programming.html

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  52
  53 # Programming strategy
  54
  55 ## Moving up a level
  56
  57 Data structures
  58
  59 Algorithms
  60
  61 Seeing alternatives
  62
  63 ---
  64
  65 layout: true
  66
  67 .indexlink[[Index](index.html)]
  68
  69 ---
  70
  71 # Data structures before algorithms
  72
  73 * What data do you need?
  74 * What operations must you perform on it?
  75
  76 These go a long way to defining the algorithms you must use.
  77
  78 ## Python built-in types
  79
  80 * Numbers (float and integer)
  81 * Strings
  82 * Tuples
  83 * Lists
  84 * Dictionaries (a.k.a. hashes or maps)
  85
  86 Many tasks will fit into these
  87
  88 More in the `collections` standard library, such as `namedtuple` and `Counter`
  89
  90 ---
  91
  92 # String
  93
  94 * Immutable in Python
  95 * Single or double quotes (beware apostrophies)
  96 * Triple-quoted contain newlines
  97
  98 ```python
  99 'This is a string'
 100 ```
 101 ```python
 102 "This isn't a problem"
 103 ```
 104 ```python
 105 """This is
 106 a multiline
 107 string"""
 108 ```
 109
 110 ---
 111 # Tuple
 112
 113 * Immutable in Python
 114 * Fixed-size collection
 115 * Indexed by position
 116
 117 ```python
 118 neil = ('Neil', 'Smith', 44)
 119 first_name = neil[0]
 120 surname = neil[1]
 121 ```
 122
 123 * Unpacking with assignment
 124
 125 ```python
 126 first_name, surname, age = neil
 127 ```
 128
 129 ```python
 130 for _, surname, age in people:
 131     ....
 132 ```
 133
 134 ---
 135
 136 # List
 137
 138 * Ordered collection
 139 * Mutable
 140 * Index by position and slices
 141
 142 ```python
 143 members = ['Freddie', 'Brian', 'Roger', 'John']
 144 print(members[1])
 145 print(members[1:2])
 146 print(members[1:3])
 147 print(members[1:1])
 148 print(members[-1])
 149 print(members[2:])
 150 print(members[:2])
 151 ```
 152
 153 ---
 154 # Lists: beware copy depth!
 155
 156 ```python
 157 members = ['Freddie', 'Brian', 'Roger', 'John']
 158 tour_lineup = members
 159 tour_lineup[0] = 'Paul'
 160 print(tour_lineup)
 161 print(members)
 162 ```
 163
 164 ---
 165
 166 # Copying a list
 167
 168 ```python
 169 tour_lineup = members[:]
 170 ```
 171
 172 ```python
 173 tour_lineup = list(members)
 174 ```
 175
 176 ```python
 177 import copy
 178 tour_lineup = copy.copy(members)
 179 tour_lineup = copy.deepcopy(members)
 180 ```
 181
 182 `==` tests value equality; `is` tests object identity
 183
 184 ```python
 185 members = ['Freddie', 'Brian', 'Roger', 'John']
 186 tour_lineup = members[:]
 187 tour_lineup == members
 188 tour_lineup is members
 189 ```
 190
 191 ## Value vs Reference
 192
 193 Must be part of your mental model
 194
 195 ---
 196
 197 # Dicts
 198
 199 * A set of key-value pairs
 200 * Mutable
 201 * Items in arbirary order
 202 * In Python, can use any immutable type as the key
 203 * Use any type as the value
 204
 205 ```python
 206 neil = {'first_name': 'Neil', 'surname': 'Smith', 'age': 44}
 207 neil['surname']
 208 ```
 209
 210 ---
 211 # Euler 11
 212
 213 ```python
 214 GRID_STRING = """08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
 215 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
 216 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
 217 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
 218 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
 219 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
 220 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
 221 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
 222 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
 223 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
 224 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
 225 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
 226 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
 227 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
 228 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
 229 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
 230 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
 231 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
 232 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
 233 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"""
 234 ```
 235
 236 How many data structures can you think of for this puzzle?
 237
 238 ---
 239
 240 # Euler 11 structures
 241
 242 * List of lists: either a list of rows or a list of columns
 243 * One large list, find a number by row × 20 + column
 244 * Tuple of tuples, one large tuple, list of tuples, tuple of lists...
 245 * Dict with keys as (row, column)
 246 * Keep it as a string: `int(row * 20 + column) * 3)`
 247     * (Beware when joining rows)
 248 * List of strings, tuple of strings, dict of strings...
