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| 55 | <H2><A NAME="SECTION004370000000000000000"></A><A NAME="types-set"></A> |
| 56 | <BR> |
| 57 | 2.3.7 Set Types -- |
| 58 | <tt class="class">set</tt>, <tt class="class">frozenset</tt> |
| 59 | |
| 60 | </H2> |
| 61 | <a id='l2h-226' xml:id='l2h-226'></a> |
| 62 | <P> |
| 63 | A <i class="dfn">set</i> object is an unordered collection of immutable values. |
| 64 | Common uses include membership testing, removing duplicates from a sequence, |
| 65 | and computing mathematical operations such as intersection, union, difference, |
| 66 | and symmetric difference. |
| 67 | |
| 68 | <span class="versionnote">New in version 2.4.</span> |
| 69 | |
| 70 | <P> |
| 71 | Like other collections, sets support <code><var>x</var> in <var>set</var></code>, |
| 72 | <code>len(<var>set</var>)</code>, and <code>for <var>x</var> in <var>set</var></code>. Being an |
| 73 | unordered collection, sets do not record element position or order of |
| 74 | insertion. Accordingly, sets do not support indexing, slicing, or |
| 75 | other sequence-like behavior. |
| 76 | |
| 77 | <P> |
| 78 | There are currently two builtin set types, <tt class="class">set</tt> and <tt class="class">frozenset</tt>. |
| 79 | The <tt class="class">set</tt> type is mutable -- the contents can be changed using methods |
| 80 | like <tt class="method">add()</tt> and <tt class="method">remove()</tt>. Since it is mutable, it has no |
| 81 | hash value and cannot be used as either a dictionary key or as an element of |
| 82 | another set. The <tt class="class">frozenset</tt> type is immutable and hashable -- its |
| 83 | contents cannot be altered after is created; however, it can be used as |
| 84 | a dictionary key or as an element of another set. |
| 85 | |
| 86 | <P> |
| 87 | Instances of <tt class="class">set</tt> and <tt class="class">frozenset</tt> provide the following operations: |
| 88 | |
| 89 | <P> |
| 90 | <div class="center"><table class="realtable"> |
| 91 | <thead> |
| 92 | <tr> |
| 93 | <th class="center">Operation</th> |
| 94 | <th class="center">Equivalent</th> |
| 95 | <th class="left" >Result</th> |
| 96 | </tr> |
| 97 | </thead> |
| 98 | <tbody> |
| 99 | <tr><td class="center" valign="baseline"><code>len(<var>s</var>)</code></td> |
| 100 | <td class="center"></td> |
| 101 | <td class="left" >cardinality of set <var>s</var></td></tr><P> |
| 102 | |
| 103 | <tr><td class="center" valign="baseline"><code><var>x</var> in <var>s</var></code></td> |
| 104 | <td class="center"></td> |
| 105 | <td class="left" >test <var>x</var> for membership in <var>s</var></td></tr> |
| 106 | <tr><td class="center" valign="baseline"><code><var>x</var> not in <var>s</var></code></td> |
| 107 | <td class="center"></td> |
| 108 | <td class="left" >test <var>x</var> for non-membership in <var>s</var></td></tr> |
| 109 | <tr><td class="center" valign="baseline"><code><var>s</var>.issubset(<var>t</var>)</code></td> |
| 110 | <td class="center"><code><var>s</var> <= <var>t</var></code></td> |
| 111 | <td class="left" >test whether every element in <var>s</var> is in <var>t</var></td></tr> |
| 112 | <tr><td class="center" valign="baseline"><code><var>s</var>.issuperset(<var>t</var>)</code></td> |
| 113 | <td class="center"><code><var>s</var> >= <var>t</var></code></td> |
| 114 | <td class="left" >test whether every element in <var>t</var> is in <var>s</var></td></tr><P> |
| 115 | |
| 116 | <tr><td class="center" valign="baseline"><code><var>s</var>.union(<var>t</var>)</code></td> |
| 117 | <td class="center"><var>s</var> | <var>t</var></td> |
| 118 | <td class="left" >new set with elements from both <var>s</var> and <var>t</var></td></tr> |
| 119 | <tr><td class="center" valign="baseline"><code><var>s</var>.intersection(<var>t</var>)</code></td> |
