YAPF is a Python formatter based on clang-format (developed by Daniel Jasper). In essence, the algorithm takes the code and calculates the best formatting that conforms to the configured style. It takes away a lot of the drudgery of maintaining your code.
The ultimate goal is that the code YAPF produces is as good as the code that a programmer would write if they were following the style guide.
Note YAPF is not an official Google product (experimental or otherwise), it is just code that happens to be owned by Google.
To install YAPF from PyPI:
$ pip install yapf
YAPF is still considered in “beta” stage, and the released version may change often; therefore, the best way to keep up-to-date with the latest development is to clone this repository or install directly from github:
$ pip install git+https://github.com/google/yapf.git
Note that if you intend to use YAPF as a command-line tool rather than as a library, installation is not necessary. YAPF supports being run as a directory by the Python interpreter. If you cloned/unzipped YAPF into DIR, it's possible to run:
$ PYTHONPATH=DIR python DIR/yapf [options] ...
YAPF is supported by multiple editors via community extensions or plugins. See Editor Support for more info.
YAPF supports Python 3.7+.
usage: yapf [-h] [-v] [-d | -i | -q] [-r | -l START-END] [-e PATTERN] [--style STYLE] [--style-help] [--no-local-style] [-p] [-m] [-vv] [files ...] Formatter for Python code. positional arguments: files reads from stdin when no files are specified. optional arguments: -h, --help show this help message and exit -v, --version show program's version number and exit -d, --diff print the diff for the fixed source -i, --in-place make changes to files in place -q, --quiet output nothing and set return value -r, --recursive run recursively over directories -l START-END, --lines START-END range of lines to reformat, one-based -e PATTERN, --exclude PATTERN patterns for files to exclude from formatting --style STYLE specify formatting style: either a style name (for example "pep8" or "google"), or the name of a file with style settings. The default is pep8 unless a .style.yapf or setup.cfg or pyproject.toml file located in the same directory as the source or one of its parent directories (for stdin, the current directory is used). --style-help show style settings and exit; this output can be saved to .style.yapf to make your settings permanent --no-local-style don't search for local style definition -p, --parallel run YAPF in parallel when formatting multiple files. -m, --print-modified print out file names of modified files -vv, --verbose print out file names while processing
Normally YAPF returns zero on successful program termination and non-zero otherwise.
If --diff is supplied, YAPF returns zero when no changes were necessary, non-zero otherwise (including program error). You can use this in a CI workflow to test that code has been YAPF-formatted.
In addition to exclude patterns provided on commandline, YAPF looks for additional patterns specified in a file named .yapfignore or pyproject.toml located in the working directory from which YAPF is invoked.
.yapfignore‘s syntax is similar to UNIX’s filename pattern matching:
* matches everything ? matches any single character [seq] matches any character in seq [!seq] matches any character not in seq
Note that no entry should begin with ./.
If you use pyproject.toml, exclude patterns are specified by ignore_patterns key in [tool.yapfignore] section. For example:
[tool.yapfignore] ignore_patterns = [ "temp/**/*.py", "temp2/*.py" ]
The formatting style used by YAPF is configurable and there are many “knobs” that can be used to tune how YAPF does formatting. See the style.py module for the full list.
To control the style, run YAPF with the --style argument. It accepts one of the predefined styles (e.g., pep8 or google), a path to a configuration file that specifies the desired style, or a dictionary of key/value pairs.
The config file is a simple listing of (case-insensitive) key = value pairs with a [style] heading. For example:
[style] based_on_style = pep8 spaces_before_comment = 4 split_before_logical_operator = true
The based_on_style setting determines which of the predefined styles this custom style is based on (think of it like subclassing). Four styles are predefined:
pep8 (default)google (based off of the Google Python Style Guide)yapf (for use with Google open source projects)facebookSee _STYLE_NAME_TO_FACTORY in style.py for details.
It's also possible to do the same on the command line with a dictionary. For example:
--style='{based_on_style: pep8, indent_width: 2}'
This will take the pep8 base style and modify it to have two space indentations.
YAPF will search for the formatting style in the following manner:
[style] section of a .style.yapf file in either the current directory or one of its parent directories.[yapf] section of a setup.cfg file in either the current directory or one of its parent directories.[tool.yapf] section of a pyproject.toml file in either the current directory or one of its parent directories.[style] section of a ~/.config/yapf/style file in your home directory.If none of those files are found, the default style PEP8 is used.
