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2to3.html
63.71
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__builtin__.html
11.79
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__future__.html
15.58
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__main__.html
8.33
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_winreg.html
73.99
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abc.html
26.82
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aepack.html
15.47
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aetools.html
18.79
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aetypes.html
27.08
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aifc.html
29.59
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al.html
22.13
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allos.html
35.48
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anydbm.html
19.31
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archiving.html
10.64
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argparse.html
269.59
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array.html
35.35
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ast.html
42.42
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asynchat.html
35.84
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asyncore.html
43.22
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atexit.html
19.23
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audioop.html
41.32
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autogil.html
9.77
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base64.html
24.8
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basehttpserver.html
40.6
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bastion.html
13.02
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bdb.html
50.06
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binascii.html
26.64
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binhex.html
12.66
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bisect.html
28.52
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bsddb.html
32.02
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bz2.html
31.92
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calendar.html
50.16
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carbon.html
54.14
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cd.html
35.24
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cgi.html
58.4
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cgihttpserver.html
15.12
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cgitb.html
13.5
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chunk.html
17.41
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cmath.html
32.41
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cmd.html
32.69
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code.html
28.92
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codecs.html
125.92
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codeop.html
16.42
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collections.html
150.36
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colorpicker.html
9.02
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colorsys.html
14.38
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commands.html
16.63
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compileall.html
21.18
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compiler.html
78.14
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configparser.html
73.92
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constants.html
14.68
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contextlib.html
22.91
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cookie.html
45.38
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cookielib.html
102.78
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copy.html
14.21
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copy_reg.html
15.82
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crypt.html
11.62
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crypto.html
8.35
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csv.html
82.79
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ctypes.html
280.57
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curses.ascii.html
28.97
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curses.html
200.94
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curses.panel.html
18.43
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custominterp.html
8.59
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datatypes.html
18.84
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datetime.html
261.02
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dbhash.html
18.4
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dbm.html
14.75
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debug.html
11.28
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decimal.html
239.14
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development.html
15.27
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difflib.html
96.93
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dircache.html
13.66
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dis.html
96.52
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distribution.html
8.27
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distutils.html
10.97
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dl.html
19.27
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doctest.html
193.18
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docxmlrpcserver.html
20.02
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dumbdbm.html
16.74
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dummy_thread.html
11.04
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dummy_threading.html
9.96
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easydialogs.html
38.83
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email-examples.html
47.2
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email.charset.html
32.45
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email.encoders.html
14.09
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email.errors.html
19.2
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email.generator.html
24.78
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email.header.html
31.12
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email.html
55.3
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email.iterators.html
14.22
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email.message.html
74.91
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email.mime.html
34.51
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email.parser.html
37.09
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email.utils.html
30.04
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ensurepip.html
20.21
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errno.html
52.31
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exceptions.html
73.4
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fcntl.html
27.85
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filecmp.html
26.49
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fileformats.html
10.21
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fileinput.html
29.36
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filesys.html
11.55
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fl.html
71.58
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fm.html
15
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fnmatch.html
17.78
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formatter.html
43.91
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fpectl.html
17.84
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fpformat.html
12.65
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fractions.html
27.17
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framework.html
44.24
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frameworks.html
8.11
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ftplib.html