| 120 | <td class="center"><var>s</var> & <var>t</var></td> |
| 121 | <td class="left" >new set with elements common to <var>s</var> and <var>t</var></td></tr> |
| 122 | <tr><td class="center" valign="baseline"><code><var>s</var>.difference(<var>t</var>)</code></td> |
| 123 | <td class="center"><var>s</var> - <var>t</var></td> |
| 124 | <td class="left" >new set with elements in <var>s</var> but not in <var>t</var></td></tr> |
| 125 | <tr><td class="center" valign="baseline"><code><var>s</var>.symmetric_difference(<var>t</var>)</code></td> |
| 126 | <td class="center"><var>s</var> ^ <var>t</var></td> |
| 127 | <td class="left" >new set with elements in either <var>s</var> or <var>t</var> but not both</td></tr> |
| 128 | <tr><td class="center" valign="baseline"><code><var>s</var>.copy()</code></td> |
| 129 | <td class="center"></td> |
| 130 | <td class="left" >new set with a shallow copy of <var>s</var></td></tr></tbody> |
| 131 | </table></div> |
| 132 | |
| 133 | <P> |
| 134 | Note, the non-operator versions of <tt class="method">union()</tt>, <tt class="method">intersection()</tt>, |
| 135 | <tt class="method">difference()</tt>, and <tt class="method">symmetric_difference()</tt>, |
| 136 | <tt class="method">issubset()</tt>, and <tt class="method">issuperset()</tt> methods will accept any |
| 137 | iterable as an argument. In contrast, their operator based counterparts |
| 138 | require their arguments to be sets. This precludes error-prone constructions |
| 139 | like <code>set('abc') & 'cbs'</code> in favor of the more readable |
| 140 | <code>set('abc').intersection('cbs')</code>. |
| 141 | |
| 142 | <P> |
| 143 | Both <tt class="class">set</tt> and <tt class="class">frozenset</tt> support set to set comparisons. |
| 144 | Two sets are equal if and only if every element of each set is contained in |
| 145 | the other (each is a subset of the other). |
| 146 | A set is less than another set if and only if the first set is a proper |
| 147 | subset of the second set (is a subset, but is not equal). |
| 148 | A set is greater than another set if and only if the first set is a proper |
| 149 | superset of the second set (is a superset, but is not equal). |
| 150 | |
| 151 | <P> |
| 152 | Instances of <tt class="class">set</tt> are compared to instances of <tt class="class">frozenset</tt> based |
| 153 | on their members. For example, "<tt class="samp">set('abc') == frozenset('abc')</tt>" returns |
| 154 | <code>True</code>. |
| 155 | |
| 156 | <P> |
| 157 | The subset and equality comparisons do not generalize to a complete |
| 158 | ordering function. For example, any two disjoint sets are not equal and |
| 159 | are not subsets of each other, so <em>all</em> of the following return |
| 160 | <code>False</code>: <code><var>a</var><<var>b</var></code>, <code><var>a</var>==<var>b</var></code>, or |
| 161 | <code><var>a</var>><var>b</var></code>. |
| 162 | Accordingly, sets do not implement the <tt class="method">__cmp__</tt> method. |
| 163 | |
| 164 | <P> |
| 165 | Since sets only define partial ordering (subset relationships), the output |
| 166 | of the <tt class="method">list.sort()</tt> method is undefined for lists of sets. |
| 167 | |
| 168 | <P> |
| 169 | Set elements are like dictionary keys; they need to define both |
| 170 | <tt class="method">__hash__</tt> and <tt class="method">__eq__</tt> methods. |
| 171 | |
| 172 | <P> |
| 173 | Binary operations that mix <tt class="class">set</tt> instances with <tt class="class">frozenset</tt> |
| 174 | return the type of the first operand. For example: |
| 175 | "<tt class="samp">frozenset('ab') | set('bc')</tt>" returns an instance of <tt class="class">frozenset</tt>. |
| 176 | |
| 177 | <P> |
