).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Treść zadania"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. podpunkt"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementacja #1\n",
    "### Tylko dla liczb całkowitych\n",
    "##### Top - down"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Omówienie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tworzymy tablicę rozmiaru $ n \\times n $, gdzie $ n $ jest wielkością przedziału $ [a, b] $, a dokładniej liczbą liczb całkowitych, jakie do niego należą (łącznie z brzegami). Ponieważ dopuszczamy również liczby ujemne oraz początek przedziału większy od 0, będziemy musieli za każdym razem \"przesunąć\" wartości do indeksów, które im odpowiadają. Najłatwiej jest sprawdzać w sposób rekurencyjny, czy bieżący przedział, jaki rozważamy w danym momencie, da się otrzymać jako połączenie innych przedziałów z tablicy wejściowej z przedziałami (tablicy $ A $) lub, czy dany przedział znajduje się w tej tablicy (przypadek bazowy - w końcu musimy trafić na przedział z tablicy $ A $, aby móc go połączyć). Najpierw jeszcze, aby przyspieszyć działanie algorytmu, odfiltrowujemy przedziały, które \"wystają\" poza przedział docelowy $ target $, a więc zaczynają się wcześniej od jego początku lub kończą później niż jego koniec. Aby nie sprawdzać dla każdego przedziału, czy zawarty jest on w tablicy $ A $, w sposób liniowy, posortujemy najpierw odfiltrowane przedziały (możemy wbudowanym sortowaniem po obu współrzędnych), a do sprawdzenia, czy bieżący przedział $ [i, j] $ znajduje się w tablicy z przedziałami, wykorzystamy wyszukiwanie binarne. Nie zmieni to co prawda całkowitej złożoności algorytmu, która wyniesie i tak $ O(n^2) $, ale nieco przyspieszy obliczenia. Jeżeli okaże się, że dany przedział nie znajduje się w tablicy z przedziałami, musimy przebiec po kolejnych indeksach $ k $ takich, że $ i \\lt k \\lt j $ i znaleźć rekurencyjnie taki podział tego przedziału, że oba otrzymane przedziały będą wynikiem połączenia innych przedziałów z tablicy z odfiltrowanymi przedziałami (lub po prostu całymi przedziałami z tej tablicy)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Złożoność"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Obliczeniowa:\n",
    "$ O(n^2) $ <br>\n",
    "(względem zakresu wartości w docelowym przedziale, tzn. $ n = b - a + 1 $ jest liczbą liczb całkowitych w przedziale $ [a, b] $)\n",
    "###### Pamięciowa:\n",
    "$ O(n^2) $ <br>\n",
    "(względem zakresu wartości w docelowym przedziale, tzn. $ n = b - a + 1 $ jest liczbą liczb całkowitych w przedziale $ [a, b] $)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def binary_search_first(arr, val):\n",
    "    l = 0\n",
    "    r = len(arr) - 1\n",
    "\n",
    "    while l <= r:\n",
    "        mid = (l + r) // 2\n",
    "        if val < arr[mid]:\n",
    "            r = mid - 1\n",
    "        else:\n",
    "            l = mid + 1\n",
    "            \n",
    "    return r if r >= 0 and arr[r] == val else -1\n",
    "\n",
    "# Leave only intervals which can be joined to the target (begin no sooner\n",
    "# than a target and end no later than a target interval)\n",
    "def filter_intervals(A: 'array of intervals', target: '[a, b]'):\n",
    "    A_filtered = []\n",
    "    \n",
    "    for span in A:\n",
    "        if span[0] >= target[0] and span[1] <= target[1]:\n",
    "            A_filtered.append(span)\n",
    "            \n",
    "    return A_filtered\n",
    "\n",
    "\n",
    "def intervals(A: 'array of intervals', target: '[a, b]') -> bool:\n",
    "    a, b = target\n",
    "    c = b - a + 1\n",
    "    F = [[None] * c for _ in range(c)]\n",
    "    # Leave only intervals which can be joined to the target one\n",
    "    A = filter_intervals(A, target)\n",
    "    # Sort all the intervals by their first coordinate in order\n",
    "    # to check quicker if an interval is in the intervals array\n",
    "    A.sort()\n",
    "\n",
    "    def can_merge(i, j):\n",
    "        # Return a cached result if exists\n",
    "        if F[i - a][j - a] is not None: return F[i - a][j - a]\n",
    "        # Check if we have a whole [i, j] span \n",
    "        if binary_search_first(A, [i, j]) >= 0:\n",
    "            F[i - a][j - a] = True\n",
    "            return True\n",
    "        # Else look for a possible split\n",
    "        F[i - a][j - a] = False\n",
    "        for k in range(i + 1, j):\n",
    "            F[i - a][j - a] = can_merge(i, k) and can_merge(k, j)\n",
    "            if F[i - a][j - a]:\n",
    "                break\n",
    "                \n",
    "        return F[i - a][j - a]\n",
    "    \n",
    "    return can_merge(a, b) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Kilka testów"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "A = [[4, 5], [2, 4], [1, 3], [3, 6], [5, 7], [1, 5], [-5, 2]]\n",
    "\n",
    "print(intervals(A, [1, 7]))\n",
    "print(intervals(A, [2, 5]))\n",
    "print(intervals(A, [-5, 5]))\n",
    "print(intervals(A, [0, 2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementacja #2\n",
    "### Dla dowolnych liczb rzeczywistych\n",
    "##### Top - down"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Omówienie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Co z liczbami rzeczywistymi?\n",
    "Ponieważ mamy liczby rzeczywiste, musimy najpierw \"zmapować\" przedziały w taki sposób, aby łatwe było \n",
    "zapamiętywanie obliczonych wcześniej wartości w pomocniczej tablicy. Nejlepiej warto odfiltrować zbędne przedziały (te, których napewno nie użyjemy, bo wystają poza przedział docelowy, np. zaczynają się wcześniej od niego lub kończą później od niego). Kolejnym krokiem jest \"wypakowanie\" wszystkich współrzędnych przedziałów (również docelowego) do jednej tablicy (początki i końce razem) i posortowanie ich niemalejąco. Następnie, ponieważ chcemy przekształcić na jak najbliższe sobie współrzędne naturalne wszystkie rzeczywiste wartości współrzędnych, przy czym, chcemy zachować wzajemny rozkład odcinków (przedziałów) (tzn., jeżeli dwa przedziały zaczynały się lub kończyły na tej samej pozycji, to muszą się dalej zaczynać lub kończyć na tej samej pozycji, która będzie zazwyczaj inna od poprzedniej, ale taka sama dla wszystkich przedziałów, które miały początek/koniec w tym punkcie), więc konieczne jest usunięcie wszystkich powtarzających się współrzędnych z uzyskanej po sortowaniu tablicy. Ostatnim krokiem jest wykonanie samego mapowania. Możemy albo zamienić współrzędne odcinków w miejscu, albo utworzyć nową tablicę odcinków, które będą zmapowanymi odcinkami (przedziałami) z początkowej tablicy. Zrobimy to, przy pomocy algorytmu wyszukiwania binarnego, które znajdzie nam indeks danej rzeczywistej liczby (współrzędnej), czyli nową współrzędną przedziału (jest to przekształcenie jednoznaczne, zachowujące kolejność przedziałów (ale nie ich długości, które ulegają zmianie).\n",
    "<br><br>\n",
