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",[951,1052,1053],{"class":965},"==",[951,1055,1056],{"class":1012}," b",[951,1058,1059],{"class":965},";",[951,1061,1063],{"class":1062},"sHwdD"," \u002F\u002F 编译错误：operator== 未定义\n",[951,1065,1067],{"class":953,"line":1066},8,[951,1068,1069],{"class":965},"}\n",[918,1071,1072],{},"但通过显式地指明使用预置比较运算符，就可以添加全部六个（或七个）比较运算符：",[941,1074,1076],{"className":943,"code":1075,"language":945,"meta":946,"style":946},"#include \u003Ccompare> \u002F\u002F 使用预置比较必须引入\nstruct Coord {\n    int x, y;\n    \u002F\u002F 通过 =default 指明使用预置比较\n    auto operator\u003C=>(const Coord&) const = default;\n};\nint main() {\n    Coord a{1, 2};\n    Coord b{1, 3};\n    a == b; \u002F\u002F false\n    a \u003C b;  \u002F\u002F true\n    b >= a; \u002F\u002F true\n    b != a; \u002F\u002F true\n}\n",[948,1077,1078,1097,1105,1117,1122,1158,1162,1172,1186,1201,1215,1230,1247,1261],{"__ignoreMap":946},[951,1079,1080,1084,1087,1091,1094],{"class":953,"line":954},[951,1081,1083],{"class":1082},"s7zQu","#include",[951,1085,1086],{"class":965}," \u003C",[951,1088,1090],{"class":1089},"sfazB","compare",[951,1092,1093],{"class":965},">",[951,1095,1096],{"class":1062}," \u002F\u002F 使用预置比较必须引入\n",[951,1098,1099,1101,1103],{"class":953,"line":969},[951,1100,958],{"class":957},[951,1102,962],{"class":961},[951,1104,966],{"class":965},[951,1106,1107,1109,1111,1113,1115],{"class":953,"line":988},[951,1108,972],{"class":957},[951,1110,976],{"class":975},[951,1112,979],{"class":965},[951,1114,982],{"class":975},[951,1116,985],{"class":965},[951,1118,1119],{"class":953,"line":994},[951,1120,1121],{"class":1062},"    \u002F\u002F 通过 =default 指明使用预置比较\n",[951,1123,1124,1127,1130,1133,1136,1139,1141,1144,1147,1150,1153,1156],{"class":953,"line":1009},[951,1125,1126],{"class":957},"    auto",[951,1128,1129],{"class":1019}," operator",[951,1131,1132],{"class":961},"\u003C=>",[951,1134,1135],{"class":965},"(",[951,1137,1138],{"class":957},"const",[951,1140,962],{"class":961},[951,1142,1143],{"class":957},"&",[951,1145,1146],{"class":965},")",[951,1148,1149],{"class":957}," const",[951,1151,1152],{"class":965}," =",[951,1154,1155],{"class":1019}," default",[951,1157,985],{"class":965},[951,1159,1160],{"class":953,"line":1030},[951,1161,991],{"class":965},[951,1163,1164,1166,1168,1170],{"class":953,"line":1047},[951,1165,997],{"class":957},[951,1167,1001],{"class":1000},[951,1169,1004],{"class":965},[951,1171,966],{"class":965},[951,1173,1174,1176,1178,1180,1182,1184],{"class