1 .. _tut-structures: 2 3 *************** 4 Data Structures 5 *************** 6 7 This chapter describes some things you've learned about already in more detail, 8 and adds some new things as well. 9 10 .. _tut-morelists: 11 12 More on Lists 13 ============= 14 15 The list data type has some more methods. Here are all of the methods of list 16 objects: 17 18 19 .. method:: list.append(x) 20 :noindex: 21 22 Add an item to the end of the list. Equivalent to ``a[len(a):] = [x]``. 23 24 25 .. method:: list.extend(iterable) 26 :noindex: 27 28 Extend the list by appending all the items from the iterable. Equivalent to 29 ``a[len(a):] = iterable``. 30 31 32 .. method:: list.insert(i, x) 33 :noindex: 34 35 Insert an item at a given position. The first argument is the index of the 36 element before which to insert, so ``a.insert(0, x)`` inserts at the front of 37 the list, and ``a.insert(len(a), x)`` is equivalent to ``a.append(x)``. 38 39 40 .. method:: list.remove(x) 41 :noindex: 42 43 Remove the first item from the list whose value is *x*. It is an error if 44 there is no such item. 45 46 47 .. method:: list.pop([i]) 48 :noindex: 49 50 Remove the item at the given position in the list, and return it. If no index 51 is specified, ``a.pop()`` removes and returns the last item in the list. (The 52 square brackets around the *i* in the method signature denote that the parameter 53 is optional, not that you should type square brackets at that position. You 54 will see this notation frequently in the Python Library Reference.) 55 56 57 .. method:: list.clear() 58 :noindex: 59 60 Remove all items from the list. Equivalent to ``del a[:]``. 61 62 63 .. method:: list.index(x[, start[, end]]) 64 :noindex: 65 66 Return zero-based index in the list of the first item whose value is *x*. 67 Raises a :exc:`ValueError` if there is no such item. 68 69 The optional arguments *start* and *end* are interpreted as in the slice 70 notation and are used to limit the search to a particular subsequence of 71 the list. The returned index is computed relative to the beginning of the full 72 sequence rather than the *start* argument. 73 74 75 .. method:: list.count(x) 76 :noindex: 77 78 Return the number of times *x* appears in the list. 79 80 81 .. method:: list.sort(key=None, reverse=False) 82 :noindex: 83 84 Sort the items of the list in place (the arguments can be used for sort 85 customization, see :func:`sorted` for their explanation). 86 87 88 .. method:: list.reverse() 89 :noindex: 90 91 Reverse the elements of the list in place. 92 93 94 .. method:: list.copy() 95 :noindex: 96 97 Return a shallow copy of the list. Equivalent to ``a[:]``. 98 99 100 An example that uses most of the list methods:: 101 102 >>> fruits = ['orange', 'apple', 'pear', 'banana', 'kiwi', 'apple', 'banana'] 103 >>> fruits.count('apple') 104 2 105 >>> fruits.count('tangerine') 106 0 107 >>> fruits.index('banana') 108 3 109 >>> fruits.index('banana', 4) # Find next banana starting a position 4 110 6 111 >>> fruits.reverse() 112 >>> fruits 113 ['banana', 'apple', 'kiwi', 'banana', 'pear', 'apple', 'orange'] 114 >>> fruits.append('grape') 115 >>> fruits 116 ['banana', 'apple', 'kiwi', 'banana', 'pear', 'apple', 'orange', 'grape'] 117 >>> fruits.sort() 118 >>> fruits 119 ['apple', 'apple', 'banana', 'banana', 'grape', 'kiwi', 'orange', 'pear'] 120 >>> fruits.pop() 121 'pear' 122 123 You might have noticed that methods like ``insert``, ``remove`` or ``sort`` that 124 only modify the list have no return value printed -- they return the default 125 ``None``. [1]_ This is a design principle for all mutable data structures in 126 Python. 