Full Code of nivwusquorum/6.006-2015-notebooks for AI

Repository: nivwusquorum/6.006-2015-notebooks
Branch: master
Commit: 60d406e00096
Files: 93
Total size: 7.8 MB

Directory structure:
gitextract_8z7fqhuo/

├── .gitignore
├── Lecture 17.ipynb
├── challenge1/
│   ├── .gitignore
│   ├── README.md
│   ├── coins.cpp
│   ├── coins.py
│   ├── run_tests.sh
│   ├── tests/
│   │   ├── mon0.in
│   │   ├── mon0.out
│   │   ├── mon10a.in
│   │   ├── mon10a.out
│   │   ├── mon10b.in
│   │   ├── mon10b.out
│   │   ├── mon10c.in
│   │   ├── mon10c.out
│   │   ├── mon1a.in
│   │   ├── mon1a.out
│   │   ├── mon1b.in
│   │   ├── mon1b.out
│   │   ├── mon1c.in
│   │   ├── mon1c.out
│   │   ├── mon1d.in
│   │   ├── mon1d.out
│   │   ├── mon2a.in
│   │   ├── mon2a.out
│   │   ├── mon2b.in
│   │   ├── mon2b.out
│   │   ├── mon2c.in
│   │   ├── mon2c.out
│   │   ├── mon3a.in
│   │   ├── mon3a.out
│   │   ├── mon3b.in
│   │   ├── mon3b.out
│   │   ├── mon3c.in
│   │   ├── mon3c.out
│   │   ├── mon3d.in
│   │   ├── mon3d.out
│   │   ├── mon4a.in
│   │   ├── mon4a.out
│   │   ├── mon4b.in
│   │   ├── mon4b.out
│   │   ├── mon5a.in
│   │   ├── mon5a.out
│   │   ├── mon5b.in
│   │   ├── mon5b.out
│   │   ├── mon5c.in
│   │   ├── mon5c.out
│   │   ├── mon6a.in
│   │   ├── mon6a.out
│   │   ├── mon6b.in
│   │   ├── mon6b.out
│   │   ├── mon7a.in
│   │   ├── mon7a.out
│   │   ├── mon7b.in
│   │   ├── mon7b.out
│   │   ├── mon8a.in
│   │   ├── mon8a.out
│   │   ├── mon8b.in
│   │   ├── mon8b.out
│   │   ├── mon9a.in
│   │   ├── mon9a.out
│   │   ├── mon9b.in
│   │   └── mon9b.out
│   └── url.txt
├── challenge2/
│   ├── .gitignore
│   ├── README.md
│   ├── download_test.sh
│   ├── pilots.cpp
│   ├── pilots_n.py
│   ├── pilots_n2.py
│   ├── pilots_n3.py
│   ├── pilots_nlog2n.py
│   ├── pilots_nlogn.py
│   ├── run_tests.sh
│   └── url.txt
├── hello.txt
├── lecture1/
│   ├── Fast exponentiation and fibonacci sequence.ipynb
│   └── Stock Exchange.ipynb
├── lecture11/
│   └── BFS.ipynb
├── lecture12/
│   ├── DFS.ipynb
│   └── Google BFS.ipynb
├── lecture15/
│   └── Dijkstra's algorithm.ipynb
├── lecture16/
│   └── Bignums.ipynb
├── lecture2/
│   ├── Document distance.ipynb
│   └── binary_search.ipynb
├── lecture4/
│   └── Heaps.ipynb
├── lecture5/
│   └── BST.ipynb
├── lecture6/
│   ├── AVL_and_more.ipynb
│   └── Counting BST.ipynb
├── lecture7/
│   ├── Radix Sort Performance.ipynb
│   └── Understanding Radix Sort.ipynb
├── lecture8/
│   └── Hashing and hashtables.ipynb
└── lecture9/
    └── Hashing.ipynb

================================================
FILE CONTENTS
================================================

================================================
FILE: .gitignore
================================================
.ipynb_checkpoints/