":953,"line":1066},[951,1175,1013],{"class":1012},[951,1177,1016],{"class":965},[951,1179,1020],{"class":1019},[951,1181,979],{"class":965},[951,1183,1025],{"class":1019},[951,1185,991],{"class":965},[951,1187,1189,1191,1193,1195,1197,1199],{"class":953,"line":1188},9,[951,1190,1033],{"class":1012},[951,1192,1016],{"class":965},[951,1194,1020],{"class":1019},[951,1196,979],{"class":965},[951,1198,1042],{"class":1019},[951,1200,991],{"class":965},[951,1202,1204,1206,1208,1210,1212],{"class":953,"line":1203},10,[951,1205,1050],{"class":1012},[951,1207,1053],{"class":965},[951,1209,1056],{"class":1012},[951,1211,1059],{"class":965},[951,1213,1214],{"class":1062}," \u002F\u002F false\n",[951,1216,1218,1220,1223,1225,1227],{"class":953,"line":1217},11,[951,1219,1050],{"class":1012},[951,1221,1222],{"class":965},"\u003C",[951,1224,1056],{"class":1012},[951,1226,1059],{"class":965},[951,1228,1229],{"class":1062},"  \u002F\u002F true\n",[951,1231,1233,1236,1239,1242,1244],{"class":953,"line":1232},12,[951,1234,1235],{"class":1012},"    b ",[951,1237,1238],{"class":965},">=",[951,1240,1241],{"class":1012}," a",[951,1243,1059],{"class":965},[951,1245,1246],{"class":1062}," \u002F\u002F true\n",[951,1248,1250,1252,1255,1257,1259],{"class":953,"line":1249},13,[951,1251,1235],{"class":1012},[951,1253,1254],{"class":965},"!=",[951,1256,1241],{"class":1012},[951,1258,1059],{"class":965},[951,1260,1246],{"class":1062},[951,1262,1264],{"class":953,"line":1263},14,[951,1265,1069],{"class":965},[918,1267,1268,1269,1272],{},"停停停，太多新鲜事物了。最奇怪的就是这个 ",[948,1270,1271],{},"operator\u003C=>","，它是什么意思呢？这个东西叫做三路比较运算符（Three-way compare operator），俗称飞船运算符（Spaceship operator）。",[1274,1275,1276],"h2",{"id":1276},"三路比较运算符",[1278,1279,1280,1296],"table",{},[1281,1282,1283],"thead",{},[1284,1285,1286,1290,1293],"tr",{},[1287,1288,1289],"th",{},"运算符",[1287,1291,1292],{},"名称",[1287,1294,1295],{},"作用",[1297,1298,1299],"tbody",{},[1284,1300,1301,1306,1308],{},[1302,1303,1304],"td",{},[948,1305,1132],{},[1302,1307,1276],{},[1302,1309,1310],{},"用以快速生成其它六种比较运算符",[918,1312,1313,1314,1317,1318,1321,1322,1324],{},"三路比较运算符是用来比较的。它与其它六个比较运算符的最大不同就是这个“三路”。原先六个运算符可以称为“两路比较”，因为它们运算的结果只有两种可能：",[948,1315,1316],{},"true"," 或 ",[948,1319,1320],{},"false","。