    "W kolejnym kroku operujemy już tylko na zmapowanych przedziałach (mapujemy również przedział docelowy). Tym razem, jak łatwo możemy zauważyć, uzyskamy tablicę $ F $ rozmiaru maksymalnie $ 2n \\cdot 2n $, gdzie $ n $ oznacza liczbę przedziałów, jakie otrzymaliśmy w tablicy wejściowej, ponieważ współrzędne będą maksymalnie z zakresu $ 0, 1, 2, ..., 2n - 1, 2n $ (wynika to z mapowania na kolejne liczby naturalne). Również znika problem z indeksowaniem tablicy $ F $, bo działamy już tylko na liczbach naturalnych. Konieczne jest jeszcze posortowanie tych zmapowanych przedziałów, najpierw po mniej znaczącej współrzędnej (współrzędnej końca), a następnie, po współrzędnej początkowej (nie musimy w tym celu wymyślać żadnych specjalnie skomplikowanych algorytmów, bo operator porównania w Pythonie automatycznie porówna przedziały, które mają taką samą pierwszą współrzędną, w pożądany przez nas sposób, więc wystarczy zastosować zwykłego QuickSorta lub wbudowany algorytm sortowania, jeżeli jest dozwolony). Dalej postępujemy już analogicznie jak w powyższym algorytmie.\n",
    "\n",
    "###### Ważne uwagi:\n",
    "Z tego względu, że możemy mieć niewielką liczbę przedziałów o dużym zakresie oraz duży przedział docelowy, I Sposób nie nadaje się za bardzo do większości zastosowań, bo tworzy on dużą tablicę (wielkości rónwej liczbie liczb całkowitych w przedziale $ [a, b] $). Co więcej, nie poradzi on sobie z liczbami rzeczywistymi, więc poniższy algorytm (opisany w tym omówieniu) jest dużo lepszym rozwiązaniem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Złożoność"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Obliczeniowa:\n",
    "$ O(n^2) $ <br>\n",
    "(względem liczby przedziałów równej $ n $ - dużo lepsza złożoność - prawdziwie wielomianowa)\n",
    "###### Pamięciowa:\n",
    "$ O(n^2) $ <br>\n",
    "(względem liczby przedziałów równej $ n $ - dużo lepsza złożoność - prawdziwie wielomianowa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def quick_sort(arr):\n",
    "    _quick_sort(arr, 0, len(arr) - 1)\n",
    "    \n",
    "\n",
    "def _quick_sort(arr, left_idx, right_idx):\n",
    "    while left_idx < right_idx:\n",
    "        pivot_position = _partition(arr, left_idx, right_idx)\n",
    "        \n",
    "        if pivot_position - left_idx < right_idx - pivot_position:\n",
    "            _quick_sort(arr, left_idx, pivot_position)\n",
    "            left_idx = pivot_position + 1\n",
    "        else:\n",
    "            _quick_sort(arr, pivot_position + 1, right_idx)\n",
    "            right_idx = pivot_position\n",
    "        \n",
    "        \n",
    "def _partition(arr, left_idx, right_idx):\n",
    "    pivot = arr[left_idx]\n",
    "    i = left_idx - 1\n",
    "    j = right_idx + 1\n",
    "    while True:\n",
    "        i += 1\n",
    "        while arr[i] < pivot: i += 1\n",
    "            \n",
    "        j -= 1\n",
    "        while arr[j] > pivot: j -= 1\n",
    "        \n",
    "        if i < j:\n",
    "            _swap(arr, i, j)\n",
    "        else:\n",
    "            return j\n",
    "\n",
    "    \n",
    "def _swap(arr, i, j):\n",
    "    arr[i], arr[j] = arr[j], arr[i]\n",
    "    \n",
    "    \n",
    "def remove_duplicates(A):\n",
    "    res = [A[0]]\n",
    "    for i in range(1, len(A)):\n",
    "        if A[i] != A[i - 1]:\n",
    "            res.append(A[i])\n",
    "    return res\n",
    "    \n",
    "    \n",
    "def binary_search_first(arr: 'sorted sequence', el: 'searched element') -> int:\n",
    "    left_idx = 0\n",
    "    right_idx = len(arr)-1\n",
    "    \n",
    "    while left_idx <= right_idx:\n",
    "        mid_idx = (left_idx + right_idx) // 2\n",
    "        if el > arr[mid_idx]:\n",
    "            left_idx = mid_idx + 1\n",
    "        else:\n",
    "            right_idx = mid_idx - 1\n",
    "            \n",
    "    return left_idx if left_idx < len(arr) and arr[left_idx] == el else -1\n",
    "\n",
    "\n",
    "def map_span(span: 'span to map', C: 'array of sorted coordinates'):\n",
    "    a = binary_search_first(C, span[0])\n",
    "    b = binary_search_first(C, span[1])\n",
    "    return [a, b]\n",
    "\n",
    "    \n",
    "def map_spans(A: 'array of spans', C: 'array of sorted coordinates'):\n",
    "    res = []\n",
    "    for span in A:\n",
    "        res.append(map_span(span, C))\n",
    "    return res\n",
    "    \n",
    "\n",
    "def prepare_intervals(A: 'array of intervals', target: 'target interval'):\n",
    "    \"\"\"\n",
    "    This function filters intervals which cannot be a part of the resulting\n",
    "    interval and maps coordinates of each valid interval to a proper natural number.\n",
    "    \"\"\"\n",
    "    # Filter intervals which don't need to be checked (and unpack all valid coordinates)\n",
    "    C = [target[0], target[1]]\n",
    "    A_cp = []\n",
    "    for span in A:\n",
    "        if span[0] >= target[0] and span[1] <= target[1]:\n",
    "            C.append(span[0])\n",
    "            C.append(span[1])\n",
    "            A_cp.append(span)\n",
    "    A = A_cp\n",
    "    # Sort an array of coordinates\n",
    "    quick_sort(C)\n",
    "    # Remove duplicates\n",
    "    C = remove_duplicates(C)\n",
    "    # Map all coordinates of all the intervals to natural numbers using a Binary Search\n",
    "    # (we will look for an index of a coordinate in a C array and replace this coordinate\n",
    "    # with an index found)\n",
    "    target = map_span(target, C)\n",
    "    A = map_spans(A, C)\n",
    "    return A, target\n",
    "    \n",
    "    \n",
    "def intervals(A: 'array of intervals', target: 'target interval') -> bool:\n",
    "    A, target = prepare_intervals(A, target)\n",
    "    n = target[1] + 1  # All indices will be from range 0, 1, ..., target[1] - 1, target[1] \n",
    "    F = [[None] * n for _ in range(n)]\n",
    "    \n",
    "    # Sort an array of spans in order to use Binary Search for checking if\n",
    "    # a span is included in A\n",
    "    quick_sort(A)\n",
    "    \n",
    "    def can_merge(i, j):\n",
    "        if F[i][j] is None:\n",
    "            if binary_search_first(A, [i, j]) >= 0:\n",
    "                F[i][j] = True\n",
    "            else:\n",
    "                # Set False as a placeholder value (by default we can't find intervals such\n",
    "                # that can be merged to the [i, j] interval and then we search for a possible\n",
    "                # solution).\n",
    "                F[i][j] = False\n",
    "                for k in range(i + 1, j):\n",
    "                    F[i][j] = can_merge(i, k) and can_merge(k, j) \n",
    "                    if F[i][j]:\n",
    "                        break\n",
    "        return F[i][j]\n",
    "\n",
    "    can_merge(target[0], target[1])\n",
    "#     print(*F, sep='\\n')\n",
    "        \n",
    "    return F[0][target[1]]  # target[0] = 0 - always after filtering intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Kilka testów"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "A = [[4.1, 5.2], [2.15, 4.4], [1.5, 3.2], [3.2, 6.83], [5.2, 7.1], [1.2, 5.2], [-5.75, 2.15]]\n",
    "\n",
    "# print(prepare_intervals(A, [1.2, 7.1]))\n",
    "print(intervals(A, [1.2, 7.1]))\n",
    "print(intervals(A, [-5.75, 4.4]))\n",