An example of the type of formatting that YAPF can do, it will take this ugly code:
x = { 'a':37,'b':42, 'c':927} y = 'hello ''world' z = 'hello '+'world' a = 'hello {}'.format('world') class foo ( object ): def f (self ): return 37*-+2 def g(self, x,y=42): return y def f ( a ) : return 37+-+a[42-x : y**3]
and reformat it into:
x = {'a': 37, 'b': 42, 'c': 927} y = 'hello ' 'world' z = 'hello ' + 'world' a = 'hello {}'.format('world') class foo(object): def f(self): return 37 * -+2 def g(self, x, y=42): return y def f(a): return 37 + -+a[42 - x:y**3]
The two main APIs for calling YAPF are FormatCode and FormatFile, these share several arguments which are described below:
>>> from yapf.yapflib.yapf_api import FormatCode # reformat a string of code >>> formatted_code, changed = FormatCode("f ( a = 1, b = 2 )") >>> formatted_code 'f(a=1, b=2)\n' >>> changed True
A style_config argument: Either a style name or a path to a file that contains formatting style settings. If None is specified, use the default style as set in style.DEFAULT_STYLE_FACTORY.
>>> FormatCode("def g():\n return True", style_config='pep8')[0] 'def g():\n return True\n'
A lines argument: A list of tuples of lines (ints), [start, end], that we want to format. The lines are 1-based indexed. It can be used by third-party code (e.g., IDEs) when reformatting a snippet of code rather than a whole file.
>>> FormatCode("def g( ):\n a=1\n b = 2\n return a==b", lines=[(1, 1), (2, 3)])[0] 'def g():\n a = 1\n b = 2\n return a==b\n'
A print_diff (bool): Instead of returning the reformatted source, return a diff that turns the formatted source into reformatted source.
>>> print(FormatCode("a==b", filename="foo.py", print_diff=True)[0]) --- foo.py (original) +++ foo.py (reformatted) @@ -1 +1 @@ -a==b +a == b
Note: the filename argument for FormatCode is what is inserted into the diff, the default is <unknown>.
FormatFile returns reformatted code from the passed file along with its encoding:
>>> from yapf.yapflib.yapf_api import FormatFile # reformat a file >>> print(open("foo.py").read()) # contents of file a==b >>> reformatted_code, encoding, changed = FormatFile("foo.py") >>> formatted_code 'a == b\n' >>> encoding 'utf-8' >>> changed True
The in_place argument saves the reformatted code back to the file:
>>> FormatFile("foo.py", in_place=True)[:2] (None, 'utf-8') >>> print(open("foo.py").read()) # contents of file (now fixed) a == b
Options:
usage: yapf-diff [-h] [-i] [-p NUM] [--regex PATTERN] [--iregex PATTERN][-v] [--style STYLE] [--binary BINARY] This script reads input from a unified diff and reformats all the changed lines. This is useful to reformat all the lines touched by a specific patch. Example usage for git/svn users: git diff -U0 --no-color --relative HEAD^ | yapf-diff -i svn diff --diff-cmd=diff -x-U0 | yapf-diff -p0 -i It should be noted that the filename contained in the diff is used unmodified to determine the source file to update. Users calling this script directly should be careful to ensure that the path in the diff is correct relative to the current working directory. optional arguments: -h, --help show this help message and exit -i, --in-place apply edits to files instead of displaying a diff -p NUM, --prefix NUM strip the smallest prefix containing P slashes --regex PATTERN custom pattern selecting file paths to reformat (case sensitive, overrides -iregex) --iregex PATTERN custom pattern selecting file paths to reformat (case insensitive, overridden by -regex) -v, --verbose be more verbose, ineffective without -i --style STYLE specify formatting style: either a style name (for example "pep8" or "google"), or the name of a file with style settings. The default is pep8 unless a .style.yapf or setup.cfg or pyproject.toml file located in the same directory as the source or one of its parent directories (for stdin, the current directory is used). --binary BINARY location of binary to use for YAPF
ALIGN_CLOSING_BRACKET_WITH_VISUAL_INDENTAlign closing bracket with visual indentation.
ALLOW_MULTILINE_LAMBDASAllow lambdas to be formatted on more than one line.