56.56
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functions.html
216.84
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functools.html
31.06
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future_builtins.html
15.9
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gc.html
30.74
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gdbm.html
19.35
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gensuitemodule.html
14.54
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getopt.html
26.56
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getpass.html
12.5
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gettext.html
91.32
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gl.html
26.71
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glob.html
15.42
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grp.html
12.33
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gzip.html
21.95
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hashlib.html
27.4
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heapq.html
36.72
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hmac.html
15.97
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hotshot.html
22.69
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htmllib.html
29.9
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htmlparser.html
45.11
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httplib.html
78.55
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i18n.html
10.61
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ic.html
22.03
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idle.html
45.74
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imageop.html
20.94
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imaplib.html
69.9
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imgfile.html
14.91
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imghdr.html
13.43
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imp.html
41.48
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importlib.html
10.27
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imputil.html
36.11
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index.html
82.54
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inspect.html
64.31
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internet.html
26.77
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intro.html
9.76
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io.html
122.3
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ipc.html
17.18
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itertools.html
129.91
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jpeg.html
15.36
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json.html
79.09
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keyword.html
9.27
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language.html
12.35
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linecache.html
12.7
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locale.html
68.54
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logging.config.html
82.23
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logging.handlers.html
91.96
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logging.html
123.15
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mac.html
24.49
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macos.html
18.51
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macosa.html
14.55
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macostools.html
19.67
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macpath.html
9.19
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mailbox.html
185.53
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mailcap.html
15.3
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markup.html
20.37
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marshal.html
19.88
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math.html
50.52
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md5.html
16.65
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mhlib.html
30.04
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mimetools.html
23.84
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mimetypes.html
35.82
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mimewriter.html
18.19
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mimify.html
16.96
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miniaeframe.html
14.5
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misc.html
7.77
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mm.html
10.19
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mmap.html
33.52
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modulefinder.html
19.85
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modules.html
9.68
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msilib.html
72.78
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msvcrt.html
24.1
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multifile.html
28.82
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multiprocessing.html
423.97
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mutex.html
13.56
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netdata.html
19.28
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netrc.html
15.51
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new.html
16.1
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nis.html
13.19
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nntplib.html
51.08
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numbers.html
40.91
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numeric.html
14.85
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operator.html
118.32
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optparse.html
251.08
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os.html
270.49
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os.path.html
48.87
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ossaudiodev.html
49.79
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othergui.html
9.98
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parser.html
44.52
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pdb.html
41.44
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persistence.html
16.25
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pickle.html
107.94
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pickletools.html
13.21
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pipes.html
21.85
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pkgutil.html
30.59
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platform.html
40.14
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plistlib.html
20.96
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popen2.html
30.13
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poplib.html
27.93
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posix.html
17.27
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posixfile.html
23.68
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pprint.html
36.42
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profile.html
76.65
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pty.html
11.42
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pwd.html
13.53
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py_compile.html
13.33
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pyclbr.html
18.14
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pydoc.html
14.33
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pyexpat.html
93.28
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python.html
13.53
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queue.html
29.64
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quopri.html
14.5
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random.html
47.78
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re.html
163.11
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readline.html
41.2
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repr.html
24.57
