Update chapter 14 sorting

Colab Codes/Colab Notebooks/suffix_array.ipynb

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-{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"suffix_array.ipynb","version":"0.3.2","provenance":[],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"metadata":{"id":"3s7lvSxaj9Fi","colab_type":"text"},"cell_type":"markdown","source":["## sort cyclic shifts of string s + '$' to construct the suffix array"]},{"metadata":{"id":"JjYArMUrkDIu","colab_type":"code","colab":{}},"cell_type":"code","source":["from collections import OrderedDict\n","\n","def getCharOrder(s):\n","  n = len(s)\n","  numChars = 256\n","  count = [0]*numChars # totally 256 chars, if you want, can print it out to see these chars\n","  \n","  order = [0]*(n)\n","  \n","  #count the occurrence of each char\n","  for c in s:\n","    count[ord(c)] += 1\n","    \n","  # prefix sum of each char\n","  for i in range(1, numChars):\n","    count[i] += count[i-1]\n","    \n","  # assign from count down to be stable\n","  for i in range(n-1,-1,-1):\n","    count[ord(s[i])] -=1\n","    order[count[ord(s[i])]] = i # put the index into the order instead the suffix string\n","    \n","  return order\n","    "],"execution_count":0,"outputs":[]},{"metadata":{"id":"CXthy2Rqt6nm","colab_type":"code","colab":{}},"cell_type":"code","source":["def getCharClass(order, cls):\n","  n = len(order)\n","  cls = [0]*n\n","  # if it all differs, then cls[i] = order[i]\n","  cls[order[0]] = 0 #the 6th will be 0\n","  for i in range(1, n):\n","    # use order[i] as index, so the last index\n","    if s[order[i]] != s[order[i-1]]:\n","      print('diff',s[order[i]],s[order[i-1]])\n","      cls[order[i]] = cls[order[i-1]] + 1\n","    else:\n","      cls[order[i]] = cls[order[i-1]]\n","  return cls\n","      "],"execution_count":0,"outputs":[]},{"metadata":{"id":"yfCeF3b77m4M","colab_type":"code","colab":{}},"cell_type":"code","source":["'''It is a counting sort using the first part as class'''\n","def sortDoubled(s, L, order, cls):\n","  n = len(s)\n","  count = [0] * n\n","  new_order = [0] * n\n","  # their key is the class\n","  for i in range(n):\n","    count[cls[i]] += 1\n","    \n","  # prefix sum\n","  for i in range(1, n):\n","    count[i] += count[i-1]\n","    \n","  # assign from count down to be stable\n","  # sort the first half\n","  for i in range(n-1, -1, -1):\n","    start = (order[i] - L + n) % n #get the start index of the first half, \n","    count[cls[start]] -= 1\n","    new_order[count[cls[start]]] = start\n","    \n","  return new_order"],"execution_count":0,"outputs":[]},{"metadata":{"id":"2I1nIvImB3O8","colab_type":"code","colab":{}},"cell_type":"code","source":["def updateClass(order, cls, L):\n","  n = len(order)\n","  new_cls = [0]*n\n","  # if it all differs, then cls[i] = order[i]\n","  new_cls[order[0]] = 0 #the 6th will be 0\n","  for i in range(1, n):\n","    cur_order, prev_order = order[i], order[i-1]\n","    # use order[i] as index, so the last index\n","    if cls[cur_order] != cls[prev_order] or cls[(cur_order+L) % n] != cls[(prev_order+L) % n]:\n","      new_cls[cur_order] = new_cls[prev_order] + 1\n","    else:\n","      new_cls[cur_order] = new_cls[prev_order]\n","  return new_cls"],"execution_count":0,"outputs":[]},{"metadata":{"id":"2Wv3muUHkNl_","colab_type":"code","colab":{}},"cell_type":"code","source":["\n","def cyclic_shifts_sort(s):\n","  s = s + '$'\n","  n = len(s)\n","  order = getCharOrder(s)\n","  cls = getCharClass(s, order)\n","  print(order, cls)\n","  L = 1\n","  while L < n:\n","    order = sortDoubled(s, 1, order, cls)\n","    cls = updateClass(order, cls, L)\n","    print(order, cls)\n","    L *= 2\n","  \n","  return order"],"execution_count":0,"outputs":[]},{"metadata":{"id":"OpqYr3Z6rsM_","colab_type":"code","outputId":"eb382cee-6f8d-459c-911f-10c955b45dad","executionInfo":{"status":"ok","timestamp":1549232253713,"user_tz":480,"elapsed":336,"user":{"displayName":"Li Yin","photoUrl":"https://lh5.googleusercontent.com/-KgiTKdqPRUg/AAAAAAAAAAI/AAAAAAAAAIE/aHQ6xO5vQpY/s64/photo.jpg","userId":"13365523799853678553"}},"colab":{"base_uri":"https://localhost:8080/","height":146}},"cell_type":"code","source":["s = 'ababaa'\n","cyclic_shifts_sort(s)"],"execution_count":32,"outputs":[{"output_type":"stream","text":["diff a $\n","diff b a\n","[6, 0, 2, 4, 5, 1, 3] [1, 2, 1, 2, 1, 1, 0]\n","[6, 5, 4, 0, 2, 1, 3] [3, 4, 3, 4, 2, 1, 0]\n","[6, 5, 4, 0, 2, 3, 1] [3, 6, 4, 5, 2, 1, 0]\n","[6, 5, 4, 0, 2, 3, 1] [3, 6, 4, 5, 2, 1, 0]\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["[6, 5, 4, 0, 2, 3, 1]"]},"metadata":{"tags":[]},"execution_count":32}]},{"metadata":{"id":"5nNbGVRTjvvL","colab_type":"text"},"cell_type":"markdown","source":[""]}]}
+{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"suffix_array.ipynb","version":"0.3.2","provenance":[],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"metadata":{"id":"3s7lvSxaj9Fi","colab_type":"text"},"cell_type":"markdown","source":["## sort cyclic shifts of string s + '$' to construct the suffix array"]},{"metadata":{"id":"JjYArMUrkDIu","colab_type":"code","colab":{}},"cell_type":"code","source":["from collections import OrderedDict\n","\n","def getCharOrder(s):\n","  n = len(s)\n","  numChars = 256\n","  count = [0]*numChars # total of 256 chars, if you want, can print it out to see these chars\n","  \n","  order = [0]*(n)\n","  \n","  #count the occurrence of each char\n","  for c in s:\n","    count[ord(c)] += 1\n","    \n","  # prefix sum of each char\n","  for i in range(1, numChars):\n","    count[i] += count[i-1]\n","    \n","  # assign from count down to be stable\n","  for i in range(n-1,-1,-1):\n","    count[ord(s[i])] -=1\n","    order[count[ord(s[i])]] = i # put the index into the order instead the suffix string\n","    \n","  return order\n","    "],"execution_count":0,"outputs":[]},{"metadata":{"id":"CXthy2Rqt6nm","colab_type":"code","colab":{}},"cell_type":"code","source":["def getCharClass(order, cls):\n","  n = len(order)\n","  cls = [0]*n\n","  # if it all differs, then cls[i] = order[i]\n","  cls[order[0]] = 0 #the 6th will be 0\n","  for i in range(1, n):\n","    # use order[i] as index, so the last index\n","    if s[order[i]] != s[order[i-1]]:\n","      print('diff',s[order[i]],s[order[i-1]])\n","      cls[order[i]] = cls[order[i-1]] + 1\n","    else:\n","      cls[order[i]] = cls[order[i-1]]\n","  return cls\n","      "],"execution_count":0,"outputs":[]},{"metadata":{"id":"yfCeF3b77m4M","colab_type":"code","colab":{}},"cell_type":"code","source":["'''It is a counting sort using the first part as class'''\n","def sortDoubled(s, L, order, cls):\n","  n = len(s)\n","  count = [0] * n\n","  new_order = [0] * n\n","  # their key is the class\n","  for i in range(n):\n","    count[cls[i]] += 1\n","    \n","  # prefix sum\n","  for i in range(1, n):\n","    count[i] += count[i-1]\n","    \n","  # assign from count down to be stable\n","  # sort the first half\n","  for i in