    "print(intervals(A, [-5.75, 6.83]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. podpunkt"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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e88U5zZNCcXBGF+Hv4ib8EyeIXXolOTdXJPtXEy71k8W8bw2U3xxbM9m2fNtWfaPY5MrE1jxYEkoufrkyt0WXFJcFCXZwmkjydxMu/p3ElNKyp3qw/DERrZbsg4lOk9ZodYjqYFSa2GeUt20iPa628IwfKbYptV/FH4rh8T7CzSh9IYp3TRCJ/mrhFT9MrDeKS67ekhBmbQzFtX6YiPeqLtwiHi2zF5TusNjaQqXyFi1f3KrLhTlbYYfdkeV6WCxMDhAql0CRPK+snnyXHidcTOxT8eJk4aPyFKFJ6WKN3sZZ0iP9s3OvCzrFgepsPRHSKF4MWH5U9yRLzOzgK8iBLaKaNBIxAxbr6iPlbWai8KL0fZPnk2brLzvqikX5Mkk31KRPAaLHCn0L8K1YnFxfqNQNRVL6Kp08UiS5Yv3wFsLLLcC4HSn+XExJDBBuXi3E8PW5mtQKlz8iAquHiB7v6PMp3T0qlqWEC1e9HbWlPojFooefC9nsOJFe1lBp0lJ2lemKkR1X8HLx5kEiwpnsP9W5iF4zRWapbVwuhsR6kd4Ytqt21MMVPYRfuTbYULDNVEa1KH2y1ymLdbpwQdDJUIJc+KJ+j4UG+kHvOUzX9ompbepQuu4iKm2dMalvqF2p7i3i09cZtFeWYWrru9q4faE2bteUTsLfzUfED/9QcVyOy6MBL6M6IOVFb3eqiwYhEQrqZkXiov5eVIyIUNJ3sqXN0RSJXB23J3+O1Qd5uczYHsXt0bdieUqYqB7YS7xjaJ/PLRQpoZ6lfU3Jtrv6dhFzDfo0xdtGinhPaltdyG4tOqwhp70qanust19GNskmu2hDmRQupr5nLerzvW5g08kuLksRoa7U7y21/1L3SknbZ2tb5MD6ZHMdMChO0z8V65b+RTN9ZbIXywc1EWoVtRWm7ZQmjbrCxS3KoO2n9nRYHIV3Fp4tnxfanod1XVE+xlJajpQvR/Kk6LT6Y9pHNQSv78u6CnX0Y7r+H3Edn0BtGvFTBQs6/cq0pKz/vjBZtKlJYztUN2hnvhOrU0KonTYY75XG9J1Y0SPApP9jPRnTEDC9Ycvv4m3DRCwNSFXqWDFkjXY4Zsv7toXNEnOTqHNHkFWGA8VykRSLE1NoUKoydjKUGm2jAqKCm3Kf8CJF9u4wrdwAvXB+kvAu18GxJX6dcPpBWblBuq6Bk1Ga8oaMOmgzEoU35cu95Thxwijf60RalLuAKw2st10sR0T+hl6BTJT9xEs0SJcaE2Ol08rjKgJSlhlHZzrgPLdKpLcNE4GGg3F5AWTuXhRbyXEgOVeMBg9bqSNLThpjZ8wJsSg5TIQNeM+k8yXdb0B6Ul2EGj2TKlMjEZTyTln4dQNECDl4FpcOCPWGjZxmoSlimb4h/naa6OBNTNwTxPgThqPHQrEvLYbON6lJHc2PDfJjhq1Mjq3fqoC+GTp+bM6DBcmUlrktuqS0LMQuMaWNDw20fUWHGV+YCPmNoON5ZJwMFKxwvkj2pYGYU7gY8Glu2XuSYyuokUhZrXR0livWDYoSrqgtWo7PNEmfyooaAncaeEQMel+nZ3bYmOL3xaAIqs+qBiJ5kUFN13SE3DSD7jIng3xjqRHMJrvzhZhBA3qVXL72pYkoZ6oTUUPENl2Oje0TNYprRoq2gQ2NB9gmdMz/1Hf0yw8KtelQ3Td1DuvypgpIEWtKI7ajrpgXip6YDkC+EWvS24nAQEPnljaC4nVko1ydZGwzPT8xTrR0d9I54nPFmpRgoXJuJAZtNnCOStFIdq6Bzlkr/V3PxDalNRFukkM/7FGx2sgpXdGOPqVtWqctcjF4qH/Px1BW3XN958y9uUjP0glsaz206mTYQ/agjtYpXOpkKMuPsX5IcjlK18ikLEoWvtRpdgodID419DGvThFBQSlitWKnpa6+l2tftPKOb1mb2vYoMWhdrsJScVwey9eBMhFsq5uG7A2ddtr4rMUFpX0nW9ocTdKmddz+/DlMH2TlMmd7bGmPlomUAFfhTB8ENxvpptTvihENNB+0tH/XM/ygU7xGpEVLzlZ36m8tM3baVdjBqaD9MuzH2GQXbaija1JEgMqN2u01Jv3JD6ktjrDgZDDX9tneFlmrA+ZtmUl9srkOlOm88V+26JbuTd2HYJV3ophh+OFNelz4mkiS+tFGTgZ9GqYfDLQOMRf6uFjmZFCgK0rtBImjuA/jMJ5aRtp0LTgZDk4RHXyor6qm8cZBg4Ze39Z6dhAzlQ7zDApUO55ViWrRQ8RWg/qv52D8wUZ60TFOBmXLJeTmQRStQvpz7+K4U2M88fpyLE4xXNYg90JF7tH0m8WzMX9nPrlx1IjqNwqTDE+cKMnEW68u0U1TViNm4h5cunUL13/IKL+cQtzEtb/0U6p3YPH7X6FI1EJ0u0Q0MhHRq7Y7qpUT25b4TV6u2wRJvU1ToTBGMpVLUHfjBNZ+9jUKRQ0EN21hshlmDFpG1gGu5+GbPTnmIlB2P2Yq9tIu5eL6d1jzuKmsAtevXTMfT/YSpPYYhdWez2DHjmlob/MRsP7onNIKDZ1uoODgDmRoZgTlY1vGl/ixGpVEwdf4LOOkNv2infjscA3c1z/RZE+OGPTv1xoBqr+Ru/MTrNXPKirahNX7a+D+1PvLwqvU8GvUCBE6OYsypuD5JUdRUr0xUufNwBO6M2zz1m7DV3SSiXNwLLrEGGbKC61bhsMHV5DzzRGarFoZVwX0zUCcSsuDpTK3RZcUlgW2rcL7XxRAuEeiXT/TY2vVqO1evsZqMHglo1/7AKhuncfOdzfTujTtVbRqHfar70NqX4WH4xWtx9JN53Dd+S407RJrUuBUVnQv2PkKsjd9gFWaROywMTu3IFNah+4RiTbdDQ4F9hqCNTvexayZi/HuK51N0rbwU4ndyduOz74irnL5at0UkT7OuJ5zDHvOm6YjkL3iWfR4ah08X1iDHRMN6pdpUKu/fXBPUnuZs5udUfee9ugtszROXL9mcMSwY+qKvJg/YUXqQDy12gMv7PgEE0mXyq6TWLV0K7Kvu8nYZgoV0wJNg91wPXsrlq66hOioQHjcOot3+96H+MSeSB05C2ulaf2tUvDsiIeh0eq/qqNOpIFt+mACnnvnBP5W34O0uS+jrwwLeblv011nV7iZ2vuEjvi/cHfgyglsWLpDK4ij6mFpttpi4t7fcEtcxQ9rhpTTHWP9MGRRUV0jk9K/B9oHVMOt3D14d61+WR3pwuqvob7/EfQ15WGmKIpWfYBNVN/Lty/SC9TmNL0LztfPYdPS9aV2y0xUJrcrnkfr6Sitm9ZjohmqZus5lNgwKQlb2hwlIlmQyVS3HKUP5cWyYHtsao/CEBXsiVvn3kPfJvFI7JmKkbPW0tI7f7Tq/wxG9LyXkr6Bv6r5ILJRkK6flI0Pnp6Id05dhTr2ccxd+ES5OlZe3kq8Y6NdVFwm0REI9riOc+8ORZP4RPRMfQ6z1kpLq1ui/7ND0bNVPZlMWWr77G2LzNcBU32TEUh7y1F1wCbdkpKmvvrij/BF0S24R7dBv0YmBtBLDfdqmg38DK4v8HFmDu0nVBsxbVob6FYjPL7mY6ye9RqWvvuS8tMDldoJIxkslSMFdBRPk5zL/zyD5dPfQWYB4NsuBaOblzX0+R8fRfYNFWrGtkVff/m3zd8t248huEUiOpcWTT5yCv/ELar3hfk/otB8BHY/sc/JQOu6pvYeh2Xng8jBsALvPN7MbgEUvVi0FtNe24oLNwDXsO4Y/2qK8cDyl8+xZNpb+OwXg9ikNT5Du9G6Tn94eNRBQOQz+DjH5IBWzakZdJwHaqJuoK8iUUoDKYnfNEa5jphpGLO/j+Pr7Mv09Boubp1Utn+AZr1cCl6/4Iu4+ATc21jOGJqN1MwDWlu84Gl0TWhEe1l4wCsgEj0/zrG8w/fVY5jVcQxWn/0Nvx7fh52ma6XNpFTuduee6NJYDVFwGOtW0l4VJTuxas8NdE69jwbzPyNr3WYyZWTOlmzEl/XaI7Vz+dqm7vsIHri7JkT+AWRIcdBqozNvrMMhvw4Y2MkgfLeFyNozG+0lIbIXIPX5NTj7txfin51qcGJJDnZ9fR60IStuXdyKEfp9G/T/v34BDeLuRZt7o1CrXGYceMMefStNvpLyoKjMFeqSorKgVcd7T+MHWn4O2osh0HCcZxV1GPqmdsbdrjeQv2c9VkpKhP14Y/Vp+N3/EDpZfV8XYO8RnCogQ6SqDrW/zEhPtxGuKDiDrL20StsOG3P+UDYu0ncjuNdCPVP1Du+NMWN6wyaXrhK7s+sYsv+kRG/9iK0jOpnYlyW40ID2SGhzLxobKbnA1ZPz0XFYBs5e/hnHt+9XsGeLJdDOcHVzlQmggrNrNeUb/FaorsgkT1sdn5zVH8NIVy7/ehLbd541CXQMWad+Iwe4E2qo5axALahrSBsn/4ZTWScR89wLSH+wIdwu5eLIrk+xbMFYPBLhBY8m05Hte7e2bE3rwwsfI+eGF+LSXsKr3YLlhKyC98JxTyjNBcTf+OH0NzonrIPqoUluS3bPx9CuCYik/YM8vO5CZM+PkGPxSAoH6Jr6fqQ+EEGLMn7CnoyNmnYJZz7C6kNeuH+gplVRcFHnL+sMCqjqqWqojfa70r7sBX91daioE1hw6gj2KoixLIgD8mg1PRvrpsX4LMSlxIaVxq2wzbEoi/6hBZlM33eIPphGasX22NQeheC5KcPwYGgNXMo9gl2fLsOCsY8gwrU2mkw+Cd8WUqsSgG6LdmHP7G70t/Rxbyxe+CAbNzzjkTb7BXRT6DgzzYXDfttqF5WWScyTmJJ+P0LdLiP3yC58umwexj7SDK4e7TA5uxZa6D44leVDYdtnc1tkg75ZhOqAOmCTbkk70uRg7+l8GrA6U/fMjzRJwXWejlS8KH24rIFa9WqbvBCL3mNGonc59hbitclOSPEoLEfal8HmMZEFMc0+Ovku3t6aR1LVQbOO7QycLtnY+uV31BOpgaDopsrYGiVyCruO00d6lS+i2zQ1eHIeX2X/qikzTyozqbV29GWHk+FrrHg6HXNO340JGzZVvoOBuiYbXpyPtTnSZo93IWn0qPJfcXIKUVwnEDG6j5ElmS+hY0RXjFr1LWp1ew1Hi39H3tk30SvMzSH8Kjt+eSHV1FGVzgp1Q1iv+Th8+HD5f4c2Y0FFZ5RIDqSOrdBp1Ps4Xasr5h/NR1HeWXzSK4zU0ML15zX4p76JN3s1hOrCRkwa9ib033YsvCXzqBVS7muIauJXHNi4BXkbN2HvjWZ4ZFof+mrkjMIDW/Be/hG8t/V7NLgvSfvVr1ws7THwgSia3PcL9mWsxUkaTL6zPg8R3R8y4xE9gPnPzcXGC9fh1TIVsyZ1pwFNEQ4tGIeX1l5GbU0nj76zhPXCh3LcD3+J7QserTQPf8X1rVrl5MFamdulS5bKwvq2o+VUwfBGp4fwQBNPiMKvkPHmbuDAOqw/F4DuqSYn2FiK5I8SXJUcANYu8TdK/rAw68fa+7f7eW3dKUHOYej1oYxtIb0/tH0BUoz8KrfwZ0kgUlfNQK9QJ1xYNwvD5h243ZIbpVfxuiIn/lWU+A/Eqjd7IVR1HusmTcC8M4YbTpag5KrFEa0u0pu4WkLvUcf3pY1HcTRjOoYO6IYOLaIR7OWCP3N3443hz2D8Ac0UGN1lUB9aP42FsyXblI21E57BhLUVrA9yWb0d9xxRD0vlpI3+pnZGRKd0rDpdC93m70Fx0Y84+8nDCLPYYDkio/7oNDAJTdxvoXDfp3jzZD4OvLMF5yK6IDVBxgEpm+Q1/FHyt7SphdVLXC0xv3Ga1bf/IwHsanMcxcYR+mAqixXbY2N7pG4/CRtz9iJjxjAM6NoBLaKC4OVSjNy9izF84DQYWe8zi/DctM9x4WZdtB49HbOl2cNFGZjwxEtlM0RNxb1tv5XaRaVlEoD2L21EztEPMGPoo+jaoQXN+qBdf/78HnvfSMfA8dtMcma97auctkgBYEfVARt1S4EVwkuYAAAXSUlEQVRkVTCI9XKEo3gqyH3RzqM4d4Vag5oR+L+esQZvfIN9p36V1o0irss9CmIyCZL/NU7mXqWPcw3RMsngE1VRFr44dYkCeyCCNndV2mrZIoCNToZsZKQNwuidDTD6/XcMpoxKO1SHI3HWEVvSVhb2wCJMX32KpsQ6w7v9U5g9NK7ce3lfZeMnfR+v6C0Mfvw17Mx3wz1pr2PL7Edlvvpd1w4gD0UgKqg6xXcVl34xu++pcXq2xO/QTmAsWkXXpcHuX7iYc0ZmJ1DyOq9djCVGu5iXQ2XlxhmsGDwM03b+hGr3PIlVW2YjRc6LeOh1jHopw3jqZt3mGDDxUQxaNA59wqrh123z8cyM3VbSk3vshVZ9EtGYlqRfPrwREz88Bpe2yejqdR+6JzSA6vIxbPrfUnx6zBed+phOl9fH54WE1AcQ56nClaObsWTVJ9j8cxT6PSs3mCRnwoyJePWzC7jp2wkvLZuoW+ZxDB++9x52HPsTbVs1gg95GW5ezME+uZMDsj/G60syZcpELn823nOIvgVUTh4slrk9umStLH5BcNsoBElW68ol/KL5dGjL1Rqp3WPhiUs4umktVr27Cz83fwjPmk7rsxRl5+aI8iQBbv2JwhwZASSHpzTTwjMcLTuT1zO4qc02pjSPRXk4eUxG4Up2Y9Wq3Y7Vt7a0e7iPCyl5AXL2yQ1ej2EtLYvbbSQOTe1s2QsTu4/Aopd7IMyFpktOn4gZdu18bAm6wmcOqStyafmi5YAn0H3QNLzcJxwuv+7A9Gfm0hk3+iseLaOkrzA3UFxI8xzLXQUoLKbZLzQlNKrl3cjoE4kGPVfBv/cLWPjueuz88iRyC7OwbEAUql/+Gh/plxZIjs6p4zBVb5veHovmmrh/wsEtm3EgV5rZZuZa2ROB8WPo29I/eZ3El2elE5pMj8yqSD3MwcqedHLHmN2ajBWtSMfj03YgvxotI6FlB7NTDDtm+rzvxYJRUytnYJTwELrH0fcfWhKyaclqvLu5CM37PVxu6aX5UghDZ1py50kBbhUXypSXfjqrEzyjmsOGRVLmk7xjn9jT5jgYRoX1wVQeK7bHpvZoL/oENUTPFe7oPfZ/eHfDTnx56jwKjy/EgIgauHxwA5Zu07dpmZj61Gx8RkfH+XYejbcn6mbmFB7Glg1ZyDWZFGwkdaXbHhvtopIyoRMeghr0xAr/3hi7cBU27PwSp3J/wPFljyKiehEOfpQBYzeDlbav0toiU/0w/e3AOmCTbklfeMPQNsqf5vPdou5ZoXZml6l4pr9L+0eXcOHk96ZP6TfNICC7btzvkAlm9y0r5UifSu0eE9khU+GPv0Fq1Z0ahKOF4VSQrH04cv5vqHwaoVVbNQ5M6IEHJpg6viwkeKUQl67QfIWQGBhO5i7K2I2vi25CVb89nhrdzkIE9j+ywckgfTEYjklfNcWc3SZrUktO4nReNTSI1C85kI4wmYB+3XpjqP4IK7tkJEM3djm+ukwQvFpjxIxnZBrvLfjf+uO4QlMNNZNttmUiK48soEtDtE/rYpCqvqMn3foTp/dswOaDd2Fwt8Zwp+8DJ/ftN1nvSFPsL/xOq+1NLpvi/8n07Qr8pr0GBich3PUmfv5qW/kOU8k6TBv3GjackbxS9l4HsCXrAnWVa+Lu9skGX/31HR1dvKcz8fHmw/Lrd7yewMK5/RFd/RdkzpqMqfYMOBKS0aUJTTu+fBCrPnfS7btA02wHtUe4UyEOLV6Dc+Ed8Jilr0WNHka/tv5QXTuF90etQ0nrh9Bfxk1Xsn0qnp6eiQLnEDw05WWM0g84S75HXoEb/MPpyMr+fZFMa4vFz3Q0UunaWz1j+rI5jZwUG44rOKdeqhcv4uH7H8YYzTIOBZeD9M1xeZCRWbbMbdclJWWBzr3RrRnpRvFZ7Fuv25+jVKR8XPitXI01EFiNRs/2RFtfZ1w78T5Grf0Trfsl2+a99e+B/ol30d4O+Ti2/ZgJjCJkfXYU52+5on7iw3hSs9Sho+02pnMKHr7XG6q/s5G5an/5NManY9TyAzR1zoGXV3cMTpamfufjqw07yq39Llk3B+Ne/QRnrsun6dX3ZcxNbYzqBZmYNdpwAC4fvlLuOqiumJctHH0XTkVqtBsKMt/A6KmZuqBxeLJ/G9SnfWB+PPaV8ddAKYS+g1C/Dfo/2QB/XbuK/HI2vBken/QAosnPo7809WEOtUvlbNMJapuEzPRS85JX+pOb1/GXiT+sZP0G7Mq+Sm13Czya1tFABAfUQ01s57Fty0Hk3aC9xO6+D2mG7YHe2acJ9y32fLwZBytjwSla49l+CfBVleDE+zOwtqQZ+vU32EdFAXj/Jx9GYn1XWql0AtuNZrFILx/FZ0d+xC2axZlIe0CYrp5SEP1/KIjtbY7j4VRcH+RlMmN7bGqPruHaNRn7Hj4Ek7pFosz00FHxY8Zhzv7f4BzYFVNeL+t3l+w4gwvVZJbxyQut6G41T3dyQ5a/ijadQK7kmzW5bLeLCsrkL2JDM2SN+3dqhD8+GN2ia5qKYPRbtu2r9LbInEgOrAM26ZYkD+2pNvhBNKMPhMUns7DecEKe9PhMPn6jga7xRf2jh5vBU1WMbzO3yrSdszFy1Ds46NDOjjw72XIkiSo8JpJPTvZuPToKXfqg6eThTS4b/UX1MeMLZF9TwSOmFbp7HcYnW2h/Jk/ah09z0fHo4/vi/u7pWGlumbq3H+p6OkPlUk3j0NZemXh99VcogB/aDxuOJ2TGR6VBTf/IXo0J/Xqg59D5Vh1ACp0M0tqsEfTFYCvOfrMCT0R4GJyHTgdYegzFp3/UQfg9etfLNsydOh8fbPwIb02dg6UyH/xMZS7/mwb582bhzf20GRlhaTJgJJ4z2ARDEz77fYzpMgyLj16Cs3c97WaImg1caJ6k9EVur37CPsm/aDX2/exEMwGu4cofhfjjigtq+dRGwqQpGJvoh8Ktb2Lo8rKBX0nmTAxbekSzFl/QF4bSsrMpfo/y2arAHXX3yVg8oSP8ft2Kyf2mIrO0UyctYZmHrIaPY2KabR0cY3G0GwOpaA1tfs63ZQON7DV4Y9+vqEGnn1y7UoK8P/6Gcy1vcs7IX+puw/Bsx/r0mWk/5jw9FdtlPsbKv6m/G4/+DzShUr8FVcM26KPfd6FzF7RuWB1/0aSTiMTOJptfmsao3wDyOn6/VM94w0d90JK1eHHMChy5XB2hvcZgZpp+lgw51KYvx7YfVVDXpo0E1f2wYPFzSPT7FZsmj8aMzDxdDKRXKybipaxgjJw4UMFgdT05gubi4y0fY85z4zBfSb1wlL45LA+mnLW/y5e5jbqktCzQBZNmD6Oy+B1bZ7+M5aUVU3KCTsPSQ9KMJOmL8i/yX/pLN567jEvSnh5KN3wszXYjPDFzAp6IBr5e+QrSM/SOBq1jdcR7p1Etuh9emTlApw80q8ZWG0PfK1/53yh09v8LR5dOQFqpQ0qbxsh1Lug7oq+DBxzB6L7gNUxIrIdfN81Cvxlbyvhlv4WnXzqChiNHI81sQxSMbq8OQkfabr9o/0I8PWa9PH959XHMXUfVFUvSqFPw6rPt4EtN8/454zBmu9YWeNEU4leeaAynr1dhdPr7ZXtTZK/C8BGrcbwabZD8ykulDbm4uB0zRrxlsIcF6e+yL5HrHo2k7jRfwWJ9+BBfFKpRL0y/gvJetI2lWW43L+LERml+BTk+d2ajWlRTg46KpUw54FnBbsx92iA/tCHsiPEfI1vchc5jJ2OiaduttB52TkCstzNuXjiJjVJdLzmAncedENVa6oLV1W6iKc0yy6f1wKWd2iNY9MZ+/CwtL7x2BX/kleCKswd8zDVYFcx+6eZyv19FPRs2fCxN1msAZr7SD9FOx7Fy9GRklNo06jwOn4b3jjsj+okJmPmE6UbMFRT8jnvdxjankvJfYX0wJ5es7bG1PaI9vTa/gRErDD5ylHyGZV/8CPfGHdC9lT9KNszAmMWHcZk+1PWa/BLS9LNZKdz0lV+ikPraZQOgituegI73opE0czX/B1raqruozRnx9le4LK1T/fsyftHXCZvsYhlIRWUi8rB5xstYYTBQK8n8HF/kVkfjpC5mluZKaci0fbejLZLVE0fWAVt1iwRKGIHZY2mMUriLZp0vKmvfpCUHw1bikLTvk6BZoNn6PjT1j155FS92vgvXji7H0LRlxm3nyC1Q9R2Cp2+Ld1WmHEnTpc1SKzomki0qmZvq7kloG+Bm0J5J/dpUDH7vHO2J50TbdHnDY/tG7PglAl0H6MYr6+kD0PQ1NMNoPp4btkh+BolXR6rbfriVdwbbNe3kMXyQRtse7L+GqCemYvEL7WSkMXcrH9vnTsesD9bh07dmYsZSKx9MDU64MP/nhVdEh1rS+fOapYOy/4yPV/lGLOoRTOeoOwt13Eg6dM6e62M6lrGmNi06Wqa2n5/wM/xX201znKVeHpe4dDpwQ7qkM0afEi393YXKzV80ad9JdIiLFKGxfcS8dVNEkr+bcFHXFYHNh4g1+tNBireJeQMSRKBnLeEX1UzExUaIwNDWYkh6F80Z3do09Mc32hI/Hf0TFyj8SmV1Eeq6fiI4eZr4KK2F8PerLdykc2PpWDIXdR3hF5wsZn6YJuL8fUVtNydtui5qUde/hUhbrz/u7ILInD9YdIjyFWrPu0TUPVEipH6YiE95VexSemSWhpOZYxbPLRFDWjYgudyFX5P7RFKHOBERGidS5r0nZiQFCBdJnsAEkbZmmXHeNGUUKOLS6EC59UNErJqOYNGxU9E535r7tlwXZ9FxN7VE7PBNBm8Vii+GNxXVvZPEPEVHuEg6pBbucaN15+waCqA/x5j4q2qLkHviRFyc9K+JiLjLS1suJuf5FmfOFakdokRddW0REBUrokICRGh8HzFjl8lRdObYkhTzkgOpXkhpKj3r1hH6NoNOXNdeyvMgV1gm+mytzAeNUahLp0RWenM6+tGWsnhNDGgZJDzV/iKKyi02IliEJjwu0h+8q8w+mWO8bYiIcq0l4tI3y2VS2b3izWJGSgsR4uMj/COaUPoNRF2fUPP10CYboxPh3DIxPFGvb00pjUDSu05i+Iqj2gDrzdmKlbbbnVIF2SbmpyaKqLqewjMgStwTFSLqh7YQKTM2a4/2MklT5VZb+Gns07difVozoXaRzmGWbJqTcPOKN7Bbclgv0Dtm7OBHMnnzixDJMxeayZuk47bUFTl59PdM5aK81PYV/nFpYj0dmJkW66Wtwxp9dRNemvvSdUHsmtFHxIfUI5sdLmJjw4V/3XoixMhGSEdYhgnPqCTxSIcYERgSpbE7seH1hU8gtTnLpbI1sE0udUWExi7pbJOfWpu26VnjOrvt7u4noppEkF0apDtf21I+pWdybVSAcntdevRlWzGga7TwD2hEskaJAE9PUTfqAZG+5hvzAiiqh/oyJTvuFyma0HFy8YPeNjjLns5fH5Ig/N1chJtfE9E+qZ2IiyD2KTPFuhldhL8LnTVeN1g0T3tHfOpQXTPM1kWxjY4ydjU8qtN8rs0+Kd71qkiJDxU+dRuIiFhqh/x9hE+IQd0z+6b+ganeGvQrbK5P08SHMrw0dUDO7lism46Ny2zfSbJhivsvR83bHrk+mMX8lbWv2pKoiD6YlqFC26OoPaIjLAN9RNSDD1H/MViESH1d6u+E+9UTgQlP6ezFZpEeV0vbJ60brrM7ZHvIlvnp+nRlfW2d3tlte8r0dtfUbiLCi2xGeBON/QgJbCK6jh8o4lz0/W+VqN7yBbFD309QahdL64yVMqEjLAM9o8SDj7QXUYGhmj5FXGxD4ecTIhKGLNHaG5vavjgxaNIgZeOQT21t6yzUJym/iuvAuVI6Fv9QpFuGMdAYZd5A0TKwtlD7Se0B2bLAcOL4tHjQz2BcYHT89FGxYnin0n6HNAYLCIgRicOXybJH6bjIjr6OSf222odZvVBhP1YZT2tHWBbvmiySQ+sIr5AYbb+25UAxb9enYkpSiPD0CRONAiNFxymflx21+u0skVy/uqbfVf6YU4NykfQiPoDaFIo3pI5Q+8eX9etkFcD8EZYXFz0kGlBfT6W+V6TvsjwYg2zcfPM/QMCMk+GOyrnUYIaJNlP33eZcWWNLZ3PHNxEpa3Jvs1ycnIZA1mgRV6+dmGp6jjPjYQJMwDYCpU6GHmKFbW/eQfVQcgq1EPXaTBLf2sqAw9+BBFgfql6hcplUvTL5b0pkzclgNxVqi+NDUuizgaMu804GW1JQuFyCfCR8MYF/GYGS9Wux0eyGj/9gZoqO4MQv3ohuFfwPCvFfTfo81i/dbvuGj/9VXJxvJlApBO6gekhTgZdutHXDx0qBypFWBQKsD1WhFIxl4DKpemXCEjmUQNGmU/jlrrstLOtxaHKKI2Mng2JU//aA2zA+oQ6cVHTOap+3aL+FX2mTPNpxQuWDhqV7afyb86jLn1MdJGiOG6JjLpdmQZXUR3bDR8fm1Ba2RTjw2gacjUhEb0UHCTtW0v9cbAfGIqGWC5xqtdIeDZj9KZbuVCFpcHcFe2j852hxhplA5RC4Y+oh2e/xrVDLifZ0ShhL24LRPinvZWCnqjUG27jhY+WA5lhvLwHWh9vLW0lqXCZKKHGYO4lAFt7eeBERD3ZCVRtWsJPhTtIzxXm5jsPz52DVoSvw70xHktq8+Z3ihG5jwFu4dv2mZgEfxA9YkDoSr2U3wYgXutG58rfzssKWjv98KeMaug7vL3NSyu2U87+S1k1cv6Hd0VicX4bUxxYju0UqXuge/F8BwPlkApVEgAbYe3JRIFWvkos4Wbohrlxyd1A9vHYDdKAFXTdxfsEIPPbaebQY8TS6396GRg4y3/snCLA+/BPULafJZWKZDz+9gwjQ5pBTJmFJ4f9h+DOtqly+nCfTVeWkYoEqgUAYEvvcg9p/XEbBmT34/Fx1NO07AcuXPYPGlZDa7Y+yITq3D8SNgl+Re+ggcj3b4/kls/G4fmfkShVIKVs6MeWTjTje5EnMSY0HnVvBV2UTCGiF9g1VKPg5F4f258EzcSSWLBqM8MpOl+NnAnc0gQwMje+BsevO42ZNNdTVLuH4x0vx5p4b6NWvNeiQWePrjqmHNRDQ+V40vHEJP+d+jf25tZD4/GtY9Hgz0xzz7/8EAdaHqlfMXCZVr0xYIj2Bou1v442sH3Hpx5PYd+RrnClwx73xIRUYD5zGpg/z0GTUOKRGlmt57QB/DGtnzcLcOW8jY99ZFFypibsfehwpTfWnWdkWpUrawMG2Vzg0E2ACTIAJMAEmwASYABNgAkyACTABJqCEQN6srmg77zD+MgzsFo9Rezfi+X96rcOGoYhPW4efDL0CqiA8tHgtFnWzTzh2MijRCg7DBJgAE2ACTIAJMAEmwASYABNgAkyACVglwHsyWEXEAZgAE2ACTIAJMAEmwASYABNgAkyACTABJQTYyaCEEodhAkyACTABJsAEmAATYAJMgAkwASbABKwSYCeDVUQcgAkwASbABJgAE2ACTIAJMAEmwASYABNQQoCdDEoocRgmwASYABNgAkyACTABJsAEmAATYAJMwCoBdjJYRcQBmAATYAJMgAkwASbABJgAE2ACTIAJMAElBNjJoIQSh2ECTIAJMAEmwASYABNgAkyACTABJsAErBJgJ4NVRByACTABJsAEmAATYAJMgAkwASbABJgAE1BCgJ0MSihxGCbABJgAE2ACTIAJMAEmwASYABNgAkzAKgF2MlhFxAGYABNgAkyACTABJsAEmAATYAJMgAkwASUE2MmghBKHYQJMgAkwASbABJgAE2ACTIAJMAEmwASsEmAng1VEHIAJMAEmwASYABNgAkyACTABJsAEmAATUEKAnQxKKHEYJsAEmAATYAJMgAkwASbABJgAE2ACTMAqAXYyWEXEAZgAE2ACTIAJMAEmwASYABNgAkyACTABJQT+H0MlsNN8+J7pAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementacja\n",
    "### Dla dowolnych liczb rzeczywistych\n",
    "##### Top - down"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Omówienie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Początek jest podobny jak wyżej, ale zapamiętujemy również koszt przyporządkowany danemu odcinkowi (jako trzecią wartość w tablicy, reprezentującej odcinek, postaci: $ [a, b, c] $, gdzie $ a $ - początek odcinka, $ b $ - koniec odcinka, $ c $ - koszt przyporządkowany odcinkowi). Następnie, zamiast tworzyć tablicę prawdy (zapisywać wartości $ True $ oraz $ False $ w tablicy $ F $), będziemy na każdej pozycji $ F[i][j] $ zapisywać minimalny koszt uzyskania odcinka $ [i, j] $ lub wartość $ \\infty $, jeżeli danego odcinka nie da się utworzyć. Zadanie proste, jak już zrobi się powyższe.\n",
    "\n",
    "###### UWAGA:\n",