ALLOW_MULTILINE_DICTIONARY_KEYSAllow dictionary keys to exist on multiple lines. For example:
x = { ('this is the first element of a tuple', 'this is the second element of a tuple'): value, }
ALLOW_SPLIT_BEFORE_DEFAULT_OR_NAMED_ASSIGNSAllow splitting before a default / named assignment in an argument list.
ALLOW_SPLIT_BEFORE_DICT_VALUEAllow splits before the dictionary value.
ARITHMETIC_PRECEDENCE_INDICATIONLet spacing indicate operator precedence. For example:
a = 1 * 2 + 3 / 4 b = 1 / 2 - 3 * 4 c = (1 + 2) * (3 - 4) d = (1 - 2) / (3 + 4) e = 1 * 2 - 3 f = 1 + 2 + 3 + 4
will be formatted as follows to indicate precedence:
a = 1*2 + 3/4 b = 1/2 - 3*4 c = (1+2) * (3-4) d = (1-2) / (3+4) e = 1*2 - 3 f = 1 + 2 + 3 + 4
BLANK_LINES_AROUND_TOP_LEVEL_DEFINITIONSets the number of desired blank lines surrounding top-level function and class definitions. For example:
class Foo: pass # <------ having two blank lines here # <------ is the default setting class Bar: pass
BLANK_LINE_BEFORE_CLASS_DOCSTRINGInsert a blank line before a class-level docstring.
BLANK_LINE_BEFORE_MODULE_DOCSTRINGInsert a blank line before a module docstring.
BLANK_LINE_BEFORE_NESTED_CLASS_OR_DEFInsert a blank line before a
deforclassimmediately nested within anotherdeforclass. For example:
class Foo: # <------ this blank line def method(): pass
BLANK_LINES_BETWEEN_TOP_LEVEL_IMPORTS_AND_VARIABLESSets the number of desired blank lines between top-level imports and variable definitions. Useful for compatibility with tools like isort.
COALESCE_BRACKETSDo not split consecutive brackets. Only relevant when
DEDENT_CLOSING_BRACKETSorINDENT_CLOSING_BRACKETSis set. For example:
call_func_that_takes_a_dict( { 'key1': 'value1', 'key2': 'value2', } )
would reformat to:
call_func_that_takes_a_dict({ 'key1': 'value1', 'key2': 'value2', })
COLUMN_LIMITThe column limit (or max line-length)
CONTINUATION_ALIGN_STYLEThe style for continuation alignment. Possible values are:
SPACE: Use spaces for continuation alignment. This is default behavior.FIXED: Use fixed number (CONTINUATION_INDENT_WIDTH) of columns (i.e.CONTINUATION_INDENT_WIDTH/INDENT_WIDTHtabs orCONTINUATION_INDENT_WIDTHspaces) for continuation alignment.VALIGN-RIGHT: Vertically align continuation lines to multiple ofINDENT_WIDTHcolumns. Slightly right (one tab or a few spaces) if cannot vertically align continuation lines with indent characters.
CONTINUATION_INDENT_WIDTHIndent width used for line continuations.
DEDENT_CLOSING_BRACKETSPut closing brackets on a separate line, dedented, if the bracketed expression can't fit in a single line. Applies to all kinds of brackets, including function definitions and calls. For example:
config = { 'key1': 'value1', 'key2': 'value2', } # <--- this bracket is dedented and on a separate line time_series = self.remote_client.query_entity_counters( entity='dev3246.region1', key='dns.query_latency_tcp', transform=Transformation.AVERAGE(window=timedelta(seconds=60)), start_ts=now()-timedelta(days=3), end_ts=now(), ) # <--- this bracket is dedented and on a separate line
DISABLE_ENDING_COMMA_HEURISTICDisable the heuristic which places each list element on a separate line if the list is comma-terminated.
Note: The behavior of this flag changed in v0.40.3. Before, if this flag was true, we would split lists that contained a trailing comma or a comment. Now, we have a separate flag,
DISABLE_SPLIT_LIST_WITH_COMMENT, that controls splitting when a list contains a comment. To get the old behavior, set both flags to true. More information in CHANGELOG.md.
DISABLE_SPLIT_LIST_WITH_COMMENTDon't put every element on a new line within a list that contains interstitial comments.