range(n-1, -1, -1):\n","    start = (order[i] - L + n) % n #get the start index of the first half, \n","    count[cls[start]] -= 1\n","    new_order[count[cls[start]]] = start\n","    \n","  return new_order"],"execution_count":0,"outputs":[]},{"metadata":{"id":"2I1nIvImB3O8","colab_type":"code","colab":{}},"cell_type":"code","source":["def updateClass(order, cls, L):\n","  n = len(order)\n","  new_cls = [0]*n\n","  # if it all differs, then cls[i] = order[i]\n","  new_cls[order[0]] = 0 #the 6th will be 0\n","  for i in range(1, n):\n","    cur_order, prev_order = order[i], order[i-1]\n","    # use order[i] as index, so the last index\n","    if cls[cur_order] != cls[prev_order] or cls[(cur_order+L) % n] != cls[(prev_order+L) % n]:\n","      new_cls[cur_order] = new_cls[prev_order] + 1\n","    else:\n","      new_cls[cur_order] = new_cls[prev_order]\n","  return new_cls"],"execution_count":0,"outputs":[]},{"metadata":{"id":"2Wv3muUHkNl_","colab_type":"code","colab":{}},"cell_type":"code","source":["\n","def cyclic_shifts_sort(s):\n","  s = s + '$'\n","  n = len(s)\n","  order = getCharOrder(s)\n","  cls = getCharClass(s, order)\n","  print(order, cls)\n","  L = 1\n","  while L < n:\n","    order = sortDoubled(s, 1, order, cls)\n","    cls = updateClass(order, cls, L)\n","    print(order, cls)\n","    L *= 2\n","  \n","  return order"],"execution_count":0,"outputs":[]},{"metadata":{"id":"OpqYr3Z6rsM_","colab_type":"code","outputId":"eb382cee-6f8d-459c-911f-10c955b45dad","executionInfo":{"status":"ok","timestamp":1549232253713,"user_tz":480,"elapsed":336,"user":{"displayName":"Li Yin","photoUrl":"https://lh5.googleusercontent.com/-KgiTKdqPRUg/AAAAAAAAAAI/AAAAAAAAAIE/aHQ6xO5vQpY/s64/photo.jpg","userId":"13365523799853678553"}},"colab":{"base_uri":"https://localhost:8080/","height":146}},"cell_type":"code","source":["s = 'ababaa'\n","cyclic_shifts_sort(s)"],"execution_count":32,"outputs":[{"output_type":"stream","text":["diff a $\n","diff b a\n","[6, 0, 2, 4, 5, 1, 3] [1, 2, 1, 2, 1, 1, 0]\n","[6, 5, 4, 0, 2, 1, 3] [3, 4, 3, 4, 2, 1, 0]\n","[6, 5, 4, 0, 2, 3, 1] [3, 6, 4, 5, 2, 1, 0]\n","[6, 5, 4, 0, 2, 3, 1] [3, 6, 4, 5, 2, 1, 0]\n"],"name":"stdout"},{"output_type":"execute_result","data":{"text/plain":["[6, 5, 4, 0, 2, 3, 1]"]},"metadata":{"tags":[]},"execution_count":32}]},{"metadata":{"id":"5nNbGVRTjvvL","colab_type":"text"},"cell_type":"markdown","source":[""]}]}

Colab Codes/Colab Notebooks/tree_data_structure.ipynb

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-{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"tree_data_structure.ipynb","version":"0.3.2","provenance":[],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"metadata":{"id":"3A2mprldYvXe","colab_type":"text"},"cell_type":"markdown","source":["### N-aray Tree"]},{"metadata":{"id":"h5LNx9p_ZxtH","colab_type":"text"},"cell_type":"markdown","source":["#### Define Tree Node"]},{"metadata":{"id":"9R_XYWC2Yz-G","colab_type":"code","colab":{}},"cell_type":"code","source":["class NaryNode:\n","  '''Define a n-ary node'''\n","  def __init__(self, n, val):\n","    self.children = [None] * n\n","    self.val = val\n","    "],"execution_count":0,"outputs":[]},{"metadata":{"id":"Xx5WEdJDZ4-q","colab_type":"text"},"cell_type":"markdown","source":["#### Define a Tree and implement operations"]},{"metadata":{"id":"qtAos_DOZwkw","colab_type":"code","colab":{}},"cell_type":"code","source":[""],"execution_count":0,"outputs":[]},{"metadata":{"id":"wLPjQrfnZbQY","colab_type":"text"},"cell_type":"markdown","source":["### Binary