而 ",[948,1323,1132],{}," 是三路的，意味着它的运算结果有三种可能——具体来说，这三种结果分别是 $\\tt greater$、$\\tt equal$ 和 $\\tt less$。",[918,1326,1327],{},"先不管这三种结果具体是什么东西，看一下下面的例子：",[922,1329,1330,1336,1342,1348],{},[925,1331,1332,1335],{},[948,1333,1334],{},"1 \u003C=> 2"," 的结果是 $\\tt less$。",[925,1337,1338,1341],{},[948,1339,1340],{},"0 \u003C=> 0"," 的结果是 $\\tt equal$。",[925,1343,1344,1347],{},[948,1345,1346],{},"3 \u003C=> 1"," 的结果是 $\\tt greater$。",[925,1349,1350],{},"……",[918,1352,1353,1354,1356,1357,1360,1361,1364,1365,1367,1368,1370,1371,1373,1374,1376,1377,1385,1386,1388],{},"可以这样理解 ",[948,1355,1132],{},"：",[948,1358,1359],{},"a \u003C=> b"," 的结果就是表达式 ",[948,1362,1363],{},"a - b"," 的“正负性”：如果是“负数”，那么 ",[948,1366,1359],{}," 就是 $\\tt less$；如果是“正数”，那么 ",[948,1369,1359],{}," 就是 $\\tt greater$；同理如果 ",[948,1372,1363],{}," 得到零，那么 ",[948,1375,1359],{}," 的结果就是 $\\tt equal$。事实上，",[1378,1379,1381,1382],"a",{"href":1380},"\u002Fch04\u002Fpointer\u002Fpointer_and_array#c-%E9%A3%8E%E6%A0%BC%E5%AD%97%E7%AC%A6%E4%B8%B2%E5%BA%93","第四章提到过的 ",[948,1383,1384],{},"std::strcmp"," 就是 C 风格字符串的三路比较：比如它返回正数时就代表第一个实参大于第二个实参。这样的设计使得其它六个运算符都可以从 ",[948,1387,1132],{}," 的结果推出：",[922,1390,1391,1400,1408,1416,1424,1432],{},[925,1392,1393,1396,1397,1399],{},[948,1394,1395],{},"a > b"," 等价于 ",[948,1398,1359],{}," 为 $\\tt greater$；",[925,1401,1402,1396,1405,1407],{},[948,1403,1404],{},"a >= b",[948,1406,1359],{}," 为 $\\tt greater$ 或 $\\tt equal$；",[925,1409,1410,1396,1413,1415],{},[948,1411,1412],{},"a == b",[948,1414,1359],{}," 为 $\\tt equal$；",[925,1417,1418,1396,1421,1423],{},[948,1419,1420],{},"a \u003C= b",[948,1422,1359],{}," 为 $\\tt less$ 或 $\\tt equal$；",[925,1425,1426,1396,1429,1431],{},[948,1427,1428],{},"a \u003C b",[948,1430,1359],{}," 为 $\\tt less$；",[925,1433,1434,1396,1437,1439],{},[948,1435,1436],{},"a != b",[948,1438,1359],{}," 为 $\\tt greater$ 或 $\\tt less$。",[918,1441,1442,1443,1445,1446,1448,1449,1448,1452,1454,1455,1457,1458,1460],{},"因此 ",[948,1444,1132],{}," 最大的作用在于一旦定义了它，就相当于定义了 ",[948,1447,1222],{}," ",[948,1450,1451],{},"\u003C=",[948,1453,1238],{}," 和 ",[948,1456,1093],{}," 等比较运算符。在代码中使用这些比较运算符都相当于调用 ",[948,1459,1271],{},"，编译器会按照刚刚的等价关系来推导出两路比较的结果。",[918,1462,1463,1464,1466],{},"目前为止，你至少对 ",[948,1465,1132],{}," 这个东西有一个初步的认识了。接下来我要介绍 C++ 中如何定义 $\\tt greater$、$\\tt equal$ 和 $\\tt less$ 这三种结果；但为此必须要引入一些数学知识。",[1274,1468,1469],{"id":1469},"序关系",[1471,1472,1473,1480],"blockquote",{},[918,1474,1475,1479],{},[1476,1477,1478],"strong",{},"基本概念介绍"," 我不清楚读者的数学基础，下为后文要用到的基础概念。",[922,1481,1482,1489,1496],{},[925,1483,1484,1485,1488],{},"对于集合 $A$ 和 $B$，$A\\times B={\\lang x, y\\rang\\mid x\\in A,y\\in B}$ 是 $A$ 和 $B$ 的",[1476,1486,1487],{},"笛卡尔积","，其中 $\\lang x,y\\rang$ 是有序二元组。",[925,1490,1491,1492,1495],{},"集合 $S$ 上的",[1476,1493,1494],{},"二元关系"," $R$ 是指 $S\\times S$ 上的任意子集。",[925,1497,1498,1499],{},"对于 $S$ 上的某个二元关系 $R$，$\\lang a, b\\rang\\in R$，则称 $a, b$ 具有 $R$ 关系，记作 $aRb$。