127 128 129 .. _tut-lists-as-stacks: 130 131 Using Lists as Stacks 132 --------------------- 133 134 .. sectionauthor:: Ka-Ping Yee <ping (a] lfw.org> 135 136 137 The list methods make it very easy to use a list as a stack, where the last 138 element added is the first element retrieved ("last-in, first-out"). To add an 139 item to the top of the stack, use :meth:`append`. To retrieve an item from the 140 top of the stack, use :meth:`pop` without an explicit index. For example:: 141 142 >>> stack = [3, 4, 5] 143 >>> stack.append(6) 144 >>> stack.append(7) 145 >>> stack 146 [3, 4, 5, 6, 7] 147 >>> stack.pop() 148 7 149 >>> stack 150 [3, 4, 5, 6] 151 >>> stack.pop() 152 6 153 >>> stack.pop() 154 5 155 >>> stack 156 [3, 4] 157 158 159 .. _tut-lists-as-queues: 160 161 Using Lists as Queues 162 --------------------- 163 164 .. sectionauthor:: Ka-Ping Yee <ping (a] lfw.org> 165 166 It is also possible to use a list as a queue, where the first element added is 167 the first element retrieved ("first-in, first-out"); however, lists are not 168 efficient for this purpose. While appends and pops from the end of list are 169 fast, doing inserts or pops from the beginning of a list is slow (because all 170 of the other elements have to be shifted by one). 171 172 To implement a queue, use :class:`collections.deque` which was designed to 173 have fast appends and pops from both ends. For example:: 174 175 >>> from collections import deque 176 >>> queue = deque(["Eric", "John", "Michael"]) 177 >>> queue.append("Terry") # Terry arrives 178 >>> queue.append("Graham") # Graham arrives 179 >>> queue.popleft() # The first to arrive now leaves 180 'Eric' 181 >>> queue.popleft() # The second to arrive now leaves 182 'John' 183 >>> queue # Remaining queue in order of arrival 184 deque(['Michael', 'Terry', 'Graham']) 185 186 187 .. _tut-listcomps: 188 189 List Comprehensions 190 ------------------- 191 192 List comprehensions provide a concise way to create lists. 193 Common applications are to make new lists where each element is the result of 194 some operations applied to each member of another sequence or iterable, or to 195 create a subsequence of those elements that satisfy a certain condition. 196 197 For example, assume we want to create a list of squares, like:: 198 199 >>> squares = [] 200 >>> for x in range(10): 201 ... squares.append(x**2) 202 ... 203 >>> squares 204 [0, 1, 4, 9, 16, 25, 36, 49, 64, 81] 205 206 Note that this creates (or overwrites) a variable named ``x`` that still exists 207 after the loop completes. We can calculate the list of squares without any 208 side effects using:: 209 210 squares = list(map(lambda x: x**2, range(10))) 211 212 or, equivalently:: 213 214 squares = [x**2 for x in range(10)] 215 216 which is more concise and readable. 217 218 A list comprehension consists of brackets containing an expression followed 219 by a :keyword:`for` clause, then zero or more :keyword:`for` or :keyword:`if` 220 clauses. The result will be a new list resulting from evaluating the expression 221 in the context of the :keyword:`for` and :keyword:`if` clauses which follow it. 222 For example, this listcomp combines the elements of two lists if they are not 223 equal:: 224 225 >>> [(x, y) for x in [1,2,3] for y in [3,1,4] if x != y] 226 [(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)] 227 228 and it's equivalent to:: 229 230 >>> combs = [] 231 >>> for x in [1,2,3]: 232 ... for y in [3,1,4]: 233 ... if x != y: 234 ... combs.append((x, y)) 235 ... 236 >>> combs 237 [(1, 3), (1, 4), (2, 3), (2, 1), (2, 4), (3, 1), (3, 4)] 238 239 Note how the order of the :keyword:`for` and :keyword:`if` statements is the 240 same in both these snippets. 241 242 If the expression is a tuple (e.g. the ``(x, y)`` in the previous example), 243 it must be parenthesized. :: 244 245 >>> vec = [-4, -2, 0, 2, 4] 246 >>> # create a new list with the values doubled 247 >>> [x*2 for x in vec] 248 [-8, -4, 0, 4, 8] 249 >>> # filter the list to exclude negative numbers 250 >>> [x for x in vec if x >= 0] 251 [0, 2, 4] 252 >>> # apply a function to all the elements 253 >>> [abs(x) for x in vec] 254 [4, 2, 0, 2, 4] 255 >>> # call a method on each element 256 >>> freshfruit = [' banana', ' loganberry ', 'passion fruit '] 257 >>> [weapon.strip() for weapon in freshfruit] 258 ['banana', 'loganberry', 'passion fruit'] 259 >>> # create a list of 2-tuples like (number, square) 260 >>> [(x, x**2) for x in range(6)] 261 [(0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)] 262 >>> # the tuple must be parenthesized, otherwise an error is raised 263 >>> [x, x**2 for x in range(6)] 264 File "<stdin>", line 1, in ? 