Without this flag (default):
[ a, b, # c ]With this flag:
[ a, b, # c ]This mirrors the behavior of clang-format and is useful for forming “logical groups” of elements in a list. It also works in function declarations.
EACH_DICT_ENTRY_ON_SEPARATE_LINEPlace each dictionary entry onto its own line.
FORCE_MULTILINE_DICTRespect
EACH_DICT_ENTRY_ON_SEPARATE_LINEeven if the line is shorter thanCOLUMN_LIMIT.
I18N_COMMENTThe regex for an internationalization comment. The presence of this comment stops reformatting of that line, because the comments are required to be next to the string they translate.
I18N_FUNCTION_CALLThe internationalization function call names. The presence of this function stops reformatting on that line, because the string it has cannot be moved away from the i18n comment.
INDENT_BLANK_LINESSet to
Trueto prefer indented blank lines rather than empty
INDENT_CLOSING_BRACKETSPut closing brackets on a separate line, indented, if the bracketed expression can't fit in a single line. Applies to all kinds of brackets, including function definitions and calls. For example:
config = { 'key1': 'value1', 'key2': 'value2', } # <--- this bracket is indented and on a separate line time_series = self.remote_client.query_entity_counters( entity='dev3246.region1', key='dns.query_latency_tcp', transform=Transformation.AVERAGE(window=timedelta(seconds=60)), start_ts=now()-timedelta(days=3), end_ts=now(), ) # <--- this bracket is indented and on a separate line
INDENT_DICTIONARY_VALUEIndent the dictionary value if it cannot fit on the same line as the dictionary key. For example:
config = { 'key1': 'value1', 'key2': value1 + value2, }
INDENT_WIDTHThe number of columns to use for indentation.
JOIN_MULTIPLE_LINESJoin short lines into one line. E.g., single line
ifstatements.
NO_SPACES_AROUND_SELECTED_BINARY_OPERATORSDo not include spaces around selected binary operators. For example:
1 + 2 * 3 - 4 / 5
will be formatted as follows when configured with
*,/:
1 + 2*3 - 4/5
SPACE_BETWEEN_ENDING_COMMA_AND_CLOSING_BRACKETInsert a space between the ending comma and closing bracket of a list, etc.
SPACE_INSIDE_BRACKETSUse spaces inside brackets, braces, and parentheses. For example:
method_call( 1 ) my_dict[ 3 ][ 1 ][ get_index( *args, **kwargs ) ] my_set = { 1, 2, 3 }
SPACES_AROUND_DEFAULT_OR_NAMED_ASSIGNSet to
Trueto prefer spaces around the assignment operator for default or keyword arguments.
SPACES_AROUND_DICT_DELIMITERSAdds a space after the opening ‘{’ and before the ending ‘}’ dict delimiters.
{1: 2}
will be formatted as:
{ 1: 2 }
SPACES_AROUND_LIST_DELIMITERSAdds a space after the opening ‘[’ and before the ending ‘]’ list delimiters.
[1, 2]
will be formatted as:
[ 1, 2 ]
SPACES_AROUND_POWER_OPERATORSet to
Trueto prefer using spaces around**.
SPACES_AROUND_SUBSCRIPT_COLONUse spaces around the subscript / slice operator. For example:
my_list[1 : 10 : 2]
SPACES_AROUND_TUPLE_DELIMITERSAdds a space after the opening ‘(’ and before the ending ‘)’ tuple delimiters.
(1, 2, 3)
will be formatted as:
( 1, 2, 3 )
SPACES_BEFORE_COMMENTThe number of spaces required before a trailing comment. This can be a single value (representing the number of spaces before each trailing comment) or list of values (representing alignment column values; trailing comments within a block will be aligned to the first column value that is greater than the maximum line length within the block).
Note: Lists of values may need to be quoted in some contexts (eg. shells or editor config files).
