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  52
  53 # Programming strategy ![Open University logo](oulogo_hor.png)
  54 ## Moving up a level
  55
  56 Data structures
  57
  58 Algorithms
  59
  60 Seeing alternatives
  61
  62 ---
  63
  64 layout: true
  65
  66 .indexlink[![Open University logo](oulogo_hor.png) [Index](index.html)]
  67
  68 ---
  69
  70 # Data structures before algorithms
  71
  72 * What data do you need?
  73 * What operations must you perform on it?
  74
  75 These go a long way to defining the algorithms you must use.
  76
  77 ## Python built-in types
  78
  79 * Numbers (float and integer)
  80 * Strings
  81 * Tuples
  82 * Lists
  83 * Dictionaries (a.k.a. hashes or maps)
  84
  85 Many tasks will fit into these
  86
  87 More in the `collections` standard library, such as `namedtuple` and `Counter`
  88
  89 ---
  90
  91 # String
  92
  93 * Immutable in Python
  94 * Single or double quotes (beware apostrophies)
  95 * Triple-quoted contain newlines
  96
  97 ```python
  98 'This is a string'
  99 ```
 100 ```python
 101 "This isn't a problem"
 102 ```
 103 ```python
 104 """This is
 105 a multiline
 106 string"""
 107 ```
 108
 109 ---
 110 # Tuple
 111
 112 * Immutable in Python
 113 * Fixed-size collection
 114 * Indexed by position
 115
 116 ```python
 117 neil = ('Neil', 'Smith', 44)
 118 first_name = neil[0]
 119 surname = neil[1]
 120 ```
 121
 122 * Unpacking with assignment
 123
 124 ```python
 125 first_name, surname, age = neil
 126 ```
 127
 128 ```python
 129 for _, surname, age in people:
 130     ....
 131 ```
 132
 133 ---
 134
 135 # List
 136
 137 * Ordered collection
 138 * Mutable
 139 * Index by position and slices
 140
 141 ```python
 142 members = ['Freddie', 'Brian', 'Roger', 'John']
 143 print(members[1])
 144 print(members[1:2])
 145 print(members[1:3])
 146 print(members[1:1])
 147 print(members[-1])
 148 print(members[2:])
 149 print(members[:2])
 150 ```
 151
 152 ---
 153 # Lists: beware copy depth!
 154
 155 ```python
 156 members = ['Freddie', 'Brian', 'Roger', 'John']
 157 tour_lineup = members
 158 tour_lineup[0] = 'Paul'
 159 print(tour_lineup)
 160 print(members)
 161 ```
 162
 163 ---
 164
 165 # Copying a list
 166
 167 ```python
 168 tour_lineup = members[:]
 169 ```
 170
 171 ```python
 172 tour_lineup = list(members)
 173 ```
 174
 175 ```python
 176 import copy
 177 tour_lineup = copy.copy(members)
 178 tour_lineup = copy.deepcopy(members)
 179 ```
 180
 181 `==` tests value equality; `is` tests object identity
 182
 183 ```python
 184 members = ['Freddie', 'Brian', 'Roger', 'John']
 185 tour_lineup = members[:]
 186 tour_lineup == members
 187 tour_lineup is members
 188 ```
 189
 190 ## Value vs Reference
 191
 192 Must be part of your mental model
 193
 194 ---
 195
 196 # Dicts
 197
 198 * A set of key-value pairs
 199 * Mutable
 200 * Items in arbirary order
 201 * In Python, can use any immutable type as the key
 202 * Use any type as the value
 203
 204 ```python
 205 neil = {'first_name': 'Neil', 'surname': 'Smith', 'age': 44}
 206 neil['surname']
 207 ```
 208
 209 ---
 210 # Euler 11
 211
 212 ```python
 213 GRID_STRING = """08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
 214 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
 215 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
 216 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
 217 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
 218 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
 219 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
 220 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
 221 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
 222 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
 223 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
 224 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
 225 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
 226 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
 227 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
 228 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
 229 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
 230 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
 231 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
 232 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"""
 233 ```
 234
 235 How many data structures can you think of for this puzzle?
 236
 237 ---
 238
 239 # Euler 11 structures
 240
 241 * List of lists: either a list of rows or a list of columns
 242 * One large list, find a number by row × 20 + column
 243 * Tuple of tuples, one large tuple, list of tuples, tuple of lists...
 244 * Dict with keys as (row, column)
 245 * Keep it as a string: `int(row * 20 + column) * 3)`
 246     * (Beware when joining rows)
 247 * List of strings, tuple of strings, dict of strings...
 248
 249 ---
 250
 251 # Comprehensions
 252
 253 Do something to each element of an iterable, returning a sequence of the results
 254
 255 * Iterable: anything you can use as `for item in iterable`
 256 * Sequence: `tuple`, `list`, `dict`
 257
 258 Examples:
 259
 260 * List of numbers: `[i for i in range(10)]`
 261 * List of squares: `[i ** 2 for i in range(10)]`
 262 * List of numbers from a string: `[int(n) for n in str.split()]`
 263 * Numbers and their squares: `{i: i ** 2 for i in range(10)}`
 264 * Even numbers and their squares: `{i: i ** 2 for i in range(10) if i % 2 == 0}`
 265
 266 ---
 267 # Comprehensions with multiple sequences
 268
 269 All the numbers in the Euler 11 grid:
 270 ```python
 271 [n for row in grid for n in row]
 272 ```
 273
 274 Pythagorean triples:
 275 <table>
 276 <tr valign="top">
 277  <td>
 278  ```python
 279 [(a, b, c)
 280  for a in range(1, 21)
 281  for b in range(1, 21)
 282  for c in range(1, 21)
 283  if a &lt;= b
 284  if b &lt;= c
 285  if a**2 + b**2 == c**2]
 286 ```
 287 </td>
 288 <td>
 289 ```python
 290 [(a, b, c)
 291  for a in range(1, 21)
 292  for b in range(a, 21)
 293  for c in range(b, 21)
 294  if a**2 + b**2 == c**2]
 295 ```
 296 </td>
 297 <td>
 298 ```python
 299 [(a, b, int((a**2 + b**2)**0.5))
 300  for a in range(1, 21)
 301  for b in range(a, 21)
 302  if int((a**2 + b**2)**0.5) == (a**2 + b**2)**0.5]
 303  ```
 304  </td>
 305 </tr></table>
 306
 307 ---
 308
 309 # Task
 310
 311 Turn the Euler 11 grid into:
 312
 313 * A list of lists, as a list of rows
 314 * A dict with keys of (x, y)
 315
 316 Do both with explicit iteration, then using only comprehensions.
 317
 318 ```python
 319 grid_nums = [int(n) for n in GRID_STRING.split()]
 320 ```
 321
 322 ---
 323
 324 # Solutions with explicit loops
 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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