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resource.html
30.86
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restricted.html
12.69
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rexec.html
43.59
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rfc822.html
51.25
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rlcompleter.html
15.29
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robotparser.html
15.01
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runpy.html
23.55
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sched.html
21.76
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scrolledtext.html
10.67
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select.html
50.17
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sets.html
39.92
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sgi.html
11.09
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sgmllib.html
38.77
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sha.html
14.55
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shelve.html
32.93
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shlex.html
38.43
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shutil.html
49.49
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signal.html
36.52
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simplehttpserver.html
21.57
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simplexmlrpcserver.html
40.41
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site.html
29
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smtpd.html
15.64
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smtplib.html
51.86
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sndhdr.html
12.05
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socket.html
126.94
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socketserver.html
81.38
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someos.html
17.09
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spwd.html
12.25
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sqlite3.html
154.12
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ssl.html
214.5
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stat.html
41.11
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statvfs.html
13.24
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stdtypes.html
309.83
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string.html
129.58
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stringio.html
21.1
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stringprep.html
21.4
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strings.html
16.42
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struct.html
47.68
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subprocess.html
117
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sun.html
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sunau.html
35.43
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sunaudio.html
21.05
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symbol.html
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symtable.html
29.03
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sys.html
118.12
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sysconfig.html
28.8
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syslog.html
21.29
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tabnanny.html
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tarfile.html
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telnetlib.html
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tempfile.html
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termios.html
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test.html
61.42
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textwrap.html
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thread.html
22.67
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threading.html
92.04
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time.html
65.55
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timeit.html
44.38
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tix.html
56.73
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tk.html
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tkinter.html
86.67
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token.html
27.31
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tokenize.html
21.69
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trace.html
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traceback.html
44.22
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ttk.html
123.83
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tty.html
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turtle.html
246.17
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types.html
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undoc.html
25.54
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unicodedata.html
22.64
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unittest.html
246.75
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unix.html
11.9
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urllib.html
71.61
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urllib2.html
128.77
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urlparse.html
49.04
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user.html
13.41
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userdict.html
32.96
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uu.html
13.25
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uuid.html
33.55
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warnings.html
51.86
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wave.html
29.08
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weakref.html
41.14
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webbrowser.html
29.53
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whichdb.html
10.44
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windows.html
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winsound.html
22.56
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wsgiref.html
94.38
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xdrlib.html
38.05
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xml.dom.html
110.39
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xml.dom.minidom.html
45.23
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xml.dom.pulldom.html
16.32
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xml.etree.elementtree.html
124.2
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xml.html
18.76
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xml.sax.handler.html
47.5
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xml.sax.html
26.04
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xml.sax.reader.html
51.4
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xml.sax.utils.html
18.11
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xmlrpclib.html
71.79
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zipfile.html
67.26
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zipimport.html
24.32
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zlib.html
34.41