 249
 250 ---
 251
 252 # Comprehensions
 253
 254 Do something to each element of an iterable, returning a sequence of the results
 255
 256 * Iterable: anything you can use as `for item in iterable`
 257 * Sequence: `tuple`, `list`, `dict`
 258
 259 Examples:
 260
 261 * List of numbers: `[i for i in range(10)]`
 262 * List of squares: `[i ** 2 for i in range(10)]`
 263 * List of numbers from a string: `[int(n) for n in str.split()]`
 264 * Numbers and their squares: `{i: i ** 2 for i in range(10)}`
 265 * Even numbers and their squares: `{i: i ** 2 for i in range(10) if i % 2 == 0}`
 266
 267 ---
 268 # Comprehensions with multiple sequences
 269
 270 All the numbers in the Euler 11 grid:
 271 ```python
 272 [n for row in grid for n in row]
 273 ```
 274
 275 Pythagorean triples:
 276 <table>
 277 <tr valign="top">
 278  <td>
 279  ```python
 280 [(a, b, c)
 281  for a in range(1, 21)
 282  for b in range(1, 21)
 283  for c in range(1, 21)
 284  if a &lt;= b
 285  if b &lt;= c
 286  if a**2 + b**2 == c**2]
 287 ```
 288 </td>
 289 <td>
 290 ```python
 291 [(a, b, c)
 292  for a in range(1, 21)
 293  for b in range(a, 21)
 294  for c in range(b, 21)
 295  if a**2 + b**2 == c**2]
 296 ```
 297 </td>
 298 <td>
 299 ```python
 300 [(a, b, int((a**2 + b**2)**0.5))
 301  for a in range(1, 21)
 302  for b in range(a, 21)
 303  if int((a**2 + b**2)**0.5) == (a**2 + b**2)**0.5]
 304  ```
 305  </td>
 306 </tr></table>
 307
 308 ---
 309
 310 # Task
 311
 312 Turn the Euler 11 grid into:
 313
 314 * A list of lists, as a list of rows
 315 * A dict with keys of (x, y)
 316
 317 Do both with explicit iteration, then using only comprehensions.
 318
 319 ---
 320
 321 # Solutions with explicit loops
 322 ```python
 323 grid_nums = [int(n) for n in GRID_STRING.split()]
 324 ```
 325
 326 ```python
 327 g1 = []
 328 for rowstart in range(0, ROWS * COLUMNS, COLUMNS):
 329     g1.append(grid_nums[rowstart:rowstart+COLUMNS])
 330
 331 # g1[row][column]
 332 ```
 333
 334 ```python
 335 g2 = {}
 336 for x in range(COLUMNS):
 337     for y in range(ROWS):
 338         g2[(x, y)] = grid_nums[x + y * COLUMNS]
 339
 340 # g2[(x, y)]
 341 ```
 342
 343 Note the need for the creation of the empty container
 344
 345 ---
 346
 347 # Solutions with comprehensions
 348
 349 ```python
 350 g3 = [grid_nums[row * COLUMNS:(row+1) * COLUMNS]
 351       for row in range(ROWS)]
 352
 353 # g3[row][column]
 354 ```
 355
 356 ```python
 357 g4 = {(x, y): grid_nums[x + y * COLUMNS]
 358       for x in range(COLUMNS)
 359       for y in range(ROWS)}
 360
 361 # g4[(x, y)]
 362 ```
 363
 364 ```python
 365 g4s = {(x, y): int(GRID_STRING[(x + y * COLUMNS) * 3:(x + y * COLUMNS) * 3 + 2])
 366       for x in range(COLUMNS)
 367       for y in range(ROWS)}
 368
 369 # g4s[(x, y)]
 370 ```
 371
 372 ---
 373
 374 # Other Python data structures
 375
 376 ## Set
 377 Unordered, mutable, no duplicates
 378
 379 * Useful for removing duplicates from sequences: `list(set(items))`
 380
 381 ---
 382 # collections.defaultdict
 383 Like a dict, but doesn't throw an error if you ask for missing key
 384
 385 ```python
 386 >>> d = {}
 387 >>> d[99]
 388 Traceback (most recent call last):
 389   File "<stdin>", line 1, in <module>
 390 KeyError: 99
 391 >>> import collections
 392 >>> d = collections.defaultdict(int)
 393 >>> d[99]
 394 0
 395 ```
 396
 397 ---
 398
 399 # collections.Counter
 400 Counts items in a sequence:
 401
 402 ```python
 403 collections.Counter(l for l in open('sherlock-holmes.txt').read()
 404                     if l in string.ascii_letters)
 405 ```
 406
 407 ---
 408
 409 # collections.namedtuple
 410 Dumb `object` for just storing data in named fields
 411
 412 ```python
 413 Point = collections.namedtuple('Point', ['x', 'y'])
 414 p = Point(11, y=22)
 415 p[0] + p[1]
 416 x, y = p
 417 p.x + p.y
 418 ```
 419
 420 ---
 421
 422 # Data, not algorithms
 423
 424 Don't put complex, changable logic into code
 425
 426 Build a data structure that describes it, code that reads it.
 427
 428 * Euler 11 directions
 429 * Multiple choice quiz
 430
 431 ---
 432
 433 # Algorithms: trading space for time
 434
 435 ## Euler 14
 436
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