Tree"]},{"metadata":{"id":"oUZYimKbZ1ZL","colab_type":"text"},"cell_type":"markdown","source":["#### Define Tree Node"]},{"metadata":{"id":"ZKknhNURZdA0","colab_type":"code","colab":{}},"cell_type":"code","source":["class BinaryNode:\n","  '''Define a classical binary tree node'''\n","  def __init__(self, val):\n","    self.left = None\n","    self.right = None\n","    self.val = val"],"execution_count":0,"outputs":[]},{"metadata":{"id":"yPukXXkXZ_zn","colab_type":"text"},"cell_type":"markdown","source":["#### Define a Tree and implement operations\n","      1\n","    /   \\  \n","   2      3\n"," /   \\      \\\n","4     5      6 "]},{"metadata":{"id":"CyXwZ9sf8dyG","colab_type":"code","colab":{}},"cell_type":"code","source":["root = BinaryNode(1)\n","left = BinaryNode(2)\n","right = BinaryNode(3)\n","root.left = left\n","root.right = right\n","left.left = BinaryNode(4)\n","left.right = BinaryNode(5)\n","right.right = BinaryNode(6)"],"execution_count":0,"outputs":[]},{"metadata":{"id":"gOHqKKfY_Ug0","colab_type":"code","colab":{}},"cell_type":"code","source":["def constructTree(a, idx):\n","  '''construct a binary tree recursively from input array a'''\n","  if idx >= len(a):\n","    return None\n","  node = BinaryNode(a[idx])\n","  node.left = constructTree(a, 2*idx + 1)\n","  node.right = constructTree(a, 2*idx + 2)\n","  return node"],"execution_count":0,"outputs":[]},{"metadata":{"id":"STvuN-5p_5Di","colab_type":"code","colab":{}},"cell_type":"code","source":["nums = [1, 2, 3, 4, 5, None, 6]\n","root = constructTree(nums, 0)"],"execution_count":0,"outputs":[]},{"metadata":{"id":"hrJC3v5ZAvD-","colab_type":"text"},"cell_type":"markdown","source":["#### To show the nodes at each level, we use LevelOrder function to print out the tree:"]},{"metadata":{"id":"uPxVdjRrA0UB","colab_type":"code","colab":{}},"cell_type":"code","source":["def LevelOrder(root):\n","    q = [root]\n","    while q:\n","        new_q = []\n","        for n in q:\n","            if n is not None:\n","                print(n.val, end=',')\n","            if n.left:\n","                new_q.append(n.left)\n","            if n.right:\n","                new_q.append(n.right)\n","        q = new_q\n","        print('\\n')\n"],"execution_count":0,"outputs":[]},{"metadata":{"id":"Pl2HGcHkA4rT","colab_type":"code","outputId":"2282a8ed-e1c1-4dae-b83c-0c2a8c19b470","executionInfo":{"status":"ok","timestamp":1550969967703,"user_tz":480,"elapsed":336,"user":{"displayName":"Li Yin","photoUrl":"https://lh5.googleusercontent.com/-KgiTKdqPRUg/AAAAAAAAAAI/AAAAAAAAAIE/aHQ6xO5vQpY/s64/photo.jpg","userId":"13365523799853678553"}},"colab":{"base_uri":"https://localhost:8080/","height":127}},"cell_type":"code","source":["LevelOrder(root)"],"execution_count":0,"outputs":[{"output_type":"stream","text":["1,\n","\n","2,3,\n","\n","4,5,None,6,\n","\n"],"name":"stdout"}]},{"metadata":{"id":"2edkOHbCCV7n","colab_type":"text"},"cell_type":"markdown","source":[""]}]}