\n",[922,1500,1501],{},[925,1502,1503],{},"例：在实数集 $\\mathbb R$ 上，小于等于 $\\leqslant$ 是其上的一个二元关系。一般的写法 $3\\leqslant5$ 即 $\\lang 3, 5\\rang\\in\\leqslant\\subseteq\\mathbb R\\times\\mathbb R$。",[1505,1506,1507],"style",{},"\n.bordered {\n    border: 1px solid var(--c-text); \n    padding: 0 1em;\n    margin-bottom: 0.5em;\n}\n",[1509,1510,1513,1516,1531],"div",{"className":1511},[1512],"bordered",[918,1514,1515],{},"若集合 $S$ 上的二元关系 $\\preccurlyeq$ 满足：",[1517,1518,1519,1525],"ol",{},[925,1520,1521,1524],{},[1476,1522,1523],{},"自反性","：对于 $\\forall a\\in S$，$a\\preccurlyeq a$；",[925,1526,1527,1530],{},[1476,1528,1529],{},"传递性","：对于 $\\forall a, b, c\\in S$，若 $a\\preccurlyeq b$ 且 $b\\preccurlyeq c$，则 $a\\preccurlyeq c$；",[918,1532,1533,1534,1537],{},"则称 $\\preccurlyeq$ 是",[1476,1535,1536],{},"预序关系","（Preordering）。",[1509,1539,1541,1544,1557],{"className":1540},[1512],[918,1542,1543],{},"若集合 $S$ 上的二元关系 $\\lesssim$ 满足：",[1517,1545,1546,1552],{},[925,1547,1548,1551],{},[1476,1549,1550],{},"完全性","：对于 $\\forall a, b\\in S$，$a\\lesssim b$ 或 $b\\lesssim a$。",[925,1553,1554,1556],{},[1476,1555,1529],{},"：对于 $\\forall a, b, c\\in S$，若 $a\\lesssim b$ 且 $b\\lesssim c$，则 $a\\lesssim c$；",[918,1558,1559,1560,1563],{},"则称 $\\lesssim$ 是",[1476,1561,1562],{},"弱序关系","（Weak ordering，又称预全序关系 Total pre-ordering）。完全性蕴含了自反性；因此弱序关系必然是预序关系。",[1509,1565,1567,1570,1586],{"className":1566},[1512],[918,1568,1569],{},"如果二元关系 $\\leqslant$ 满足：",[1517,1571,1572,1576,1580],{},[925,1573,1574,1551],{},[1476,1575,1550],{},[925,1577,1578,1556],{},[1476,1579,1529],{},[925,1581,1582,1585],{},[1476,1583,1584],{},"反对称性","：对于 $\\forall a, b\\in S$，若 $a\\preccurlyeq b$ 且 $b\\preccurlyeq a$，则 $a = b$。",[918,1587,1588,1589,1592],{},"则称 $\\leqslant$ 是",[1476,1590,1591],{},"全序关系","（Total ordering）。显然，全序关系必然是弱序关系。",[918,1594,1595],{},"定义列完了。这里介绍了三种序关系：预序关系、弱序关系和全序关系。直观上来看一些例子：",[922,1597,1598,1601,1618],{},[925,1599,1600],{},"全序关系是最常见的：常见的数集比如整数域 $\\mathbb N$ 上，小于等于 $\\leqslant$ 就是全序关系。自反性是显然的；传递性也很显然；完全性是指，任何两个整数之间都有大小关系，$a$ 要么大于等于 $b$，要么小于等于 $b$。",[925,1602,1603,1604,1454,1607,1610,1611,1454,1614,1617],{},"弱序关系比较少见。举一个例子，对字符串按字典序排序，但忽略大小写。此时，",[948,1605,1606],{},"aBc",[948,1608,1609],{},"Abc"," 在这种序关系定义下，前者既不小于后者，也不大于后者。但他们两个实质上也不相等，只能说在序关系下等价。弱序关系保证每两个元素之间都有大小关系，但没有反对称性——“既不大于也不小于”推导不出相等。其实之前在讲排序算法时也接触过类似的场景：结构体 ",[948,1612,1613],{},"{1, 2}",[948,1615,1616],{},"{1, 3}"," 按第一分量排序时，两者排序上“等价”但不相等。",[925,1619,1620,1621,1623,1624,1627,1628,1631,1632,1634,1635,1637,1638,1640,1641,1643,1644,1646],{},"预序关系偶尔能见到。