cs124_hash.ipynb

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     "slide_type": "slide"
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   "source": [
    "# CS 124 Lecture: Skip Lists and Hash Table\n",
    "\n",
    "__Boaz Barak__\n",
    "\n",
    "April 1, 2019"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Skip lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import graphviz\n",
    "from graphviz import Graph\n",
    "from graphviz import Digraph\n",
    "# Graph visualization library - requires graphviz on your system\n",
    "# On Anaconda can install by\n",
    "# conda install -c anaconda graphviz  (or download at https://www.graphviz.org/download/ )\n",
    "# conda install -c conda-forge python-graphviz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def method(cls,f):\n",
    "    setattr(cls,f.__name__,f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "INF = 100000000 # Our proxy for \"infinity\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "PRINT_COIN = True\n",
    "\n",
    "def coin():\n",
    "    \"\"\"Toss random coin\"\"\"\n",
    "    c =  random.choice([0,1])\n",
    "    if PRINT_COIN: print([\"TAIL\",\"HEAD\"][c], end= \" \")\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "outputs": [],
   "source": [
    "class Node:\n",
    "    \"\"\"A node in a skip list. \n",
    "    Contains the key and pointers to right and down neighbors.\"\"\"\n",
    "    def __init__(self,key,right=None,down=None): \n",
    "        self.key = key\n",
    "        self.right = right\n",
    "        self.down = down\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "class SkipList:\n",
    "    \"\"\"A skip list contains the pointer to its top left node.\n",
    "    It is initialized with top-left's key = -∞ and its right neighbor's key = +∞ \"\"\"\n",
    "    def __init__(self):\n",
    "        topright = Node(+INF)\n",
    "        self.topleft = Node(-INF,topright)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "counter = 0\n",
    "\n",
    "def valstr(v):\n",
    "    if v>=INF: return \"+∞\"\n",
    "    if v<=-INF: return \"-∞\"\n",
    "    return str(v)\n",
    "\n",
    "def list2graph(G,n,x=0,y=0):\n",
    "    # Create graph from list for  visualization. \n",
    "    # Inefficient right now: should memoize this function or mark visited vertices \n",
    "    if not n: return None\n",
    "    global counter\n",
    "    counter += 1\n",
    "    vertex = str(id(n))\n",
    "    G.node(vertex,valstr(n.key), pos = f\"{x},{y}!\")\n",
    "    right = list2graph(G,n.right,x+1,y)\n",
    "    down = list2graph(G,n.down,x,y-1)\n",
    "    if right: G.edge(vertex,right)\n",
    "    if down: G.edge(vertex,down)\n",
    "    return vertex\n",
    "\n",
    "def _repr_svg_(self):\n",
    "    G =Digraph(engine=\"neato\",graph_attr= {\"concentrate\":\"true\"} )\n",
    "    list2graph(G,self.topleft)\n",
    "    return G._repr_svg_()\n",
    "\n",
    "method(SkipList,_repr_svg_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "outputs": [],
   "source": [
    "def pred_(n,val):\n",
    "    \"\"\"Predecessor query main function: \n",
    "    Given n, find the node to the right and down from n with key ≤ val\"\"\"\n",
    "    if n.right.key<=val: return pred_(n.right,val) # move right\n",
    "    if not n.down: return n # return n if at bottom level \n",
    "    return pred_(n.down,val) # move down"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {
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     "slide_type": "fragment"
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   "source": [
    "def pred(self,val):\n",
    "    \"\"\"To compute predecessor on list, run pred_ on the topleft node.\"\"\"\n",
    "    return pred_(self.topleft,val).key"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "method(SkipList,pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "def insert_(n,val):\n",
    "    \"\"\"Add a node with key val to the right and down of node n\n",
    "    Return \"STOP\" if there is no promotion\"\"\"\n",
    "    if not n: return None\n",
    "    if n.right.key <= val: return insert_(n.right,val) # move right\n",
    "    \n",
    "    v = insert_(n.down,val)\n",
    "    if v==\"STOP\": return v # no promotion - propagate this back\n",
    "    \n",
    "    # stick temp between n and n.right, temp points down to v:\n",
    "    temp = Node(val,n.right,v) \n",
    "    n.right = temp\n",
    "    if coin(): return temp # promote temp\n",
    "    return \"STOP\" # no promotion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
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   "source": [
    "def insert(self,val):\n",
    "    \"\"\"Add a value to the list\"\"\"\n",
    "    insert_(self.topleft,val)\n",
    "    if self.topleft.right.key < +INF: # make sure top level always -∞,+∞ \n",
    "        topright = Node(+INF)\n",
    "        self.topleft = Node(-INF,topright,self.topleft)\n",
    "    return self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "slideshow": {
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   },
   "outputs": [],
   "source": [
    "method(SkipList,insert)"
   ]
  },
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   "execution_count": 181,
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    "L = SkipList()\n",
    "L"
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     "text": [
      "HEAD "
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    "L.insert(11)\n",
    "L"
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    "PRINT_COIN = False\n",
    "for i in range(5):\n",
    "    L.insert(random.randint(1,300))"
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      "text/plain": [