265 [x, x**2 for x in range(6)] 266 ^ 267 SyntaxError: invalid syntax 268 >>> # flatten a list using a listcomp with two 'for' 269 >>> vec = [[1,2,3], [4,5,6], [7,8,9]] 270 >>> [num for elem in vec for num in elem] 271 [1, 2, 3, 4, 5, 6, 7, 8, 9] 272 273 List comprehensions can contain complex expressions and nested functions:: 274 275 >>> from math import pi 276 >>> [str(round(pi, i)) for i in range(1, 6)] 277 ['3.1', '3.14', '3.142', '3.1416', '3.14159'] 278 279 Nested List Comprehensions 280 -------------------------- 281 282 The initial expression in a list comprehension can be any arbitrary expression, 283 including another list comprehension. 284 285 Consider the following example of a 3x4 matrix implemented as a list of 286 3 lists of length 4:: 287 288 >>> matrix = [ 289 ... [1, 2, 3, 4], 290 ... [5, 6, 7, 8], 291 ... [9, 10, 11, 12], 292 ... ] 293 294 The following list comprehension will transpose rows and columns:: 295 296 >>> [[row[i] for row in matrix] for i in range(4)] 297 [[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]] 298 299 As we saw in the previous section, the nested listcomp is evaluated in 300 the context of the :keyword:`for` that follows it, so this example is 301 equivalent to:: 302 303 >>> transposed = [] 304 >>> for i in range(4): 305 ... transposed.append([row[i] for row in matrix]) 306 ... 307 >>> transposed 308 [[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]] 309 310 which, in turn, is the same as:: 311 312 >>> transposed = [] 313 >>> for i in range(4): 314 ... # the following 3 lines implement the nested listcomp 315 ... transposed_row = [] 316 ... for row in matrix: 317 ... transposed_row.append(row[i]) 318 ... transposed.append(transposed_row) 319 ... 320 >>> transposed 321 [[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]] 322 323 In the real world, you should prefer built-in functions to complex flow statements. 324 The :func:`zip` function would do a great job for this use case:: 325 326 >>> list(zip(*matrix)) 327 [(1, 5, 9), (2, 6, 10), (3, 7, 11), (4, 8, 12)] 328 329 See :ref:`tut-unpacking-arguments` for details on the asterisk in this line. 330 331 .. _tut-del: 332 333 The :keyword:`del` statement 334 ============================ 335 336 There is a way to remove an item from a list given its index instead of its 337 value: the :keyword:`del` statement. This differs from the :meth:`pop` method 338 which returns a value. The :keyword:`del` statement can also be used to remove 339 slices from a list or clear the entire list (which we did earlier by assignment 340 of an empty list to the slice). For example:: 341 342 >>> a = [-1, 1, 66.25, 333, 333, 1234.5] 343 >>> del a[0] 344 >>> a 345 [1, 66.25, 333, 333, 1234.5] 346 >>> del a[2:4] 347 >>> a 348 [1, 66.25, 1234.5] 349 >>> del a[:] 350 >>> a 351 [] 352 353 :keyword:`del` can also be used to delete entire variables:: 354 355 >>> del a 356 357 Referencing the name ``a`` hereafter is an error (at least until another value 358 is assigned to it). We'll find other uses for :keyword:`del` later. 359 360 361 .. _tut-tuples: 362 363 Tuples and Sequences 364 ==================== 365 366 We saw that lists and strings have many common properties, such as indexing and 367 slicing operations. They are two examples of *sequence* data types (see 368 :ref:`typesseq`). Since Python is an evolving language, other sequence data 369 types may be added. There is also another standard sequence data type: the 370 *tuple*. 371 372 A tuple consists of a number of values separated by commas, for instance:: 373 374 >>> t = 12345, 54321, 'hello!' 375 >>> t[0] 376 12345 377 >>> t 378 (12345, 54321, 'hello!') 379 >>> # Tuples may be nested: 380 ... u = t, (1, 2, 3, 4, 5) 381 >>> u 382 ((12345, 54321, 'hello!'), (1, 2, 3, 4, 5)) 383 >>> # Tuples are immutable: 384 ... t[0] = 88888 385 Traceback (most recent call last): 386 File "<stdin>", line 1, in <module> 387 TypeError: 'tuple' object does not support item assignment 388 >>> # but they can contain mutable objects: 389 ... v = ([1, 2, 3], [3, 2, 1]) 390 >>> v 391 ([1, 2, 3], [3, 2, 1]) 392 393 394 As you see, on output tuples are always enclosed in parentheses, so that nested 395 tuples are interpreted correctly; they may be input with or without surrounding 396 parentheses, although often parentheses are necessary anyway (if the tuple is 397 part of a larger expression). It is not possible to assign to the individual 398 items of a tuple, however it is possible to create tuples which contain mutable 399 objects, such as lists. 