For example, with
spaces_before_comment=5:
1 + 1 # Adding values
will be formatted as:
1 + 1 # Adding values <-- 5 spaces between the end of the statement and comment
with
spaces_before_comment="15, 20":
1 + 1 # Adding values two + two # More adding longer_statement # This is a longer statement short # This is a shorter statement a_very_long_statement_that_extends_beyond_the_final_column # Comment short # This is a shorter statement
will be formatted as:
1 + 1 # Adding values <-- end of line comments in block aligned to col 15 two + two # More adding longer_statement # This is a longer statement <-- end of line comments in block aligned to col 20 short # This is a shorter statement a_very_long_statement_that_extends_beyond_the_final_column # Comment <-- the end of line comments are aligned based on the line length short # This is a shorter statement
SPLIT_ALL_COMMA_SEPARATED_VALUESIf a comma separated list (
dict,list,tuple, or functiondef) is on a line that is too long, split such that each element is on a separate line.
SPLIT_ALL_TOP_LEVEL_COMMA_SEPARATED_VALUESVariation on
SPLIT_ALL_COMMA_SEPARATED_VALUESin which, if a subexpression with a comma fits in its starting line, then the subexpression is not split. This avoids splits like the one forbin this code:
abcdef( aReallyLongThing: int, b: [Int, Int])
with the new knob this is split as:
abcdef( aReallyLongThing: int, b: [Int, Int])
SPLIT_ARGUMENTS_WHEN_COMMA_TERMINATEDSplit before arguments if the argument list is terminated by a comma.
SPLIT_BEFORE_ARITHMETIC_OPERATORSet to
Trueto prefer splitting before+,-,*,/,//, or@rather than after.
SPLIT_BEFORE_BITWISE_OPERATORSet to
Trueto prefer splitting before&,|or^rather than after.
SPLIT_BEFORE_CLOSING_BRACKETSplit before the closing bracket if a
listordictliteral doesn't fit on a single line.
SPLIT_BEFORE_DICT_SET_GENERATORSplit before a dictionary or set generator (
comp_for). For example, note the split before thefor:
foo = { variable: 'Hello world, have a nice day!' for variable in bar if variable != 42 }
SPLIT_BEFORE_DOTSplit before the
.if we need to split a longer expression:
foo = ('This is a really long string: {}, {}, {}, {}'.format(a, b, c, d))
would reformat to something like:
foo = ('This is a really long string: {}, {}, {}, {}' .format(a, b, c, d))
SPLIT_BEFORE_EXPRESSION_AFTER_OPENING_PARENSplit after the opening paren which surrounds an expression if it doesn't fit on a single line.
SPLIT_BEFORE_FIRST_ARGUMENTIf an argument / parameter list is going to be split, then split before the first argument.
SPLIT_BEFORE_LOGICAL_OPERATORSet to
Trueto prefer splitting beforeandororrather than after.
SPLIT_BEFORE_NAMED_ASSIGNSSplit named assignments onto individual lines.
SPLIT_COMPLEX_COMPREHENSIONFor list comprehensions and generator expressions with multiple clauses (e.g multiple
forcalls,iffilter expressions) and which need to be reflowed, split each clause onto its own line. For example:
result = [ a_var + b_var for a_var in xrange(1000) for b_var in xrange(1000) if a_var % b_var]
would reformat to something like:
result = [ a_var + b_var for a_var in xrange(1000) for b_var in xrange(1000) if a_var % b_var]
SPLIT_PENALTY_AFTER_OPENING_BRACKETThe penalty for splitting right after the opening bracket.
SPLIT_PENALTY_AFTER_UNARY_OPERATORThe penalty for splitting the line after a unary operator.
SPLIT_PENALTY_ARITHMETIC_OPERATORThe penalty of splitting the line around the
+,-,*,/,//,%, and@operators.
SPLIT_PENALTY_BEFORE_IF_EXPRThe penalty for splitting right before an
ifexpression.
SPLIT_PENALTY_BITWISE_OPERATORThe penalty of splitting the line around the
&,|, and^operators.
SPLIT_PENALTY_COMPREHENSIONThe penalty for splitting a list comprehension or generator expression.
SPLIT_PENALTY_EXCESS_CHARACTERThe penalty for characters over the column limit.
SPLIT_PENALTY_FOR_ADDED_LINE_SPLITThe penalty incurred by adding a line split to the logical line. The more line splits added the higher the penalty.
SPLIT_PENALTY_IMPORT_NAMESThe penalty of splitting a list of
import asnames. For example:
from a_very_long_or_indented_module_name_yada_yad import (long_argument_1, long_argument_2, long_argument_3)
would reformat to something like:
from a_very_long_or_indented_module_name_yada_yad import ( long_argument_1, long_argument_2, long_argument_3)
SPLIT_PENALTY_LOGICAL_OPERATORThe penalty of splitting the line around the
andandoroperators.