    "Możemy sortować odcinki po trzech wartościach przy takim zapisie, bo jeżeli będzie kilka, które się pokrywają, to najpierw zostaną wzięte te, które mają najniższy koszt. Również można my je odfiltrować, zostawiając tylko ten najtańszy, co również uczynimy.\n",
    "<br><br>\n",
    "Konieczne jest również zmodyfikowanie algorytmu wyszukiwania binarnego, by nie porównywał całych tablic, reprezentujących przedziały, tylko ich współrzędne (nie koszty, bo i tak usuniemy te o większym koszcie - patrz wyżej)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Złożoność"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Obliczeniowa:\n",
    "$ O(n^2) $ <br>\n",
    "(względem liczby przedziałów równej $ n $ - dużo lepsza złożoność - prawdziwie wielomianowa)\n",
    "###### Pamięciowa:\n",
    "$ O(n^2) $ <br>\n",
    "(względem liczby przedziałów równej $ n $ - dużo lepsza złożoność - prawdziwie wielomianowa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def quick_sort(arr):\n",
    "    if len(arr) < 2: return arr\n",
    "    _quick_sort(arr, 0, len(arr) - 1)\n",
    "    \n",
    "\n",
    "def _quick_sort(arr, left_idx, right_idx):\n",
    "    while left_idx < right_idx:\n",
    "        pivot_position = _partition(arr, left_idx, right_idx)\n",
    "        \n",
    "        if pivot_position - left_idx < right_idx - pivot_position:\n",
    "            _quick_sort(arr, left_idx, pivot_position)\n",
    "            left_idx = pivot_position + 1\n",
    "        else:\n",
    "            _quick_sort(arr, pivot_position + 1, right_idx)\n",
    "            right_idx = pivot_position\n",
    "        \n",
    "        \n",
    "def _partition(arr, left_idx, right_idx):\n",
    "    pivot = arr[left_idx]\n",
    "    i = left_idx - 1\n",
    "    j = right_idx + 1\n",
    "    while True:\n",
    "        i += 1\n",
    "        while arr[i] < pivot: i += 1\n",
    "            \n",
    "        j -= 1\n",
    "        while arr[j] > pivot: j -= 1\n",
    "        \n",
    "        if i < j:\n",
    "            _swap(arr, i, j)\n",
    "        else:\n",
    "            return j\n",
    "\n",
    "    \n",
    "def _swap(arr, i, j):\n",
    "    arr[i], arr[j] = arr[j], arr[i]\n",
    "    \n",
    "    \n",
    "def remove_duplicates(A: 'array of sorted numbers'):\n",
    "    if not A: return []\n",
    "    res = [A[0]]\n",
    "    for i in range(1, len(A)):\n",
    "        if A[i] != A[i - 1]:\n",
    "            res.append(A[i])\n",
    "    return res\n",
    "\n",
    "\n",
    "def remove_redundant_spans(A: 'array of spans sorted by first, second coordinate and cost'):\n",
    "    if not A: return []\n",
    "    res = [A[0]]\n",
    "    for i in range(1, len(A)):\n",
    "        # If have the same coordinates (both coordinates), the first one has lower\n",
    "        # cost than the next one, so remove all the spans with the same coordinates and\n",
    "        # greater costs than the first one\n",
    "        if A[i - 1][0] == A[i][0] and A[i - 1][1] == A[i][1]:\n",
    "            continue\n",
    "        res.append(A[i])\n",
    "    return res\n",
    "\n",
    "    \n",
    "def binary_search_first(arr: 'sorted sequence', el: 'searched element', fn=lambda x: x) -> int:\n",
    "    left_idx = 0\n",
    "    right_idx = len(arr)-1\n",
    "    \n",
    "    while left_idx <= right_idx:\n",
    "        mid_idx = (left_idx + right_idx) // 2\n",
    "        if el > fn(arr[mid_idx]):\n",
    "            left_idx = mid_idx + 1\n",
    "        else:\n",
    "            right_idx = mid_idx - 1\n",
    "            \n",
    "    return left_idx if left_idx < len(arr) and fn(arr[left_idx]) == el else -1\n",
    "\n",
    "    \n",
    "def map_spans(A: 'array of spans', C: 'array of sorted coordinates'):\n",
    "    res = []\n",
    "    for span in A:\n",
    "        a = binary_search_first(C, span[0])\n",
    "        b = binary_search_first(C, span[1])\n",
    "        c = span[2]  # Cost will be unchanged\n",
    "        res.append([a, b, c])\n",
    "    return res\n",
    "    \n",
    "\n",
    "def prepare_intervals(A: 'array of intervals', target: 'target interval'):\n",
    "    \"\"\"\n",
    "    This function filters intervals which cannot be a part of the resulting\n",
    "    interval and maps coordinates of each valid interval to a proper natural number.\n",
    "    \"\"\"\n",
    "    # Filter intervals which don't need to be checked (and unpack all valid coordinates)\n",
    "    C = [target[0], target[1]]\n",
    "    A_cp = []\n",
    "    for span in A:\n",
    "        if span[0] >= target[0] and span[1] <= target[1]:\n",
    "            C.append(span[0])\n",
    "            C.append(span[1])\n",
    "            A_cp.append(span)\n",
    "    A = A_cp\n",
    "    # Sort an array of coordinates\n",
    "    quick_sort(C)\n",
    "    # Remove duplicates\n",
    "    C = remove_duplicates(C)\n",
    "    # Map all coordinates of all the intervals to natural numbers using a Binary Search\n",
    "    # (we will look for an index of a coordinate in a C array and replace this coordinate\n",
    "    # with an index found)\n",
    "    target = [binary_search_first(C, target[0]), binary_search_first(C, target[1])]\n",
    "    A = map_spans(A, C)\n",
    "    \n",
    "    return A, target\n",
    "    \n",
    "    \n",
    "def min_cost_merge(A: 'array of intervals', target: 'target interval'):\n",
    "    A, target = prepare_intervals(A, target)\n",
    "    n = target[1] + 1  # All indices will be from range 0, 1, ..., target[1] - 1, target[1]\n",
    "    INF = float('inf')\n",
    "    F = [[None] * n for _ in range(n)]\n",
    "    \n",
    "    # Sort an array of spans in order to use Binary Search for checking if\n",
    "    # a span is included in A\n",
    "    quick_sort(A)\n",
    "    # Remove redundant spans (these which have the same coordinates as some other but greater\n",
    "    # cost than they have)\n",
    "    A = remove_redundant_spans(A)\n",
    "    fn = lambda span: [span[0], span[1]]\n",
    "    \n",
    "#     print(A, target)\n",
    "    \n",
    "    def recur(i, j):\n",
    "        if F[i][j] is None:\n",
    "            idx = binary_search_first(A, [i, j], fn)\n",
    "            if idx >= 0:\n",
    "                F[i][j] = A[idx][2]\n",
    "            else:\n",
    "                # Set infinity as a placeholder value (by default we can't find intervals such\n",
    "                # that can be merged to the [i, j] interval nad then we search for a possible\n",
    "                # solution).\n",
    "                F[i][j] = INF\n",
    "                \n",
    "            for k in range(i + 1, j):\n",
    "                F[i][j] = min(F[i][j], recur(i, k) + recur(k, j))\n",
    "                \n",
    "#             print('min for', [i, j], F[i][j])\n",
    "                \n",
    "        return F[i][j]\n",
    "\n",
    "    recur(target[0], target[1])\n",
    "#     print(*F, sep='\\n')\n",
    "        \n",
    "    return F[0][target[1]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Kilka testów"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.3\n",
      "13.5\n"
     ]
    }
   ],
   "source": [
    "A = [[7.1, 9.2, 1.3], \n",
    "     [9.2, 11, 0], \n",
    "     [5.2, 11, 7.3], \n",
    "     [-5.2, 5.2, 6.2], \n",
    "     [5.2, 7.1, 9], \n",
    "     [1.5, 5.2, 3], \n",
    "     [9.2, 11, 20]\n",