| 178 | The following table lists operations available for <tt class="class">set</tt> |
| 179 | that do not apply to immutable instances of <tt class="class">frozenset</tt>: |
| 180 | |
| 181 | <P> |
| 182 | <div class="center"><table class="realtable"> |
| 183 | <thead> |
| 184 | <tr> |
| 185 | <th class="center">Operation</th> |
| 186 | <th class="center">Equivalent</th> |
| 187 | <th class="left" >Result</th> |
| 188 | </tr> |
| 189 | </thead> |
| 190 | <tbody> |
| 191 | <tr><td class="center" valign="baseline"><code><var>s</var>.update(<var>t</var>)</code></td> |
| 192 | <td class="center"><var>s</var> |= <var>t</var></td> |
| 193 | <td class="left" >return set <var>s</var> with elements added from <var>t</var></td></tr> |
| 194 | <tr><td class="center" valign="baseline"><code><var>s</var>.intersection_update(<var>t</var>)</code></td> |
| 195 | <td class="center"><var>s</var> &= <var>t</var></td> |
| 196 | <td class="left" >return set <var>s</var> keeping only elements also found in <var>t</var></td></tr> |
| 197 | <tr><td class="center" valign="baseline"><code><var>s</var>.difference_update(<var>t</var>)</code></td> |
| 198 | <td class="center"><var>s</var> -= <var>t</var></td> |
| 199 | <td class="left" >return set <var>s</var> after removing elements found in <var>t</var></td></tr> |
| 200 | <tr><td class="center" valign="baseline"><code><var>s</var>.symmetric_difference_update(<var>t</var>)</code></td> |
| 201 | <td class="center"><var>s</var> ^= <var>t</var></td> |
| 202 | <td class="left" >return set <var>s</var> with elements from <var>s</var> or <var>t</var> |
| 203 | but not both</td></tr><P> |
| 204 | |
| 205 | <tr><td class="center" valign="baseline"><code><var>s</var>.add(<var>x</var>)</code></td> |
| 206 | <td class="center"></td> |
| 207 | <td class="left" >add element <var>x</var> to set <var>s</var></td></tr> |
| 208 | <tr><td class="center" valign="baseline"><code><var>s</var>.remove(<var>x</var>)</code></td> |
| 209 | <td class="center"></td> |
| 210 | <td class="left" >remove <var>x</var> from set <var>s</var>; raises KeyError if not present</td></tr> |
| 211 | <tr><td class="center" valign="baseline"><code><var>s</var>.discard(<var>x</var>)</code></td> |
| 212 | <td class="center"></td> |
| 213 | <td class="left" >removes <var>x</var> from set <var>s</var> if present</td></tr> |
| 214 | <tr><td class="center" valign="baseline"><code><var>s</var>.pop()</code></td> |
| 215 | <td class="center"></td> |
| 216 | <td class="left" >remove and return an arbitrary element from <var>s</var>; raises |
| 217 | <tt class="exception">KeyError</tt> if empty</td></tr> |
| 218 | <tr><td class="center" valign="baseline"><code><var>s</var>.clear()</code></td> |
| 219 | <td class="center"></td> |
| 220 | <td class="left" >remove all elements from set <var>s</var></td></tr></tbody> |
| 221 | </table></div> |
| 222 | |
| 223 | <P> |
| 224 | Note, the non-operator versions of the <tt class="method">update()</tt>, |
| 225 | <tt class="method">intersection_update()</tt>, <tt class="method">difference_update()</tt>, and |
| 226 | <tt class="method">symmetric_difference_update()</tt> methods will accept any iterable |
| 227 | as an argument. |
| 228 | |
| 229 | <P> |
| 230 | The design of the set types was based on lessons learned from the |
| 231 | <tt class="module">sets</tt> module. |
| 232 | |
| 233 | <P> |
| 234 | <div class="seealso"> |
| 235 | <p class="heading">See Also:</p> |
| 236 | |
| 237 | <dl compact="compact" class="seemodule"> |
| 238 | <dt>Module <b><tt class="module"><a href="module-comparison-to-builtin-set.html">sets</a></tt>:</b> |
| 239 | <dd>Differences between |
| 240 | the <tt class="module">sets</tt> module and the built-in set types. |
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