对于计算机内的浮点数来说，其上的小于等于 ",[948,1622,1451],{}," 实际是一个预序关系。浮点数计算中引入了一个叫做",[1476,1625,1626],{},"非数","（Not-a-number，",[1476,1629,1630],{},"NaN","）的特殊值。NaN 和任何浮点数都没有 ",[948,1633,1451],{}," 关系，即对于任意浮点数 $x$， $\\lang\\mathtt{NaN}, x\\rang\\notin$ ",[948,1636,1451],{},"，$\\lang x,\\mathtt{NaN}\\rang\\notin$ ",[948,1639,1451],{},"。因此浮点数上的 ",[948,1642,1451],{}," 不具有完全性。此外，浮点数还定义了正零、负零两个相等但不等同的值，因此浮点数上的 ",[948,1645,1451],{}," 也不具有反对称性。",[918,1648,1649,1650,1652,1653,1656,1657,1317,1660,1663],{},"回到 C++，",[948,1651,1132],{}," 的返回值可能是 ",[948,1654,1655],{},"std::partial_ordering","、",[948,1658,1659],{},"std::weak_ordering",[948,1661,1662],{},"std::strong_ordering"," 类型的值：",[922,1665,1666,1675,1682],{},[925,1667,1668,1669,1671,1672,1674],{},"如果 ",[948,1670,1132],{}," 返回 ",[948,1673,1655],{}," 类型的值，意味着其所导出的六种运算符的运算结果满足预序关系；",[925,1676,1668,1677,1671,1679,1681],{},[948,1678,1132],{},[948,1680,1659],{}," 类型的值，意味着其所导出的六种运算符的运算结果满足弱序关系；",[925,1683,1668,1684,1671,1686,1688],{},[948,1685,1132],{},[948,1687,1662],{}," 类型的值，意味着其所导出的六种运算符的运算结果满足全序关系。",[1471,1690,1691],{},[918,1692,1693,1694,1697],{},"一般来说，标准库要求基于比较的算法（如 ",[948,1695,1696],{},"rg::sort","）中使用的比较运算符尽可能是全序的；否则可能导致实现定义行为（对于弱序关系）或未定义行为（对于预序关系）。这也意味着对一个浮点类型的范围排序时，如果其中包含 NaN，则导致未定义行为。",[918,1699,1700,1701,1448,1704,1454,1707,1709,1710,1712,1713,1715,1716,1719,1720,1712,1722,1715,1725,1728],{},"这三个类都定义了 ",[948,1702,1703],{},"less",[948,1705,1706],{},"equivalent",[948,1708,1476],{}," 三个静态成员，表明三路比较的返回结果。比如，整数类型的三路比较是 ",[948,1711,1662],{}," 类型的，那么 ",[948,1714,1334],{}," 的返回值就是 ",[948,1717,1718],{},"std::strong_ordering::less","。浮点类型的三路比较是 ",[948,1721,1655],{},[948,1723,1724],{},"3.14 \u003C=> 3.14",[948,1726,1727],{},"std::partial_ordering::equivalent","。",[918,1730,1731,1732,1735,1736,1738,1739,1448,1741,1448,1743,1448,1745,1747,1748,1728],{},"此外，由于预序关系不保证所有元素都可比较；故还存在额外的 ",[948,1733,1734],{},"std::partial_ordering::unordered"," 静态成员，指示某次三路比较的结果是两者不可比。",[948,1737,1734],{}," 导出的 ",[948,1740,1222],{},[948,1742,1451],{},[948,1744,1238],{},[948,1746,1093],{}," 运算符结果都是 ",[948,1749,1320],{},[941,1751,1753],{"className":943,"code":1752,"language":945,"meta":946,"style":946},"#include \u003Ccompare> \u002F\u002F 三路比较相关设施定义于此\n#include \u003Climits> \u002F\u002F std::numeric_limits，见下\n\n\u002F\u002F 获取一个值为 NaN 的 double 类型常量\nconstexpr double NaN = std::numeric_limits\u003Cdouble>::quiet_NaN();\n\nint main() {\n    42 \u003C=> 42; \u002F\u002F std::strong_ordering::equivalent\n    