400 401 Though tuples may seem similar to lists, they are often used in different 402 situations and for different purposes. 403 Tuples are :term:`immutable`, and usually contain a heterogeneous sequence of 404 elements that are accessed via unpacking (see later in this section) or indexing 405 (or even by attribute in the case of :func:`namedtuples <collections.namedtuple>`). 406 Lists are :term:`mutable`, and their elements are usually homogeneous and are 407 accessed by iterating over the list. 408 409 A special problem is the construction of tuples containing 0 or 1 items: the 410 syntax has some extra quirks to accommodate these. Empty tuples are constructed 411 by an empty pair of parentheses; a tuple with one item is constructed by 412 following a value with a comma (it is not sufficient to enclose a single value 413 in parentheses). Ugly, but effective. For example:: 414 415 >>> empty = () 416 >>> singleton = 'hello', # <-- note trailing comma 417 >>> len(empty) 418 0 419 >>> len(singleton) 420 1 421 >>> singleton 422 ('hello',) 423 424 The statement ``t = 12345, 54321, 'hello!'`` is an example of *tuple packing*: 425 the values ``12345``, ``54321`` and ``'hello!'`` are packed together in a tuple. 426 The reverse operation is also possible:: 427 428 >>> x, y, z = t 429 430 This is called, appropriately enough, *sequence unpacking* and works for any 431 sequence on the right-hand side. Sequence unpacking requires that there are as 432 many variables on the left side of the equals sign as there are elements in the 433 sequence. Note that multiple assignment is really just a combination of tuple 434 packing and sequence unpacking. 435 436 437 .. _tut-sets: 438 439 Sets 440 ==== 441 442 Python also includes a data type for *sets*. A set is an unordered collection 443 with no duplicate elements. Basic uses include membership testing and 444 eliminating duplicate entries. Set objects also support mathematical operations 445 like union, intersection, difference, and symmetric difference. 446 447 Curly braces or the :func:`set` function can be used to create sets. Note: to 448 create an empty set you have to use ``set()``, not ``{}``; the latter creates an 449 empty dictionary, a data structure that we discuss in the next section. 450 451 Here is a brief demonstration:: 452 453 >>> basket = {'apple', 'orange', 'apple', 'pear', 'orange', 'banana'} 454 >>> print(basket) # show that duplicates have been removed 455 {'orange', 'banana', 'pear', 'apple'} 456 >>> 'orange' in basket # fast membership testing 457 True 458 >>> 'crabgrass' in basket 459 False 460 461 >>> # Demonstrate set operations on unique letters from two words 462 ... 463 >>> a = set('abracadabra') 464 >>> b = set('alacazam') 465 >>> a # unique letters in a 466 {'a', 'r', 'b', 'c', 'd'} 467 >>> a - b # letters in a but not in b 468 {'r', 'd', 'b'} 469 >>> a | b # letters in either a or b 470 {'a', 'c', 'r', 'd', 'b', 'm', 'z', 'l'} 471 >>> a & b # letters in both a and b 472 {'a', 'c'} 473 >>> a ^ b # letters in a or b but not both 474 {'r', 'd', 'b', 'm', 'z', 'l'} 475 476 Similarly to :ref:`list comprehensions <tut-listcomps>`, set comprehensions 477 are also supported:: 478 479 >>> a = {x for x in 'abracadabra' if x not in 'abc'} 480 >>> a 481 {'r', 'd'} 482 483 484 .. _tut-dictionaries: 485 486 Dictionaries 487 ============ 488 489 Another useful data type built into Python is the *dictionary* (see 490 :ref:`typesmapping`). Dictionaries are sometimes found in other languages as 491 "associative memories" or "associative arrays". Unlike sequences, which are 492 indexed by a range of numbers, dictionaries are indexed by *keys*, which can be 493 any immutable type; strings and numbers can always be keys. Tuples can be used 494 as keys if they contain only strings, numbers, or tuples; if a tuple contains 495 any mutable object either directly or indirectly, it cannot be used as a key. 496 You can't use lists as keys, since lists can be modified in place using index 497 assignments, slice assignments, or methods like :meth:`append` and 498 :meth:`extend`. 