================================================
FILE: Lecture 17.ipynb
================================================
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LCS "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def LCS(s1, s2):\n",
    "    # initialize state\n",
    "    n, m = len(s1) + 1, len(s2) + 1\n",
    "    dp =   [\n",
    "        [ 0 for _ in range(m)] \n",
    "        for _ in range(n)\n",
    "    ]\n",
    "    pred = [\n",
    "        [ (-1,-1) for _ in range(m)]\n",
    "        for _ in range(n)\n",
    "    ]\n",
    "    \n",
    "    for i in range(1,n):\n",
    "        for j in range(1,m):\n",
    "            # CASE 1: ignore character in s1\n",
    "            dp[i][j], pred[i][j] = dp[i-1][j], (i-1,j)\n",
    "            # CASE 2: ignore character in s2\n",
    "            if dp[i][j] < dp[i][j-1]:\n",
    "                dp[i][j], pred[i][j] = dp[i][j-1], (i,j-1)\n",
    "            # CASE 3: extend\n",
    "            if s1[i-1] == s2[j-1] and dp[i][j] < dp[i-1][j-1] + 1:\n",
    "                dp[i][j], pred[i][j] = dp[i-1][j-1] + 1, (i-1,j-1)\n",
    "    \n",
    "    print (np.array(dp))\n",
    "\n",
    "    # recover the solution\n",
    "    x,y = (n-1,m-1)\n",
    "    solution = []\n",
    "    while pred[x][y] != (-1,-1):\n",
    "        if pred[x][y] == (x-1, y-1):\n",
    "            solution.append(s1[x-1])\n",
    "        (x,y) = pred[x][y]\n",
    "    solution.reverse()\n",
    "    \n",
    "    return solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 0 0]\n",
      " [0 1 1 1 1]\n",
      " [0 1 2 2 2]\n",
      " [0 1 2 2 2]\n",
      " [0 1 2 3 3]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['b', 'a', 'b']"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LCS(\"bacb\", \"babd\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 1 1 1 1 1 1]\n",
      " [0 0 0 1 2 2 2 2 2 2]\n",
      " [0 1 1 1 2 2 2 2 2 2]\n",
      " [0 1 2 2 2 2 2 2 2 2]\n",
      " [0 1 2 3 3 3 3 3 3 3]\n",
      " [0 1 2 3 4 4 4 4 4 4]\n",
      " [0 1 2 3 4 4 4 5 5 5]\n",
      " [0 1 2 3 4 4 4 5 6 6]\n",
      " [0 1 2 3 4 4 5 5 6 7]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['t', 'h', 'i', 's', 'l', 'c', 's']"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LCS(\"isthislcs\", \"thisislcs\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Viterbi algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "states = ('Healthy', 'Fever')\n",
    " \n",
    "observations = ('normal', 'cold', 'dizzy')\n",
    " \n",
    "start_probability = {'Healthy': 0.6, 'Fever': 0.4}\n",
    " \n",
    "transition_probability = {\n",
    "   'Healthy' : {'Healthy': 0.7, 'Fever': 0.3},\n",
    "   'Fever' : {'Healthy': 0.4, 'Fever': 0.6}\n",
    "   }\n",
    " \n",
    "emission_probability = {\n",
    "   'Healthy' : {'normal': 0.5, 'cold': 0.4, 'dizzy': 0.1},\n",
    "   'Fever' : {'normal': 0.1, 'cold': 0.3, 'dizzy': 0.6}\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def viterbi(obs, states, start_p, trans_p, emit_p):\n",
    "    V = [{}]\n",
    "    predecessor = [{}]\n",
    "    \n",
    "    # Initialize base cases (t == 0)\n",
    "    for y in states:\n",
    "        V[0][y] = start_p[y] * emit_p[y][obs[0]]\n",
    "        predecessor[0][y] = None\n",
    "    \n",
    "    # Run Viterbi for t > 0\n",
    "    for t in range(1, len(obs)):\n",
    "        V.append({})\n",
    "        predecessor.append({})\n",
    "\n",
    "        for y in states:\n",
    "            highest_probability, best_y_prev = 0.0, None\n",
    "            for y_prev in states:\n",
    "                probability_from_y_prev = V[t-1][y_prev] * trans_p[y_prev][y] * emit_p[y][obs[t]]\n",
    "                if probability_from_y_prev > highest_probability:\n",
    "                    highest_probability, best_y_prev = probability_from_y_prev, y_prev\n",
    "            V[t][y] = highest_probability\n",
    "            predecessor[t][y] = best_y_prev\n",
    "    \n",
    "    print(*dptable(V), sep='')\n",
    "    \n",
    "    # Return the most likely sequence over the given time frame\n",
    "    n = len(obs) - 1\n",
    "    (prob, state) = max((V[n][y], y) for y in states)\n",
    "    \n",
    "    # Recover the path\n",
    "    path = []\n",
    "    for t in range(n,-1,-1):\n",
    "        path.append(state)\n",
    "        state = predecessor[t][state]\n",
    "    path.reverse()\n",
    "    \n",
    "    return (prob, path)\n",
    "\n",
    "# Don't study this; it just prints a table of the steps.\n",
    "def dptable(V):\n",
    "    yield \"    \"\n",
    "    yield \" \".join((\"%7d\" % i) for i in range(len(V)))\n",
    "    yield \"\\n\"\n",
    "    for y in V[0]:\n",
    "        yield \"%.5s: \" % y\n",
    "        yield \" \".join(\"%.7s\" % (\"%f\" % v[y]) for v in V)\n",
    "        yield \"\\n\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          0       1       2\n",
      "Fever: 0.04000 0.02700 0.01512\n",
      "Healt: 0.30000 0.08400 0.00588\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.01512, ['Healthy', 'Healthy', 'Fever'])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "viterbi(observations, states, start_probability, transition_probability, emission_probability)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}