USE_TABSUse the Tab character for indentation.
YAPF tries very hard to get the formatting correct. But for some code, it won't be as good as hand-formatting. In particular, large data literals may become horribly disfigured under YAPF.
The reasons for this are manyfold. In short, YAPF is simply a tool to help with development. It will format things to coincide with the style guide, but that may not equate with readability.
What can be done to alleviate this situation is to indicate regions YAPF should ignore when reformatting something:
# yapf: disable FOO = { # ... some very large, complex data literal. } BAR = [ # ... another large data literal. ] # yapf: enable
You can also disable formatting for a single literal like this:
BAZ = { (1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), } # yapf: disable
To preserve the nice dedented closing brackets, use the dedent_closing_brackets in your style. Note that in this case all brackets, including function definitions and calls, are going to use that style. This provides consistency across the formatted codebase.
We wanted to use clang-format‘s reformatting algorithm. It’s very powerful and designed to come up with the best formatting possible. Existing tools were created with different goals in mind, and would require extensive modifications to convert to using clang-format's algorithm.
Please do! YAPF was designed to be used as a library as well as a command line tool. This means that a tool or IDE plugin is free to use YAPF.
YAPF tries very hard to be fully PEP 8 compliant. However, it is paramount to not risk altering the semantics of your code. Thus, YAPF tries to be as safe as possible and does not change the token stream (e.g., by adding parentheses). All these cases however, can be easily fixed manually. For instance,
from my_package import my_function_1, my_function_2, my_function_3, my_function_4, my_function_5 FOO = my_variable_1 + my_variable_2 + my_variable_3 + my_variable_4 + my_variable_5 + my_variable_6 + my_variable_7 + my_variable_8
won't be split, but you can easily get it right by just adding parentheses:
from my_package import (my_function_1, my_function_2, my_function_3, my_function_4, my_function_5) FOO = (my_variable_1 + my_variable_2 + my_variable_3 + my_variable_4 + my_variable_5 + my_variable_6 + my_variable_7 + my_variable_8)
The main data structure in YAPF is the LogicalLine object. It holds a list of FormatToken\s, that we would want to place on a single line if there were no column limit. An exception being a comment in the middle of an expression statement will force the line to be formatted on more than one line. The formatter works on one LogicalLine object at a time.
An LogicalLine typically won't affect the formatting of lines before or after it. There is a part of the algorithm that may join two or more LogicalLine\s into one line. For instance, an if-then statement with a short body can be placed on a single line:
if a == 42: continue
YAPF‘s formatting algorithm creates a weighted tree that acts as the solution space for the algorithm. Each node in the tree represents the result of a formatting decision --- i.e., whether to split or not to split before a token. Each formatting decision has a cost associated with it. Therefore, the cost is realized on the edge between two nodes. (In reality, the weighted tree doesn’t have separate edge objects, so the cost resides on the nodes themselves.)
For example, take the following Python code snippet. For the sake of this example, assume that line (1) violates the column limit restriction and needs to be reformatted.
def xxxxxxxxxxx(aaaaaaaaaaaa, bbbbbbbbb, cccccccc, dddddddd, eeeeee): # 1 pass # 2
For line (1), the algorithm will build a tree where each node (a FormattingDecisionState object) is the state of the line at that token given the decision to split before the token or not. Note: the FormatDecisionState objects are copied by value so each node in the graph is unique and a change in one doesn't affect other nodes.
Heuristics are used to determine the costs of splitting or not splitting. Because a node holds the state of the tree up to a token's insertion, it can easily determine if a splitting decision will violate one of the style requirements. For instance, the heuristic is able to apply an extra penalty to the edge when not splitting between the previous token and the one being added.
There are some instances where we will never want to split the line, because doing so will always be detrimental (i.e., it will require a backslash-newline, which is very rarely desirable). For line (1), we will never want to split the first three tokens: def, xxxxxxxxxxx, and (. Nor will we want to split between the ) and the : at the end. These regions are said to be “unbreakable.” This is reflected in the tree by there not being a “split” decision (left hand branch) within the unbreakable region.
Now that we have the tree, we determine what the “best” formatting is by finding the path through the tree with the lowest cost.
And that's it!