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<!DOCTYPE html> <html> <head> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" /> <title>8.5. bisect — Array bisection algorithm — Python 2.7.18 documentation</title> <link rel="stylesheet" type="text/css" href="../_static/pygments.css" /> <link rel="stylesheet" type="text/css" href="../_static/classic.css" /> <script data-url_root="../" id="documentation_options" src="../_static/documentation_options.js"></script> <script src="../_static/jquery.js"></script> <script src="../_static/underscore.js"></script> <script src="../_static/doctools.js"></script> <script src="../_static/sidebar.js"></script> <link rel="search" type="application/opensearchdescription+xml" title="Search within Python 2.7.18 documentation" href="../_static/opensearch.xml"/> <link rel="author" title="About these documents" href="../about.html" /> <link rel="index" title="Index" href="../genindex.html" /> <link rel="search" title="Search" href="../search.html" /> <link rel="copyright" title="Copyright" href="../copyright.html" /> <link rel="next" title="8.6. array — Efficient arrays of numeric values" href="array.html" /> <link rel="prev" title="8.4. heapq — Heap queue algorithm" href="heapq.html" /> <link rel="shortcut icon" type="image/png" href="../_static/py.png" /> <link rel="canonical" href="file:///usr/share/doc/python2.7/html/library/bisect.html" /> <script type="text/javascript" src="../_static/copybutton.js"></script> </head><body> <div id="outdated-warning" style="padding: .5em; text-align: center; background-color: #FFBABA; color: #6A0E0E;"> This document is for an old version of Python that is <a href="https://devguide.python.org/devcycle/#end-of-life-branches">no longer supported</a>. You should install the python3 and python3-doc packages and read the <a href="file:///usr/share/doc/python3-doc/html/library/bisect.html"> Python documentation for the Python3 version packaged in this release</a>. </div> <div class="related" role="navigation" aria-label="related navigation"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" accesskey="I">index</a></li> <li class="right" > <a href="../py-modindex.html" title="Python Module Index" >modules</a> |</li> <li class="right" > <a href="array.html" title="8.6. array — Efficient arrays of numeric values" accesskey="N">next</a> |</li> <li class="right" > <a href="heapq.html" title="8.4. heapq — Heap queue algorithm" accesskey="P">previous</a> |</li> <li><img src="../_static/py.png" alt="" style="vertical-align: middle; margin-top: -1px"/></li> <li><a href="https://www.python.org/">Python</a> »</li> <li> <a href="../index.html">Python 2.7.18 documentation</a> » </li> <li class="nav-item nav-item-1"><a href="index.html" >The Python Standard Library</a> »</li> <li class="nav-item nav-item-2"><a href="datatypes.html" accesskey="U"><span class="section-number">8. </span>Data Types</a> »</li> <li class="nav-item nav-item-this"><a href=""><span class="section-number">8.5. </span><code class="xref py py-mod docutils literal notranslate"><span class="pre">bisect</span></code> — Array bisection algorithm</a></li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body" role="main"> <section id="module-bisect"> <span id="bisect-array-bisection-algorithm"></span><h1><span class="section-number">8.5. </span><a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-mod docutils literal notranslate"><span class="pre">bisect</span></code></a> — Array bisection algorithm<a class="headerlink" href="#module-bisect" title="Permalink to this headline">¶</a></h1> <div class="versionadded"> <p><span class="versionmodified added">New in version 2.1.</span></p> </div> <p><strong>Source code:</strong> <a class="reference external" href="https://github.com/python/cpython/tree/2.7/Lib/bisect.py">Lib/bisect.py</a></p> <hr class="docutils" /> <p>This module provides support for maintaining a list in sorted order without having to sort the list after each insertion. For long lists of items with expensive comparison operations, this can be an improvement over the more common approach. The module is called <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-mod docutils literal notranslate"><span class="pre">bisect</span></code></a> because it uses a basic bisection algorithm to do its work. The source code may be most useful as a working example of the algorithm (the boundary conditions are already right!).</p> <p>The following functions are provided:</p> <dl class="py function"> <dt class="sig sig-object py" id="bisect.bisect_left"> <span class="sig-prename descclassname"><span class="pre">bisect.</span></span><span class="sig-name descname"><span class="pre">bisect_left</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">len(a)</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.bisect_left" title="Permalink to this definition">¶</a></dt> <dd><p>Locate the insertion point for <em>x</em> in <em>a</em> to maintain sorted order. The parameters <em>lo</em> and <em>hi</em> may be used to specify a subset of the list which should be considered; by default the entire list is used. If <em>x</em> is already present in <em>a</em>, the insertion point will be before (to the left of) any existing entries. The return value is suitable for use as the first parameter to <code class="docutils literal notranslate"><span class="pre">list.insert()</span></code> assuming that <em>a</em> is already sorted.</p> <p>The returned insertion point <em>i</em> partitions the array <em>a</em> into two halves so that <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre"><</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[lo:i])</span></code> for the left side and <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre">>=</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[i:hi])</span></code> for the right side.</p> </dd></dl> <dl class="py function"> <dt class="sig sig-object py" id="bisect.bisect_right"> <span class="sig-prename descclassname"><span class="pre">bisect.</span></span><span class="sig-name descname"><span class="pre">bisect_right</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">len(a)</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.bisect_right" title="Permalink to this definition">¶</a></dt> <dt class="sig sig-object py" id="bisect.bisect"> <span class="sig-prename descclassname"><span class="pre">bisect.</span></span><span class="sig-name descname"><span class="pre">bisect</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">len(a)</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.bisect" title="Permalink to this definition">¶</a></dt> <dd><p>Similar to <a class="reference internal" href="#bisect.bisect_left" title="bisect.bisect_left"><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect_left()</span></code></a>, but returns an insertion point which comes after (to the right of) any existing entries of <em>x</em> in <em>a</em>.</p> <p>The returned insertion point <em>i</em> partitions the array <em>a</em> into two halves so that <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre"><=</span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[lo:i])</span></code> for the left side and <code class="docutils literal notranslate"><span class="pre">all(val</span> <span class="pre">></span> <span class="pre">x</span> <span class="pre">for</span> <span class="pre">val</span> <span class="pre">in</span> <span class="pre">a[i:hi])</span></code> for the right side.</p> </dd></dl> <dl class="py function"> <dt class="sig sig-object py" id="bisect.insort_left"> <span class="sig-prename descclassname"><span class="pre">bisect.</span></span><span class="sig-name descname"><span class="pre">insort_left</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">len(a)</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.insort_left" title="Permalink to this definition">¶</a></dt> <dd><p>Insert <em>x</em> in <em>a</em> in sorted order. This is equivalent to <code class="docutils literal notranslate"><span class="pre">a.insert(bisect.bisect_left(a,</span> <span class="pre">x,</span> <span class="pre">lo,</span> <span class="pre">hi),</span> <span class="pre">x)</span></code> assuming that <em>a</em> is already sorted. Keep in mind that the O(log n) search is dominated by the slow O(n) insertion step.</p> </dd></dl> <dl class="py function"> <dt class="sig sig-object py" id="bisect.insort_right"> <span class="sig-prename descclassname"><span class="pre">bisect.</span></span><span class="sig-name descname"><span class="pre">insort_right</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">len(a)</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.insort_right" title="Permalink to this definition">¶</a></dt> <dt class="sig sig-object py" id="bisect.insort"> <span class="sig-prename descclassname"><span class="pre">bisect.