499 500 It is best to think of a dictionary as an unordered set of *key: value* pairs, 501 with the requirement that the keys are unique (within one dictionary). A pair of 502 braces creates an empty dictionary: ``{}``. Placing a comma-separated list of 503 key:value pairs within the braces adds initial key:value pairs to the 504 dictionary; this is also the way dictionaries are written on output. 505 506 The main operations on a dictionary are storing a value with some key and 507 extracting the value given the key. It is also possible to delete a key:value 508 pair with ``del``. If you store using a key that is already in use, the old 509 value associated with that key is forgotten. It is an error to extract a value 510 using a non-existent key. 511 512 Performing ``list(d.keys())`` on a dictionary returns a list of all the keys 513 used in the dictionary, in arbitrary order (if you want it sorted, just use 514 ``sorted(d.keys())`` instead). [2]_ To check whether a single key is in the 515 dictionary, use the :keyword:`in` keyword. 516 517 Here is a small example using a dictionary:: 518 519 >>> tel = {'jack': 4098, 'sape': 4139} 520 >>> tel['guido'] = 4127 521 >>> tel 522 {'sape': 4139, 'guido': 4127, 'jack': 4098} 523 >>> tel['jack'] 524 4098 525 >>> del tel['sape'] 526 >>> tel['irv'] = 4127 527 >>> tel 528 {'guido': 4127, 'irv': 4127, 'jack': 4098} 529 >>> list(tel.keys()) 530 ['irv', 'guido', 'jack'] 531 >>> sorted(tel.keys()) 532 ['guido', 'irv', 'jack'] 533 >>> 'guido' in tel 534 True 535 >>> 'jack' not in tel 536 False 537 538 The :func:`dict` constructor builds dictionaries directly from sequences of 539 key-value pairs:: 540 541 >>> dict([('sape', 4139), ('guido', 4127), ('jack', 4098)]) 542 {'sape': 4139, 'jack': 4098, 'guido': 4127} 543 544 In addition, dict comprehensions can be used to create dictionaries from 545 arbitrary key and value expressions:: 546 547 >>> {x: x**2 for x in (2, 4, 6)} 548 {2: 4, 4: 16, 6: 36} 549 550 When the keys are simple strings, it is sometimes easier to specify pairs using 551 keyword arguments:: 552 553 >>> dict(sape=4139, guido=4127, jack=4098) 554 {'sape': 4139, 'jack': 4098, 'guido': 4127} 555 556 557 .. _tut-loopidioms: 558 559 Looping Techniques 560 ================== 561 562 When looping through dictionaries, the key and corresponding value can be 563 retrieved at the same time using the :meth:`items` method. :: 564 565 >>> knights = {'gallahad': 'the pure', 'robin': 'the brave'} 566 >>> for k, v in knights.items(): 567 ... print(k, v) 568 ... 569 gallahad the pure 570 robin the brave 571 572 When looping through a sequence, the position index and corresponding value can 573 be retrieved at the same time using the :func:`enumerate` function. :: 574 575 >>> for i, v in enumerate(['tic', 'tac', 'toe']): 576 ... print(i, v) 577 ... 578 0 tic 579 1 tac 580 2 toe 581 582 To loop over two or more sequences at the same time, the entries can be paired 583 with the :func:`zip` function. :: 584 585 >>> questions = ['name', 'quest', 'favorite color'] 586 >>> answers = ['lancelot', 'the holy grail', 'blue'] 587 >>> for q, a in zip(questions, answers): 588 ... print('What is your {0}? It is {1}.'.format(q, a)) 589 ... 590 What is your name? It is lancelot. 591 What is your quest? It is the holy grail. 592 What is your favorite color? It is blue. 593 594 To loop over a sequence in reverse, first specify the sequence in a forward 595 direction and then call the :func:`reversed` function. :: 596 597 >>> for i in reversed(range(1, 10, 2)): 598 ... print(i) 599 ... 600 9 601 7 602 5 603 3 604 1 605 606 To loop over a sequence in sorted order, use the :func:`sorted` function which 607 returns a new sorted list while leaving the source unaltered. :: 608 609 >>> basket = ['apple', 'orange', 'apple', 'pear', 'orange', 'banana'] 610 >>> for f in sorted(set(basket)): 611 ... print(f) 612 ... 613 apple 614 banana 615 orange 616 pear 617 618 It is sometimes tempting to change a list while you are looping over it; 619 however, it is often simpler and safer to create a new list instead. :: 620 621 >>> import math 622 >>> raw_data = [56.2, float('NaN'), 51.7, 55.3, 52.5, float('NaN'), 47.8] 623 >>> filtered_data = [] 624 >>> for value in raw_data: 625 ... if not math.isnan(value): 626 ... filtered_data.append(value) 627 ... 