       "<__main__.SkipList at 0x25cec5929e8>"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L.insert(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L.pred(14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "PRINT_COIN = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Hash tables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "filename = 'cs124.csv'\n",
    "# filename = 'CSV_Database_of_Last_Names.csv'\n",
    "\n",
    "import csv\n",
    "students = []\n",
    "with open(filename,encoding='utf8') as csvfile:\n",
    "    dialect = csv.Sniffer().sniff(csvfile.read(1024))\n",
    "    csvfile.seek(0)\n",
    "    reader = csv.reader(csvfile,dialect)\n",
    "    for row in reader:\n",
    "        students += [\"\".join([s.strip() for s in row])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "students = students[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "283"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(students)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "N = 307 # nice prime number slightly bigger than 283"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def letter2number(let): \n",
    "    # Given letter let, returns number from 1 to 26 based on alphabetical order\n",
    "    return ord(let.lower())-ord('a')+1\n",
    "\n",
    "def silly_hash(name):\n",
    "    # Hash  name into a number from 0 to N-1\n",
    "    # N is a global constant\n",
    "    # Simply output first initial (as number from 1 to 26) times the length modulo N \n",
    "    return letter2number(name[0])*len(name) % N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "silly_hash(\"Boaz Barak\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "130"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "silly_hash(\"Jelani Nelson\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "buckets =  [0]*N\n",
    "for name in students:\n",
    "    buckets[silly_hash(name)] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Silly hash bucket distribution\n",
    "plt.plot(buckets); plt.xlabel('Buckets'); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.19434628975265"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum([i*i for i in buckets])/sum(buckets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "NUMBERS = [random.randint(0,N-1) for i in range(30)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[196, 290, 37, 185, 141, 57, 32, 249, 96, 199, 14, 247, 306, 283, 189, 113, 124, 37, 190, 140, 271, 276, 142, 53, 200, 300, 220, 141, 58, 287]\n"
     ]
    }
   ],
   "source": [
    "print(NUMBERS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def better_hash(name):\n",
    "    # DISCLAIMER: Despite name, DONT USE IT IN YOUR CODE - \n",
    "    # always use BUILT IN or CRYPTOGRAPHIC hash functions\n",
    "    #\n",
    "    # Hashes name into a number from 0 to N-1\n",
    "    # N is a global constant\n",
    "    # Treat name as a sequence (x0,x1,x2,...) of numbers from 1 to 26\n",
    "    # Return sum of xi*NUMBERS[i] mod N\n",
    "    # NUMBERS is a global constant array of numbers that we chose at random once\n",
    "    # and then fixed once and for all\n",
    "    name = name.replace(' ',\"\") # hack to ensure only letters\n",
    "    return sum([letter2number(name[i])*NUMBERS[i] for i in range(len(name))]) % N\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "143"
      ]
     },
     "execution_count": 276,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "better_hash(\"Boaz Barak\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "242"
      ]
     },
     "execution_count": 277,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "better_hash(\"Jelani Nelson\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "242"
      ]
     },
     "execution_count": 278,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "better_hash(\"Jelani Nelson\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "buckets =  [0]*N\n",
    "for name in students:\n",
    "    buckets[better_hash(name) % N] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Better hash bucket distribution\n",
    "plt.plot(buckets); plt.xlabel('Buckets'); plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9328621908127208"
      ]
     },
     "execution_count": 281,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum([i*i for i in buckets])/sum(buckets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Some issues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Semantically equal ≠ Hash equal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "143"
      ]
     },
     "execution_count": 282,
     "metadata": {},
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   ],
   "source": [
    "better_hash(\"Boaz Barak\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "221"
      ]
     },
     "execution_count": 283,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "better_hash(\"Boaz M. Barak\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
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   "source": [
    "Need to ensure that $hash(x)=hash(x') \\Leftrightarrow$ $x$ and $x'$ are semantically identical"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "## Adversarial data "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![](hashdos.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "If $h:\\{0,1\\}^* \\rightarrow [n]$ is chosen __independently__ of $x_1,\\ldots,x_n$ then expected list size $=O(1)$:\n",
    "\n",
    "$\\Rightarrow$ _total running time_ $=O(n)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "If  $x_1,\\ldots,x_n$ chosen __based on__ $h$ then can ensure $h(x_1)=\\ldots = h(x_n)$:\n",
    "\n",
    "$\\Rightarrow$ _total running time_ $=O(n^2)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Used in __denial of service attack__ against PHP, .net, Python, Java, Ruby, Apache,..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "![](mspatch.png)"
   ]
  }
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