    "]\n",
    "\n",
    "print(min_cost_merge(A, [1.5, 11]))\n",
    "print(min_cost_merge(A, [-5.2, 11]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. podpunkt"
   ]
  },
  {
   "attachments": {
    "image-3.png": {
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BX5buWTjFiHR9RxcKW8uRuDmRLBrKUPGCJOGlcBdBieliraG8icOCTu0WDibpLYiZyS3dc66icWCojLFgezs0BeaJ7eltBX0VaCL/ZYxnas/SwS2EUhoPRhy11dfpBrcA0X2ygf6RftbJBnxF72WGI80yI7nyWbj0MeHnSvK62FBnHxZLkpsKZ914k+rl3Egkztpbyrl4vUiPrS8UcBN+vTO1uoZ+/v4V0d7dgfRTpEjbbShkxeKb9Fjh6t5WpG/W6UlrPWmrPq4A9+IPxMhYT+HkFm6gS6ncETHUT47CPW6s0LS6rLFm0Ddl6mTTcWuDTrBkL4rfFkleLkIZlCjS135jDaLB79bGhaPwCI8UoZEDxVLdODz9uujk4SgU3klivlF3Sty8hJuRviQduH286KxSCo/YESJbp+9tkR+bdeAmssF1ST+THCYv0No33bh0Fo16z5Np8yRMMvrYaPxJ9t9DeCdOK9XhIk9sJp3grpB0b28xX6/PisX3kzsId9IVjuFpYrdRr22mfOoJ99jRYrOamQ32V6587H1exNRWkN4JFslLtRanOJvGsAfNGfxE7yUGdlg3D3JSilD9PILoZA8XUWQLFe7x4uW91gxIFbRBx8xSm6mXZc+hpJ7W2sLK2jNNlcqyA1rZVNQTUSM+0M4nST5GtiLbbCiv2obJ1kVGwmP+R3WNIZ38mM7FixeLZD8Xk/mdTv4dhVfS26VzaxovmwaHkd9wv5hkMO+SP1aEkGvrhF1kxBy3pTuFmYmivn6sk15ZOkhEN+ss0lcv1NgbOAvf5CWWHjW7V5w9QsR6KE18CZK5V7sKlZuXiB2pky3tozbOZfV+j9XxLkM/yraBVFdL47gs26YeG/LsTeV9DrMusOkG5KemQZH5uIiPiRExMeHC191deIbfLx6fvslggMjPTVZKHXQ4CLd63sLHx0f/TxUYIdp26iuGZW62XL7uWYVuQnNYLEsfKFLSl6ongMXrB4tQZwdRO+4lYeimqOt17CURV9tBOIcOFuv1jqDOgW4oEjNNJzLHxPykxjTBrEuO/qbSplkSmu+niE71yfGqHS/GHTNwWGnA706LFPSluQhP+0ibh65M88mBxjmBuYOkLVPhmyzWyoK8RCT7OgtHausmw+qI8+KLwZGisQ0OtBAfkFPsRkbacBIp5ROmdoyMnPrCTJHkQxPZj88a19JuzHTlkSJYliFSUjLEMvUEZ7t4tb2XUCi8RadpX5oQ+kZkJjY0caA1HBoaGgJy/tMipMWU2iJ44BLtpI3Gx7TOoj5Npsxlar1IC68t4EyOxubzMvvWgtK1xIak/9irNFlTT+JKHWghtLKjCBAUhk2WJJQmWiB6+ziZOH62l2PsQFM/rB0tOviFGC9YGdTMksMtp+K2jQXb26Gvg6UFpP3jRXvJ6ajfWUwzWGBRP1P4pkiUxrqpA02LdJOTmmqca6OFIl1JunFv6kBrJhDGixJ5Yv3AMBpbBhMVMkAjouqRPqotgpLnaR3es2JtcoBQOIaJwZtMnNovSBc21i7ySf/d0HABjBzMtBaCInQL5+D/iNVGc2md3nMVQQNXGOjhH8Tq5DDhn7zYsm620Kk262ObuZ8V6weHC2dTPaR1YJxg6EBTBS2ONani1nSy4bi1USeYlnl6pUjvECz8TBdmLfCzdMvauDB3pizpDB23eiJuXI5JMTSWxsWTg1BbhA5epenr9bRQTQ546QKqboGC5CcoWSwxWjSzhaVU9E7S3Q00Czl6B5pu22zztM0w5a1vnaXxJ9m2YKNF4OLsp0WEGzmqzqFi4GrNErY+C8m+eZMOdWhqbOMkh8M/TCSv1i2M2WB/Tetblnwcm0ALW5LeMXCg1ZikBU1ju6IZdwqzRRP1YpsT3ZflQFdBG3QgTdss3bdpDiU9YB97pu9bS3ZAfCFejtMuMhrK5uGRgkKxCkXgQLFen4GNukj/nKX/qK4x9INY1tvX7OWCUM8TLczvJDtCL7CMF+MkexFMcyZDW0Ftkj1W5No6e8mIJd6m96Q6hZBOkl7QrNA6z901L2bOz1Dbf4VbM/Ef3UKW6eOGfxevIh1D80Qz30BKlCPGxdUjXRMuBq8/q33K1rmszu+ROd4tjT11ybbKHD1imldZuosW9DR2Wqa9sYfPoaVZkf+zYQu3EmGjllP4ooM4ePA48g7OwAM3D+L9Fx9BRO+3cNLC22373aqNiCFZBnGgC3D+R/oGe9uHmDeqK8o9K7J2ENo8JJ3MTVvNZ76PNTMH0Ulu32Hloi+Qe8MNAdFtYXZud2RbRAe44UbuF1i08juTZrigdj3TEiPRq30z1KHzqY9sWIfN5TQ8f91mfF14C44BUegeaZiPB9rFNYUXruLMN4doM6fh5YVWiR1hfn6bIzxbdcSj5j9A3LgOs+g5FusVjPAAd4pzvQL9WsSic59UjJ6xjrZ5qZAw4BmM6tPG4lOWb7ZDcjuK/St+w/5Pt9GWVOnaQ9vsz8PF9TYu7N+q3z5flLUVB93jMODhAMtZGdytGDN3NGvThpjRaYJPzMCaNTPwhHSq6OaVWPXlBYjazXB/f9PAa0rUq+1iUp+b+NvFC83C/LVylos1wydi8fG/oIwahFnzntT2yzGs+/QICkUtCzIVibhmDYAb+fhmp/HmX1CPW+5bgRvXKS6y1UuJyIk7cfn2bdz4KQuDTGVB3ML1v823pVvN1ixBZcoRtKXpWfR+ej3cX1yLrRMfKH/MmpUt54bcsVCZdpjWowCbF3yIL4tuo3ZEe/QPM9ELHkrUdjGJw1e0BKmtn8byGw2hskH7mpZs+LfiHhXCDOQza9SrWHj0MlwjBmD2omHakys9ERHuhzq3T+H9fvchtnMfpI6egXXStteEZDw76hFNGMK/XdGgWRhCtU0pWjMezy0+hmvKVkib9ZpJmMBIDOjfDr6Kazi77X9Yp/s0pugTrN5TCw+kyu1nW/VxBbjjS3yUcwY3UA+R7dsZ6NIwDFr7EVbPeBOL3p+A+PJAG/0mZ9xWVCdQQbkLkdp7DFa7P4OtW6dUInRH2eMCni2Q+KiFj68MdUZRNhZ9cho3HJsgurvp8Tg0luhegONV5H6yBiul/lco4RNmID9Zr2LswsMocW2O1NnT8KTFk53lsJTgd8DEXRdxW/yFn9YONbOH8m2e7E42SHgbLg2CEBZaV3OvaCmGP7cSx6/VRVTaa5jXzyTck0cS+nf0heL2OWx7f5PWFgJFK9djj/I+pPbTBYGsoP0tTz4iJ2PX5Zs0B/gBaweZ9q+hXcnHto920TxIgTqRCehlYDs8Bi3G1tWzMH3RfLweb2pUTPlVQRtMizD4u2LzAdMM7WkHpLy74fUtH+Ldt1diq6FsakOxir9KDD7nsbcuksq/U2NIhW7JCQhxuGkwvyP9nPUVfnahudSFI/iUouOor6Jt+PRgLdw3oLOx/Zc9Vki9yLJ19BlRhebZmmra9r+675/vQf3iVegz7Vf0nv8eJtLYhyoDn/9xE7f/OomVZuPQvJSilWvwCZ0xZO4bSGnJX4huAscbp/HJomyNPrF5Lmuv8a6ru1yZM2lrebrLVnuDqvE5zHvH8p2KT+GaDsX01DZwF38iL3sGnpm+13IJd/oufePqZ3Y2z1HsPX6R9lY6oJZSaxCN6lkXSvquCeIiju+V9w2pqmFd1KY8bv90ArvOldXoM9h+5BzotHvcPv8FRum/o9J+TzU3D41j2qB9m3AY18oRzm6Woocr4OjsUklnpAOee3UEHgqqhctnD2H7x0sw54XHEOpcDy0mfQfvtrbEgSRlmtoVzV1u4cLeTVheQF+DrN+InVfbIbUzfZ9+4SDWL5e+rzuEheuOo2H3PmR2rF0VZXYPPP28zTI/t+sEfpJOnbMoF2bJ6YYves7fjp0ze9J/a47Vf3FNLm66xyJt5ovoqfeZvsWR3CuU5jrOf/FK6bej6j5Oxtw8b8TExqNN84YmhZTVt5bqUs496XuqYT3pW3UV6tRpAN9mz+CjM/KWUMrJ1fwnm8sR+Ou7THQZkYVTV37Ft1v2WPgGz7wY2+/YOBZsboelGp3BrhMFdAaDI4mTD0mKjMujDR55Mwvf/DcO7mXGuJeRjz6JuXyOff8Errm3wbOzxxvIJ00Yn3sR6Q+FwO3yWRza/jGWzHkBj4V6oE6Lqcj1vlfjaPech707Z2oO7sidg9QXP8KZmx6ISZuAN3oGmFVM2e8xPHjvPRAF+5ClHtslOPnOehzw6YTHu8o9WdJWfVwB7ucoTud5aUGqFuo2rGfSjig8mjEaj1p07syarL0hZ9xWUCf8dRQzumRg9amL+P3b3dgm+9teS3UtZ1xQ9Aw307Vg0yx2HcLxCzdp5uoKpcqCI0XfTdciORYXTmLvLvqmzFR+xq7FqWseiH12MmZakB9NcXJYllasZEcmhvWIRzP6rreORxM06/MhzthjjdC07UZ/J2P+3s2Y2VGS6UNYkDoFa85cg3vMIMx841ELNjgY/VK74V7nmyjYma22hdJi8jurT8DngYfRVZ93BeyvLPmQvnMcjh7xYXQeRh14+DZDn4/OmETQ+AkHcmkxmeZBtevWN4ltTwvPj45GxqNR5VLR/FhVbbBUdEXnA5byont2sQPavJUd8dSIRGDdFKT2oDNJghrDKzoTFMLW+LK7LpKyv4NjqFsfdG+uJB2gnd+VbMPKnTdpLngfufW/Yu/6TZDEv2DhRnzVsCNS1WcVGV5yx4pcW2dnGTGprdGf332Nb87R988oxKHsfbjeuD4KT/1g+Vvl8vKhU0J27T2JC/SOX1FLaTIWpQc9oFK6UsQhWqg4fgi76I7tc1l7jXddQ2yTOfVT1nSXrfaGSNnf5yi3o4x+tO5AF63CyIRQ+Ed0R8a60mONpFx0TiPEHzi251AFhEZ+Re2bsgQlf8mxuLfwV4nsk8FkVNEF9dSDgNRdcF98oH6bb/rvK2yZ8x+z1XUZmVc4ibLjK9h4Zheypo3AwB6d0DbcHx5OxTi7awFGPj4F+2zJOSER90kT6sJD2LhiBzauPYCb/9cXUwbQmyr8jn0bP6edBJvxxbf1cR+tXFq/7iJmJ+fjuSmfIe+WJ9o9PxUzu5LLVJSF8U9OoLdvSlp0caTmuCG4b6aFfqV+PrAJc5JtWZCwTkdKUZIzAV1Ce2DMyu9Rt+ebOFz8B/JP/Rd9g93kZSAzVcXKuY0/S/yQunIa+gY5IG/9DIyYbZNEyayd/GQVa4f8/MtPGYkHHkqwMOEu/ylZv+rlswHinp2AVyT5JFM7Z8xkzdth5QOYsPEwDmdNxbCBPdGpbQQCPJzw59kdeGfkMxi3r8igmH3IfG4WNubdgEe74Zg3sxfVORfrxj+D8UZ2oCMefzCcNvH+ht1Z62hvzx4szs5HaK+HbXibe6f0sSyqlUhUQZ3w53WoUv+L//YNgSJvI14Z8d8q3uFVThMvleAvmtRZvcQ1lFwy3DFjID9xqZjxiiQ/RTgw5yVMMJlHWM1bn4AOx5rcDaFd07HyRF30zNyJ4qKfcep/jyBYUr3VctECUeYkTNl4Drc82uH5eRPRlRYhitZNwJPjs/RvmtVV6fowHmzhTrbwa2T9dwewbz2yT/uiV2o7o5rabH+tyQcd6DW5SwK6jlmFE3V7IPNwAYryT+F/fYPJzaqay+5tKLOa9psP2NsOqA9/igtDi/50oOzFemjbcxTmbR8NOsfnLrqqYgwlIPm+ELgIzfwuf+Mn2HWzJR6bkoKOvo4o3Pc5VhQcwoovfkTj+xI1O51MicgcK/rHyrV19pMR02qa/l3w2dc4cZWOAQlPw87tr6C9+BqLh/eowK7c67hUck068MnqZbybwWryuyuBNd1VEXtjd59DPjKrDnTR+yuwal8u8k5swXu0XVG9kGp2OcCNTva0tpht9tgduxGLuHDpLcRNFBdesFCLCygslpYN6yE8LtbC7+a38vMuophuO/iHo0OA+e+aO77okBAGL/Kgb50/g92WfPPcjzB3YU41LkZrdu1NAAAVLUlEQVTQSZX+IeizrDYefeFtvL9hG746fg6F387DwNBauLJ/AxZtttzroLOIl/eh08szdhg0OAEpXe+lt/GFOLhxAT742gkdUjrBo0c3xPs64crBTXj7rY046n8/naZq4Y2GGTr7MgvoEA5/SeqvXsZvZTXLrA7SjRxMfnomPj1/C97dnsd7EztqUhUexOcb9uLs31FIiPCkxZG/cf7MSQv9R2+v1y3AwjJPd7dYqPWbRe9iyKA3sa3ADa3S5uLzmf+xEGz+RiUnrlSNCpdDW0jj+mJir1GY/1pvBDvR9q6pEzHtgKGzZr2ZdktR4XZYqgGdvh+uovc3t0mcCsvQjZaeq4p7OzDtmVla+UzHktcf0ujjMxuxYuEmHL0snabaDI37rITq0Rcx7/1sbPvqO5wt3IslA8PheuUIPly0VVsxcnQmv4TJn+bhlndXTHjvBbRW//IL9n++CfvOSjstdJcH4lMfRAy9Tr96eBMWrvwfNv0ajv7PGjsJBg9Y+E9b9XEFuAdEI9zflcq+jLzvfrRQB3pjR1vodljSyRZSy7tVQZ3g2RoDJ/4Hg+e/hJRgF/y+ORPPTNshr0h7p+rWGuHupDBv/4nCMxYU5plCFEs7etybIq6bblsyyc+0iXhDJz9LJmq3oB/FBytWYOvR3ypUy6Jl6Rg0ZSsKXOhzAuqrmcmW3o4aLBhVqBQrDx2Yjqcnb8L5W/TmY8JUTGytsWGF+zdjw74fTT6bop1XvaLgTjJ3+JN1WPn+dvza+mE8a/SpRwXsb7nycRLLhozAlG2/wKXVU1j5+UwkW9pZcWAuxkw4h/9T669bKMr7AZb22pXsoK35Vm2WvdtQXh/YaT5gVztA9T3wGh7pPw4rDrnggblbcGbfRizOHItH6XSp0uso1s1dih2ed0IXaWpRNWPIAwkpndGcPt+9cnAjJn5wFE4dktDD4z70im8MxZWj+OTtRfj4qDe6ppT10kTOWNGRtGbr7CQj5Ymh+rdcfPHVDzTvp5cmcZ3Q4f4xWLRhFO73/Bt5mz7EynNSmk8x/tFheNeC6jTOPhjd6BNOOngQt4sLTaJ8SCl1IXspbHB4a/XOTdvnsjq7Wdnxblxzm/4qV3dRThWyN/b2OeS3yKoD7RHgjbrSK1OnxojvFm+wtaAIew+fJTeJLgUdX5+o+3pMCi0yHv17Pophc8o4dl1+/aooZQyeGtAejejbvZ+Pfm3+hnXvbhw6dw2KRu0x4KkYkzpcx1VaJTG+9mL1jlO4qqiPNo8kl7st2WNAPyQ1rQ3x6yFsWGf65fg5rJ9CE48N39K3etV1Xcf16wX4esNW49Vz2qL/Ss9mcgKFm1SUJtRPdEELSZnu+wifubTRfOdMb78GdwmCw5UDWLD4LJp2T5L9hsquzLo9ip4t6wLFp7A7W/ttjr4FBci7SHGuza58bMl4CW/tuQhHvx54de4z+rBtJVtPIs+lLhqq6HvQIYlo6nwLv369ufR7UF1eJesx5aU3seHkZbPcK3Vjcw725tNWbacQdEzrbpCVbhFIuvUnTuzcgE37f6l4UXYox6Pfa5iV2hyuF3Iw4/lZFNjiDlx2aEdprWkSPeQhtCRZL/5uL7JN1wROFuDiVXWUehsvV7ibfYsvZUETkWM/07Kf6SXJ54uYmvObuXzuz8eFuio0DbiFv6//hQIz2WyJQa88iAiDtyQlWyZj+Ft7UOQYiIdffQ1jdBP+kmM4mSfMt0CHPYL+HVRQXD+OVWPWo6TdwxggZ21M3wxb9XFFuHfBkEda0rb5Ynyf84UFnT8To8csxn5pFdRuVyV1gseTmDdrACJcf0POjEmYfCcWnVS9MaBzE/qWtwBHt5i6WDQH+PQwzt12RqPOj+Ap7c5MtfxMzcEFM/n5EfkX3KBqarqFUw7wc9j8+X7k36Szse69D2mG3+XqnHh1Nt9j50ebsF89MbFyudAZBa4WvqMoOoRjZ6VtmSZXSTYyhs/DniJn+D08FnPH6OY8J7H15K9wsbANOuzZPujg7Yjrx1ZhzLo/0a5/ksnuskrYX4vysQ+f780jHXEP7u1oaGN1E3Btm07k4KNNRxE6pCfa0ALJte93YqXRDhQp3acYN3oclu7/3ZSEyd/2bkP5xdllPmBXOyCdybAKWwquwTE0Ec+lGcwZCwx3cHxFZ/C8h09/uxO6SGJaBWNI11XxSejeguZVV/Zj5WcO2u+caWv24I5o6lCIAwvW4nTTTniizO/p6Ywlq2NFKkyOraMNz9Uyz/4Gu4//Lp2Uhoj20RoSRYW4LNn8e+rCi3BgM50Nsudn0CmcVi/VU4+gcyNn3P75GLaYjcXD+PTQz7itaILOA3pr/DCb57KS3bTHeLfaFOsJLOoueqwC9kba3l4pnyN3Ncb3740+wzJtXkC36kCj1zCMfIhikgVFISagdFZUkjMLE9d9j+uKuoh4cjymP6k7rGIzZk3OxJqNdKDC5LewyOrKi3XW9IUVbl637/ecHrTt9vUnm8PhyEo8n76q9LvM3JUYOWo1vnVpjidfp21ZJhNBxT3XcHjeJMzWr8pKW2ImYc6uK/DpNgZvv27lq15lf8xZ8Bw6+/yOTyY9j2k5ulhkUuy4iZiwNwCjJz5erVu41d/tbnoHowxjPpZ8iiVf/ozazTuhV4J2wkMLKFH1HXEr7ztslL7LK9mHbd86ILyd7s2Dti8jH8SDMbT0essVIZ0e0i4o6A6b+BuXrgeic4q8N/vqHO3KrDtemTmC+P+BL2a+hqX67wulfpyCRQekyL3SzoTf9G+RSzZMQ8aCg7hCTmrfSROQplvRJ0ZTl3+FwvoNIRFQ9pqEBeO7wOf3LzCp/2Rt3GepAUewbPhs7A0ZhIlpkVpIdvq/iFAE1KGNebcu4Mwu3YIMydL81dj9K8VipL69eqkQl646oS7F5K7wZZdyAtDzjcHo4q1A0Z55GJ6RbeFNfYVrKO9Bu7TDoKj4UZj5AvV54XbMHDa/VI9I2yhHLMeBP2lTFp0TUZirG+faZ69cB/kC1G838Lfpehwtz3RpG0y7OIpRoH9O0g9v4b0v/6A+Fbh2+Q99WeXK59xt+NmVDsfTFivOb8G0Ue8afIdOcr/kK5ytHYHEXvSeuWQdXs5YhkNXXBHUNwPT9ZNBSjf1A3xZqETDYKPXKpSz7jCxG/jjckMbDg8r5WizPraZOxnZ19/Ay92a4PrhpRiWtsRY54/+HIp+QzG8Ir5dOZJXWZ2g7DkCz3ZpRDtA9uCt4ZOxxUxWyincLj+F4cnp4/FkBGmx5a8jXR9XXrNQPmrFCbhE9Mfr0wdqbFa58rMUm39WQFnP9KBGORXVHoIn7d4qoG/g9YtVhzD/nT34Vfp85vpVXMovwVXHOvCSDiSxdvm2RdsweudDZzPkfqcDS7p61DJ8eUVa+LqGy7/pnMdz2PDyFCw4VASnoF6YND1Vv9OnJGcJln9ZiPoNKcij6aU/IOkKLkvff+oPDzNMKNP+muZNf5vLh+ZALwXVveDM96WL4rlr8c7u3+l7dUGYSpB/iZw9cvhrx7+It1/uCtX1I1g0bCyW6+3hUWSNfB3rFQ9g1HDTlwgWKiJ3DmHhUfM2WEhkeMse8wG72gE3ivdch95Dkqr/+09c1I/RI1j6zm787Gwgm5TK3eXO6CKgCsaQvl9iMeDBFvQG9TZFim2PFN13zt26o12IK/6maVVo527mB/Ya9quMsSLb1tlDRqyIIY7ux9GfrtF5OiGIS9R+mudEMQlcHeDg2Rj3epBumrsXDg/2k7eg7DEQ01/vjwiHb7H8+UkGce2lsTgFK751NPG1bJ/Lwm7j3Roc679bHvc22htdMRX2OQqwZdZUzFizHh+/Ox3TFh2xXnHDFPKO7qYQUCMfEC18lNpwUg2E0slZKP1ai94vryqNC6rO7Bsxn+K5SmFBlDGjKWiQ7Vfe9CQRQCGrPJUUBkLynqV/FLfM00clApKmUTS58i4KMRTjJ3zqudHR8tKz2hBYAUliutmDFF9tWoqIDWwoPFVNRVRUU6HypJjLsSlimj5Ona6s/WJ6UpSIH7lSbJ7WV0Q28hPhFNIrKpBYeIaLziOXGHAwrYMTpfExqntxziyR2imc2lhP+IZHifBAXxGkLzePQse0FSqfesJNmi1LMX6VDYSP1IYP00SMylvUc6P4q3ouoSJp+jyTdpuXaZkahaDw8xLhDz0sOoUHiMDwlhSmrIVo6tNQ+MU/XRojVP2wFOPuaRFHsT9r+zQTLUJDRezg90z6X1PK+dkUG881Woz80jDuzSdiZFRdUT9xBgU/ML0sMfMVMWmlwbhsY0YLg271KOyZxGa/aWGiOOdNMTDOX7grVZp+DA0QQfGDRPpDTUplTiGFgPpYG3uU+sCzKbGRwrjRP5IVH618GsfFphjlmUOIpbdQujcR4a3CRWCjYBGb/IY23rW9+lbHRtcntam9KtGiY1fRKaaZCIpKEbPXv6qJd630FH6th4q11sJ56ilZDvuh6XsZ5XxsLKPqflBJMbm/J7luSbqDZnG6sekRK9LeGmIu0+r0ZgPWuB+zKzIWKsHLYvgSqUrU57MfF3F+9YTSJ0w9fkL9mor4ocPFQ1I4MK0O04SWk+Tc10C3Sfqpoblek0Jd9QgTHkpv0TSK5C08SPhF9BLjBkeTbtXqRAqbFzduiVY+Sd7rBYpWevkMFU20OlAjn1IYq2DhHp4oHusUKfwCw9VyHNW0kfDyayeGqmPM62JkS/rWU4Tq8pLaQ7pfXa5pSC59j3xEodpIL8Q8r42lbDbkZNywRR/byl1XvGTLuopwT3fh7ksMokKFr2+kgf4uSw8tr4BO1ukdazrBpEyFm6jn46fRfdlDKR6vgQxRLFBDnWgRqs3jYor4sCx7oxuCxZvEtOS2ItDLS6hCW4io0MbC0yvIQK9JNTGQH4qHG9hKqysl+WniobFlavmpiA6UWFJs9aHxFA/VSbj5tBAdE+8XMaFkt5Oni/XTuguVNCfxDBCt01bIjgddvH2S6BEq2fBgERXTkuxwgIjoMUIMjpHCFGrHmWucGLdVG1uZwtV4hkbr7UBUqI9WnykphGWOxe4Qm4eKcGeTEJf6lHLsr43yMThDDI1rTLxrC58W94nETjEiNChGJM9eIaYl+gonaS7lFy/S1upCb0mhHkeIzjqbJfWXr78I7zxCG/rRcrNK71ZBG9JesTqfKX8+YFjnStozU7tpyQ6ox0esWjaVvi1FJ7VsBpMsPS9eeciX5qLSfMxUNq3povK4V/cYKiuMlUEd1WGb6oqokZ8Y3CwUX46MFq71E8Vs80mfeQPLHSu6OPDWbF1ptpWTEfPqGd3JplBdTm4U6vVtg/msFLO5u/Bz9xahLUJEUJvhNsy7NLkXb39DJMcGCS/PxiI0isaiykt4BbYVydMshwyWP5c9q62+tfFuTxto4pfItW2y7I1x/9juc2iePz//YdFYCtmnbCPSt8sR0tJybYgDbUWY+GcmwAT+IQQsTTj+IU2rTDMsTZwqk98/6llpchMs2k/e/Y9qFTeGCVSawF5yvhveLyabxomvdMacgTwCdrZn1uzA6Q/F2+9tp9cNeWJzelvRIKiXmJVjZTFYXkPuYCoZDrQ9anfHxoqdZcQeLDiPu57AXXU+oG3vzjk1E2ACTIAJ3A0ESrLXYSMdHjbapsPD7oaacx2YQFUSOIfsRVvo8LDBJoeHVWWZnPcdJdC0L0bQjt6S7FQ8O/cCuiyl79/vlxXk8I5W+84XzmPlzvcB18AWAta/gbYlN07LBJhAzSOw7wXE13WCwjkEKcvoO+r8X3Gx+BYdoheCVqZhq2te6ypY4yLsG5eAug4OcPZPxjL65lJz0r4LGoXci38tFjXNzRgX3wAODg0QP24z/U0hShbthSIxRd63XhXsEX6MCdz1BLS61KFugiYsXO7HWLRNgcQhvar5XJO7nlTVVdCu9qyidiAf2z7ahdybddAwTGctdmDGUxlYbnrYZNWRqETOWh2vqAX/lHfpW/rf6YDVP+lrQi+EtLLTYsCdHCt2lZFKYOZHazQBdqBrdPdx5ZmAnQmIE8gcswYHrjVBt+Fp6FdzYtPZGYRxduLgDIqzfQTXVJ0w/PneNShkX1VguY3rN26pPxCF+AlzUkfjzdwWGPViz385l6pgzXnWLAK3cOOm5uR9cW4JUp9YgNy2qXixV0DNasY/pbZ2tmfy7YASXh5KON86iXWj0rEg51NkpozG28cdEGpThIK7oSNu4GDmW1h54CpU3QbjeYsH4VWknnfJWLGzjFSEBD9TMwk4TqKrZlada80EmIBdCPh2RUq8Oy5d+h0nt27Haedo9Js8F0uGxtkl+5qZSS340qmh8fWu49KFU9j62Q9wjk7B5KVzMLS5FJ/i33yFoFtHP9y88DvOHtiPs+4dMXbhTAyyFG/234yJ2/7vI+CbgI4hClz49SwO7MmHe+fRWDh/iP7E7n8fkDvQYrvas4raAXquvT/E4V3YkrMN2cvX4esbsRgxexL+E1gT7EcwRUpphXqXruDCyZ347LQrovuNx9Ilz6C5vbr0To4Vu8qIvYBwPjWNgEL6SrumVZrrywSYABNgAkyACTABJsAEmAATYAJMoLoJ8Bbu6ibO5TEBJsAEmAATYAJMgAkwASbABJhAjSTADnSN7DauNBNgAkyACTABJsAEmAATYAJMgAlUNwF2oKubOJfHBJgAE2ACTIAJMAEmwASYABNgAjWSADvQNbLbuNJMgAkwASbABJgAE2ACTIAJMAEmUN0E2IGubuJcHhNgAkyACTABJsAEmAATYAJMgAnUSALsQNfIbuNKMwEmwASYABNgAkyACTABJsAEmEB1E2AHurqJc3lMgAkwASbABJgAE2ACTIAJMAEmUCMJsANdI7uNK80EmAATYAJMgAkwASbABJgAE2AC1U2AHejqJs7lMQEmwASYABNgAkyACTABJsAEmECNJMAOdI3sNq40E2ACTIAJMAEmwASYABNgAkyACVQ3AXagq5s4l8cEmAATYAJMgAkwASbABJgAE2ACNZIAO9A1stu40kyACTABJsAEmAATYAJMgAkwASZQ3QTYga5u4lweE2ACTIAJMAEmwASYABNgAkyACdRIAuxA18hu40ozASbABJgAE2ACTIAJMAEmwASYQHUTYAe6uolzeUyACTABJsAEmAATYAJMgAkwASZQIwmwA10ju40rzQSYABNgAkyACTABJsAEmAATYALVTeD/Ab4ueAnbUx+hAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image-3.png](attachment:image-3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementacja\n",
    "### Dla dowolnych liczb rzeczywistych\n",
    "##### Top - down"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Omówienie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analogicznie jak wyżej, ale tym razem jako koszt (czy tak jakkolwiek nazwany 3. parametr) traktujemy długość odcinka (początkową - przed zmapowaniem) i chcemy ją zmaksymalizować, a nie zminimalizować, jak miało to miejsce wyżej."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Złożoność"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Obliczeniowa:\n",
    "$ O(n^2) $ <br>\n",
    "(względem liczby przedziałów równej $ n $ - dużo lepsza złożoność - prawdziwie wielomianowa)\n",
    "###### Pamięciowa:\n",
    "$ O(n^2) $ <br>\n",
    "(względem liczby przedziałów równej $ n $ - dużo lepsza złożoność - prawdziwie wielomianowa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def quick_sort(arr):\n",
    "    if len(arr) < 2: return arr\n",
    "    _quick_sort(arr, 0, len(arr) - 1)\n",
    "    \n",
    "\n",
    "def _quick_sort(arr, left_idx, right_idx):\n",