628 >>> filtered_data 629 [56.2, 51.7, 55.3, 52.5, 47.8] 630 631 632 .. _tut-conditions: 633 634 More on Conditions 635 ================== 636 637 The conditions used in ``while`` and ``if`` statements can contain any 638 operators, not just comparisons. 639 640 The comparison operators ``in`` and ``not in`` check whether a value occurs 641 (does not occur) in a sequence. The operators ``is`` and ``is not`` compare 642 whether two objects are really the same object; this only matters for mutable 643 objects like lists. All comparison operators have the same priority, which is 644 lower than that of all numerical operators. 645 646 Comparisons can be chained. For example, ``a < b == c`` tests whether ``a`` is 647 less than ``b`` and moreover ``b`` equals ``c``. 648 649 Comparisons may be combined using the Boolean operators ``and`` and ``or``, and 650 the outcome of a comparison (or of any other Boolean expression) may be negated 651 with ``not``. These have lower priorities than comparison operators; between 652 them, ``not`` has the highest priority and ``or`` the lowest, so that ``A and 653 not B or C`` is equivalent to ``(A and (not B)) or C``. As always, parentheses 654 can be used to express the desired composition. 655 656 The Boolean operators ``and`` and ``or`` are so-called *short-circuit* 657 operators: their arguments are evaluated from left to right, and evaluation 658 stops as soon as the outcome is determined. For example, if ``A`` and ``C`` are 659 true but ``B`` is false, ``A and B and C`` does not evaluate the expression 660 ``C``. When used as a general value and not as a Boolean, the return value of a 661 short-circuit operator is the last evaluated argument. 662 663 It is possible to assign the result of a comparison or other Boolean expression 664 to a variable. For example, :: 665 666 >>> string1, string2, string3 = '', 'Trondheim', 'Hammer Dance' 667 >>> non_null = string1 or string2 or string3 668 >>> non_null 669 'Trondheim' 670 671 Note that in Python, unlike C, assignment cannot occur inside expressions. C 672 programmers may grumble about this, but it avoids a common class of problems 673 encountered in C programs: typing ``=`` in an expression when ``==`` was 674 intended. 675 676 677 .. _tut-comparing: 678 679 Comparing Sequences and Other Types 680 =================================== 681 682 Sequence objects may be compared to other objects with the same sequence type. 683 The comparison uses *lexicographical* ordering: first the first two items are 684 compared, and if they differ this determines the outcome of the comparison; if 685 they are equal, the next two items are compared, and so on, until either 686 sequence is exhausted. If two items to be compared are themselves sequences of 687 the same type, the lexicographical comparison is carried out recursively. If 688 all items of two sequences compare equal, the sequences are considered equal. 689 If one sequence is an initial sub-sequence of the other, the shorter sequence is 690 the smaller (lesser) one. Lexicographical ordering for strings uses the Unicode 691 code point number to order individual characters. Some examples of comparisons 692 between sequences of the same type:: 693 694 (1, 2, 3) < (1, 2, 4) 695 [1, 2, 3] < [1, 2, 4] 696 'ABC' < 'C' < 'Pascal' < 'Python' 697 (1, 2, 3, 4) < (1, 2, 4) 698 (1, 2) < (1, 2, -1) 699 (1, 2, 3) == (1.0, 2.0, 3.0) 700 (1, 2, ('aa', 'ab')) < (1, 2, ('abc', 'a'), 4) 701 702 Note that comparing objects of different types with ``<`` or ``>`` is legal 703 provided that the objects have appropriate comparison methods. For example, 704 mixed numeric types are compared according to their numeric value, so 0 equals 705 0.0, etc. Otherwise, rather than providing an arbitrary ordering, the 706 interpreter will raise a :exc:`TypeError` exception. 707 708 709 .. rubric:: Footnotes 710 711 .. [1] Other languages may return the mutated object, which allows method 712 chaining, such as ``d->insert("a")->remove("b")->sort();``. 713 714 .. [2] Calling ``d.keys()`` will return a :dfn:`dictionary view` object. It 715 supports operations like membership test and iteration, but its contents 716 are not independent of the original dictionary -- it is only a *view*. 717