+{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"tree_data_structure.ipynb","version":"0.3.2","provenance":[],"toc_visible":true},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"metadata":{"id":"3A2mprldYvXe","colab_type":"text"},"cell_type":"markdown","source":["### N-ary Tree"]},{"metadata":{"id":"h5LNx9p_ZxtH","colab_type":"text"},"cell_type":"markdown","source":["#### Define Tree Node"]},{"metadata":{"id":"9R_XYWC2Yz-G","colab_type":"code","colab":{}},"cell_type":"code","source":["class NaryNode:\n","  '''Define a n-ary node'''\n","  def __init__(self, n, val):\n","    self.children = [None] * n\n","    self.val = val\n","    "],"execution_count":0,"outputs":[]},{"metadata":{"id":"Xx5WEdJDZ4-q","colab_type":"text"},"cell_type":"markdown","source":["#### Define a Tree and implement operations"]},{"metadata":{"id":"qtAos_DOZwkw","colab_type":"code","colab":{}},"cell_type":"code","source":[""],"execution_count":0,"outputs":[]},{"metadata":{"id":"wLPjQrfnZbQY","colab_type":"text"},"cell_type":"markdown","source":["### Binary Tree"]},{"metadata":{"id":"oUZYimKbZ1ZL","colab_type":"text"},"cell_type":"markdown","source":["#### Define Tree Node"]},{"metadata":{"id":"ZKknhNURZdA0","colab_type":"code","colab":{}},"cell_type":"code","source":["class BinaryNode:\n","  '''Define a classical binary tree node'''\n","  def __init__(self, val):\n","    self.left = None\n","    self.right = None\n","    self.val = val"],"execution_count":0,"outputs":[]},{"metadata":{"id":"yPukXXkXZ_zn","colab_type":"text"},"cell_type":"markdown","source":["#### Define a Tree and implement operations\n","      1\n","    /   \\  \n","   2      3\n"," /   \\      \\\n","4     5      6 "]},{"metadata":{"id":"CyXwZ9sf8dyG","colab_type":"code","colab":{}},"cell_type":"code","source":["root = BinaryNode(1)\n","left = BinaryNode(2)\n","right = BinaryNode(3)\n","root.left = left\n","root.right = right\n","left.left = BinaryNode(4)\n","left.right = BinaryNode(5)\n","right.right = BinaryNode(6)"],"execution_count":0,"outputs":[]},{"metadata":{"id":"gOHqKKfY_Ug0","colab_type":"code","colab":{}},"cell_type":"code","source":["def constructTree(a, idx):\n","  '''construct a binary tree recursively from input array a'''\n","  if idx >= len(a):\n","    return None\n","  node = BinaryNode(a[idx])\n","  node.left = constructTree(a, 2*idx + 1)\n","  node.right = constructTree(a, 2*idx + 2)\n","  return node"],"execution_count":0,"outputs":[]},{"metadata":{"id":"STvuN-5p_5Di","colab_type":"code","colab":{}},"cell_type":"code","source":["nums = [1, 2, 3, 4, 5, None, 6]\n","root = constructTree(nums, 0)"],"execution_count":0,"outputs":[]},{"metadata":{"id":"hrJC3v5ZAvD-","colab_type":"text"},"cell_type":"markdown","source":["#### To show the nodes at each level, we use the LevelOrder function to print out the tree:"]},{"metadata":{"id":"uPxVdjRrA0UB","colab_type":"code","colab":{}},"cell_type":"code","source":["def LevelOrder(root):\n","    q = [root]\n","    while q:\n","        new_q = []\n","        for n in q:\n","            if n is not None:\n","                print(n.val, end=',')\n","            if n.left:\n","                new_q.append(n.left)\n","            if n.right:\n","                new_q.append(n.right)\n","        q = new_q\n","        print('\\n')\n"],"execution_count":0,"outputs":[]},{"metadata":{"id":"Pl2HGcHkA4rT","colab_type":"code","outputId":"2282a8ed-e1c1-4dae-b83c-0c2a8c19b470","executionInfo":{"status":"ok","timestamp":1550969967703,"user_tz":480,"elapsed":336,"user":{"displayName":"Li Yin","photoUrl":"https://lh5.googleusercontent.com/-KgiTKdqPRUg/AAAAAAAAAAI/AAAAAAAAAIE/aHQ6xO5vQpY/s64/photo.jpg","userId":"13365523799853678553"}},"colab":{"base_uri":"https://localhost:8080/","height":127}},"cell_type":"code","source":["LevelOrder(root)"],"execution_count":0,"outputs":[{"output_type":"stream","text":["1,\n","\n","2,3,\n","\n","4,5,None,6,\n","\n"],"name":"stdout"}]},{"metadata":{"id":"2edkOHbCCV7n","colab_type":"text"},"cell_type":"markdown","source":[""]}]}