    "    while left_idx < right_idx:\n",
    "        pivot_position = _partition(arr, left_idx, right_idx)\n",
    "        \n",
    "        if pivot_position - left_idx < right_idx - pivot_position:\n",
    "            _quick_sort(arr, left_idx, pivot_position)\n",
    "            left_idx = pivot_position + 1\n",
    "        else:\n",
    "            _quick_sort(arr, pivot_position + 1, right_idx)\n",
    "            right_idx = pivot_position\n",
    "        \n",
    "        \n",
    "def _partition(arr, left_idx, right_idx):\n",
    "    pivot = arr[left_idx]\n",
    "    i = left_idx - 1\n",
    "    j = right_idx + 1\n",
    "    while True:\n",
    "        i += 1\n",
    "        while arr[i] < pivot: i += 1\n",
    "            \n",
    "        j -= 1\n",
    "        while arr[j] > pivot: j -= 1\n",
    "        \n",
    "        if i < j:\n",
    "            _swap(arr, i, j)\n",
    "        else:\n",
    "            return j\n",
    "\n",
    "    \n",
    "def _swap(arr, i, j):\n",
    "    arr[i], arr[j] = arr[j], arr[i]\n",
    "    \n",
    "    \n",
    "def remove_duplicates(A: 'array of sorted numbers'):\n",
    "    if not A: return []\n",
    "    res = [A[0]]\n",
    "    for i in range(1, len(A)):\n",
    "        if A[i] != A[i - 1]:\n",
    "            res.append(A[i])\n",
    "    return res\n",
    "\n",
    "\n",
    "def remove_duplicated_spans(A: 'array of spans sorted by first, second coordinate and length'):\n",
    "    if not A: return []\n",
    "    res = [A[0]]\n",
    "    for i in range(1, len(A)):\n",
    "        # If have the same coordinates (both coordinates), both of them have the same length,\n",
    "        # so we will filter them out\n",
    "        if A[i - 1][0] == A[i][0] and A[i - 1][1] == A[i][1]:\n",
    "            continue\n",
    "        res.append(A[i])\n",
    "    return res\n",
    "\n",
    "    \n",
    "def binary_search_first(arr: 'sorted sequence', el: 'searched element', fn=lambda x: x) -> int:\n",
    "    left_idx = 0\n",
    "    right_idx = len(arr)-1\n",
    "    \n",
    "    while left_idx <= right_idx:\n",
    "        mid_idx = (left_idx + right_idx) // 2\n",
    "        if el > fn(arr[mid_idx]):\n",
    "            left_idx = mid_idx + 1\n",
    "        else:\n",
    "            right_idx = mid_idx - 1\n",
    "            \n",
    "    return left_idx if left_idx < len(arr) and fn(arr[left_idx]) == el else -1\n",
    "\n",
    "    \n",
    "def map_spans(A: 'array of spans', C: 'array of sorted coordinates'):\n",
    "    res = []\n",
    "    for span in A:\n",
    "        a = binary_search_first(C, span[0])\n",
    "        b = binary_search_first(C, span[1])\n",
    "        l = span[1] - span[0]  # Length will be unchanged\n",
    "        res.append([a, b, l])\n",
    "    return res\n",
    "    \n",
    "\n",
    "def prepare_intervals(A: 'array of intervals'):\n",
    "    \"\"\"\n",
    "    This function maps coordinates of intervals to the natural number coordinates and\n",
    "    removes duplicated intervals\n",
    "    \"\"\"\n",
    "    # Unpack all coordinates\n",
    "    C = []\n",
    "    for span in A:\n",
    "        C.append(span[0])\n",
    "        C.append(span[1])\n",
    "    # Sort an array of coordinates\n",
    "    quick_sort(C)\n",
    "    # Remove duplicates\n",
    "    C = remove_duplicates(C)\n",
    "    # Map all coordinates of all the intervals to natural numbers using a Binary Search\n",
    "    # (we will look for an index of a coordinate in a C array and replace this coordinate\n",
    "    # with an index found)\n",
    "    A = map_spans(A, C)\n",
    "    \n",
    "    return A\n",
    "    \n",
    "    \n",
    "def max_length_merge(A: 'array of intervals'):\n",
    "    A = prepare_intervals(A)\n",
    "    A = remove_duplicated_spans(A)\n",
    "    n = len(A)\n",
    "    # An array will have at most 2n x 2n elements (spans)\n",
    "    F = [[None] * (2 * n) for _ in range(2 * n)]\n",
    "    \n",
    "    # Sort an array of spans in order to use Binary Search for checking if\n",
    "    # a span is included in A\n",
    "    quick_sort(A)\n",
    "    fn = lambda span: [span[0], span[1]]\n",
    "    global_max = 0\n",
    "    \n",
    "    def recur(i, j):\n",
    "        if F[i][j] is None:\n",
    "            nonlocal global_max\n",
    "            idx = binary_search_first(A, [i, j], fn)\n",
    "            if idx >= 0:\n",
    "                F[i][j] = A[idx][2]\n",
    "            # This time we will look for a split only if there is no span found above\n",
    "            # (as finding spans which after merging will give the same span as above\n",
    "            # is pointless because it will have the same length)\n",
    "            else:\n",
    "                # Set 0 as a placeholder value (by default we can't find intervals such\n",
    "                # that can be merged to the [i, j] interval nad then we search for a possible\n",
    "                # solution).\n",
    "                F[i][j] = float('-inf')\n",
    "                \n",
    "                for k in range(i + 1, j):\n",
    "                    F[i][j] = max(F[i][j], recur(i, k) + recur(k, j))\n",
    "            \n",
    "            global_max = max(global_max, F[i][j])\n",
    "            \n",
    "        return F[i][j]\n",
    "\n",
    "    recur(0, 2 * n - 1)\n",
    "    print(*F, sep='\\n')\n",
    "        \n",
    "    return global_max"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Kilka testów"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[None, -inf, -inf, 7.9, -inf, -inf, 10.15, -inf, -inf, -inf, -inf, -inf, -inf, -inf]\n",
      "[None, None, -inf, -inf, -inf, -inf, -inf, 4.0, -inf, 5.8999999999999995, -inf, -inf, -inf, -inf]\n",
      "[None, None, None, -inf, 1.7000000000000002, -inf, -inf, -inf, 5.33, -inf, -inf, -inf, -inf, -inf]\n",
      "[None, None, None, None, -inf, -inf, 2.2500000000000004, -inf, -inf, -inf, -inf, -inf, -inf, -inf]\n",
      "[None, None, None, None, None, -inf, -inf, -inf, 3.63, -inf, -inf, -inf, -inf, -inf]\n",
      "[None, None, None, None, None, None, -inf, 1.1000000000000005, -inf, 3.0, -inf, -inf, -inf, -inf]\n",
      "[None, None, None, None, None, None, None, -inf, -inf, -inf, -inf, -inf, -inf, -inf]\n",
      "[None, None, None, None, None, None, None, None, -inf, 1.8999999999999995, -inf, -inf, -inf, -inf]\n",
      "[None, None, None, None, None, None, None, None, None, -inf, -inf, -inf, -inf, -inf]\n",
      "[None, None, None, None, None, None, None, None, None, None, -inf, -inf, -inf, -inf]\n",
      "[None, None, None, None, None, None, None, None, None, None, None, -inf, -inf, -inf]\n",
      "[None, None, None, None, None, None, None, None, None, None, None, None, -inf, -inf]\n",
      "[None, None, None, None, None, None, None, None, None, None, None, None, None, -inf]\n",
      "[None, None, None, None, None, None, None, None, None, None, None, None, None, None]\n",
      "10.15\n"
     ]
    }
   ],
   "source": [
    "A = [[4.1, 5.2], [2.15, 4.4], [1.5, 3.2], [3.2, 6.83], [5.2, 7.1], [1.2, 5.2], [-5.75, 2.15]]\n",
    "#                     ^                                                               ^\n",
    "\n",
    "print(max_length_merge(A))"
   ]
  }
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