================================================
FILE: challenge1/.gitignore
================================================
coins


================================================
FILE: challenge1/README.md
================================================
# The coins challenge

To run c++ solution run
```bash
g++ coins.cpp -O2 -o coins
./run_tests.sh ./coins
```

To run Python solution run

```bash
./run_tests.sh python2 coins.py
```


================================================
FILE: challenge1/coins.cpp
================================================
#include <algorithm>
#include <cstdio>

// OVERALL COMPLEXITY: O(n lg n)
// (due to sorting)

// maximum number of coins
const int MAXN = 1000005;

// n - number of coins
// k - we need k as many tails as heads
int n, k;
// c - buffer to hold all the characters
char c[MAXN];
// array of (prefix_sum[i], i) values
std::pair<long long, int> seq_and_index[MAXN];

int main() {
    scanf("%d%d", &n, &k);
    scanf("%s", c);
    // for prefix sums it is important to add an extra element
    // for empty sequence at the beginning.
    // this is so that when we compute
    //
    //     seq_and_index[n].second - seq_and_index[0].second
    //
    // we get sum of elements for indexes 1 <= i <= n

    // We reuse seq_and_index for two things
    // initially it just stores values k and -1
    // later we compute prefix sum
    seq_and_index[0] = std::make_pair(0,0);
    for (int i=0; i <n; ++i) {
        // we convert R to k and O to -1
        if (c[i] == 'R') {
            seq_and_index[i + 1].first = k;
        } else {
            seq_and_index[i + 1].first = -1;
        }
        seq_and_index[i+1].second = i + 1;
    }

    // NEW PROBLEM: find longest contiguous subsequence of
    // sum 0 (sum zero implies k times as many heads)

    // compute the prefix sum
    for (int i=1; i <=n; ++i) {
        seq_and_index[i].first += seq_and_index[i-1].first;
    }

    // new problem: find a pair of elements in the array,
    // that have the same value and that are furthest
    // away possible.

    int res = 0;

    // sort by value.
    std::sort(seq_and_index, seq_and_index + n + 1);

    // for all groups with the same value
    // compute max and min index in that group.
    // update result with the difference between those indexes

    int min_index, max_index;
    for (int i=0; i <=n; ++i) {
        if ( i == 0 || seq_and_index[i].first != seq_and_index[i - 1].first) {
            min_index = seq_and_index[i].second;
            max_index = seq_and_index[i].second;
        }
        min_index = std::min(min_index, seq_and_index[i].second);
        max_index = std::max(max_index, seq_and_index[i].second);
        res = std::max(res, max_index - min_index);
    }
    printf("%d\n", res);
}


================================================
FILE: challenge1/coins.py
================================================
# OVERALL COMPLEXITY: O(n)
# here we use a dictionary

def main():
    # n - number of coins
    # k - we need k as many tails as heads
    n, k = [int(v) for v in raw_input().split()]
    # coins - buffer to hold all the characters
    coins = list(raw_input())
    assert len(coins) == n
    coins_as_numbers = []
    for coin in coins:
        if coin == 'R':
            coins_as_numbers.append(k)
        elif coin == 'O':
            coins_as_numbers.append(-1)
        else:
            assert False
    # NEW PROBLEM: find longest contiguous subsequence of
    # sum 0 (sum zero implies k times as many heads)


    # for prefix sums it is important to add an extra element
    # for empty sequence at the beginning.
    prefix_sums = [0]

    # compute the prefix sums
    for coin in coins_as_numbers:
        prefix_sums.append(prefix_sums[-1] + coin)

    # new problem: find a pair of elements in the array,
    # that have the same value and that are furthest
    # away possible.

    # this dictionary maps from array values,
    # to the index of prefix_sums, where the value
    # occurs for the first time
    # Specifically leftmost_index_of_value[S]
    # is equal to smallest such i that prefix_sums[i] = S
    # NOTE: it is build iteratively left to right
    leftmost_index_of_value = {}
    for s_idx, s in enumerate(prefix_sums):
        if s not in leftmost_index_of_value:
            leftmost_index_of_value[s] = s_idx

    res = 0
    for s_idx, s in enumerate(prefix_sums):
        res = max(res, s_idx - leftmost_index_of_value[s])

    print(res)

if __name__ == '__main__':
    main()


================================================
FILE: challenge1/run_tests.sh
================================================
#!/bin/bash

# stop script on error and print it
set -e
# inform me of undefined variables
set -u
# handle cascading failures well
set -o pipefail

SCRIPT_DIR=$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )

for filename in $SCRIPT_DIR/tests/*.in; do
    output_filename=${filename::-3}.out
    time $@ < $filename | diff -bs - $output_filename
done


================================================
FILE: challenge1/tests/mon0.in
================================================
15 3
RORROOROOROOORO


================================================
FILE: challenge1/tests/mon0.out
================================================
8


================================================
FILE: challenge1/tests/mon10a.in
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1000000 2
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