</span></span><span class="sig-name descname"><span class="pre">insort</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">lo</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">hi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">len(a)</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#bisect.insort" title="Permalink to this definition">¶</a></dt> <dd><p>Similar to <a class="reference internal" href="#bisect.insort_left" title="bisect.insort_left"><code class="xref py py-func docutils literal notranslate"><span class="pre">insort_left()</span></code></a>, but inserting <em>x</em> in <em>a</em> after any existing entries of <em>x</em>.</p> </dd></dl> <div class="admonition seealso"> <p class="admonition-title">See also</p> <p><a class="reference external" href="https://code.activestate.com/recipes/577197-sortedcollection/">SortedCollection recipe</a> that uses bisect to build a full-featured collection class with straight-forward search methods and support for a key-function. The keys are precomputed to save unnecessary calls to the key function during searches.</p> </div> <section id="searching-sorted-lists"> <h2><span class="section-number">8.5.1. </span>Searching Sorted Lists<a class="headerlink" href="#searching-sorted-lists" title="Permalink to this headline">¶</a></h2> <p>The above <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> functions are useful for finding insertion points but can be tricky or awkward to use for common searching tasks. The following five functions show how to transform them into the standard lookups for sorted lists:</p> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">index</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Locate the leftmost value exactly equal to x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_left</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="ow">and</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">x</span><span class="p">:</span> <span class="k">return</span> <span class="n">i</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_lt</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Find rightmost value less than x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_left</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span><span class="p">:</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_le</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Find rightmost value less than or equal to x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_right</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span><span class="p">:</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_gt</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Find leftmost value greater than x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_right</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">):</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> <span class="k">def</span> <span class="nf">find_ge</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span> <span class="s1">'Find leftmost item greater than or equal to x'</span> <span class="n">i</span> <span class="o">=</span> <span class="n">bisect_left</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">a</span><span class="p">):</span> <span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">raise</span> <span class="ne">ValueError</span> </pre></div> </div> </section> <section id="other-examples"> <h2><span class="section-number">8.5.2. </span>Other Examples<a class="headerlink" href="#other-examples" title="Permalink to this headline">¶</a></h2> <p id="bisect-example">The <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> function can be useful for numeric table lookups. This example uses <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> to look up a letter grade for an exam score (say) based on a set of ordered numeric breakpoints: 90 and up is an ‘A’, 80 to 89 is a ‘B’, and so on:</p> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">def</span> <span class="nf">grade</span><span class="p">(</span><span class="n">score</span><span class="p">,</span> <span class="n">breakpoints</span><span class="o">=</span><span class="p">[</span><span class="mi">60</span><span class="p">,</span> <span class="mi">70</span><span class="p">,</span> <span class="mi">80</span><span class="p">,</span> <span class="mi">90</span><span class="p">],</span> <span class="n">grades</span><span class="o">=</span><span class="s1">'FDCBA'</span><span class="p">):</span> <span class="go"> i = bisect(breakpoints, score)</span> <span class="go"> return grades[i]</span> <span class="gp">>>> </span><span class="p">[</span><span class="n">grade</span><span class="p">(</span><span class="n">score</span><span class="p">)</span> <span class="k">for</span> <span class="n">score</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">33</span><span class="p">,</span> <span class="mi">99</span><span class="p">,</span> <span class="mi">77</span><span class="p">,</span> <span class="mi">70</span><span class="p">,</span> <span class="mi">89</span><span class="p">,</span> <span class="mi">90</span><span class="p">,</span> <span class="mi">100</span><span class="p">]]</span> <span class="go">['F', 'A', 'C', 'C', 'B', 'A', 'A']</span> </pre></div> </div> <p>Unlike the <a class="reference internal" href="functions.html#sorted" title="sorted"><code class="xref py py-func docutils literal notranslate"><span class="pre">sorted()</span></code></a> function, it does not make sense for the <a class="reference internal" href="#module-bisect" title="bisect: Array bisection algorithms for binary searching."><code class="xref py py-func docutils literal notranslate"><span class="pre">bisect()</span></code></a> functions to have <em>key</em> or <em>reversed</em> arguments because that would lead to an inefficient design (successive calls to bisect functions would not “remember” all of the previous key lookups).</p> <p>Instead, it is better to search a list of precomputed keys to find the index of the record in question:</p> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">data</span> <span class="o">=</span> <span class="p">[(</span><span class="s1">'red'</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="s1">'blue'</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="s1">'yellow'</span><span class="p">,</span> <span class="mi">8</span><span class="p">),</span> <span class="p">(</span><span class="s1">'black'</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="gp">>>> </span><span class="n">data</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">r</span><span class="p">:</span> <span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="gp">>>> </span><span class="n">keys</span> <span class="o">=</span> <span class="p">[</span><span class="n">r</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="k">for</span> <span class="n">r</span> <span class="ow">in</span> <span class="n">data</span><span class="p">]</span> <span class="c1"># precomputed list of keys</span> <span class="gp">>>> </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">0</span><span class="p">)]</span> <span class="go">('black', 0)</span> <span class="gp">>>> </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span> <span class="go">('blue', 1)</span> <span class="gp">>>> </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">5</span><span class="p">)]</span> <span class="go">('red', 5)</span> <span class="gp">>>> </span><span class="n">data</span><span class="p">[</span><span class="n">bisect_left</span><span class="p">(</span><span class="n">keys</span><span class="p">,</span> <span class="mi">8</span><span class="p">)]</span> <span class="go">('yellow', 8)</span> </pre></div> </div> </section> </section> <div class="clearer"></div> </div> </div> </div> <div class="sphinxsidebar" role="navigation" aria-label="main navigation"> <div class="sphinxsidebarwrapper"> <h3><a href="../contents.html">Table of Contents</a></h3> <ul> <li><a class="reference internal" href="#">8.5. <code class="xref py py-mod docutils literal notranslate"><span class="pre">bisect</span></code> — Array bisection algorithm</a><ul> <li><a class="reference internal" href="#searching-sorted-lists">8.5.1. Searching Sorted Lists</a></li> <li><a class="reference internal" href="#other-examples">8.5.2. 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