NaN \u003C=> 1.0; \u002F\u002F std::partial_ordering::unordered\n\n    \u002F\u002F static_assert 是静态断言；如果括号内表达式为 false 导致编译错误\n    static_assert(42 \u003C=> 42 == std::strong_ordering::equivalent);\n    static_assert(NaN \u003C=> 1.0 == std::partial_ordering::unordered);\n}\n",[948,1754,1755,1768,1782,1788,1793,1830,1834,1844,1860,1875,1879,1884,1915,1944],{"__ignoreMap":946},[951,1756,1757,1759,1761,1763,1765],{"class":953,"line":954},[951,1758,1083],{"class":1082},[951,1760,1086],{"class":965},[951,1762,1090],{"class":1089},[951,1764,1093],{"class":965},[951,1766,1767],{"class":1062}," \u002F\u002F 三路比较相关设施定义于此\n",[951,1769,1770,1772,1774,1777,1779],{"class":953,"line":969},[951,1771,1083],{"class":1082},[951,1773,1086],{"class":965},[951,1775,1776],{"class":1089},"limits",[951,1778,1093],{"class":965},[951,1780,1781],{"class":1062}," \u002F\u002F std::numeric_limits，见下\n",[951,1783,1784],{"class":953,"line":988},[951,1785,1787],{"emptyLinePlaceholder":1786},true,"\n",[951,1789,1790],{"class":953,"line":994},[951,1791,1792],{"class":1062},"\u002F\u002F 获取一个值为 NaN 的 double 类型常量\n",[951,1794,1795,1798,1801,1804,1807,1810,1813,1816,1818,1821,1824,1827],{"class":953,"line":1009},[951,1796,1797],{"class":957},"constexpr",[951,1799,1800],{"class":957}," double",[951,1802,1803],{"class":1012}," NaN ",[951,1805,1806],{"class":965},"=",[951,1808,1809],{"class":961}," std",[951,1811,1812],{"class":965},"::",[951,1814,1815],{"class":961},"numeric_limits",[951,1817,1222],{"class":965},[951,1819,1820],{"class":957},"double",[951,1822,1823],{"class":965},">::",[951,1825,1826],{"class":1000},"quiet_NaN",[951,1828,1829],{"class":965},"();\n",[951,1831,1832],{"class":953,"line":1030},[951,1833,1787],{"emptyLinePlaceholder":1786},[951,1835,1836,1838,1840,1842],{"class":953,"line":1047},[951,1837,997],{"class":957},[951,1839,1001],{"class":1000},[951,1841,1004],{"class":965},[951,1843,966],{"class":965},[951,1845,1846,1849,1852,1855,1857],{"class":953,"line":1066},[951,1847,1848],{"class":1019},"    42",[951,1850,1851],{"class":965}," \u003C=>",[951,1853,1854],{"class":1019}," 42",[951,1856,1059],{"class":965},[951,1858,1859],{"class":1062}," \u002F\u002F std::strong_ordering::equivalent\n",[951,1861,1862,1865,1867,1870,1872],{"class":953,"line":1188},[951,1863,1864],{"class":1012},"    NaN ",[951,1866,1132],{"class":965},[951,1868,1869],{"class":1019}," 1.0",[951,1871,1059],{"class":965},[951,1873,1874],{"class":1062}," \u002F\u002F std::partial_ordering::unordered\n",[951,1876,1877],{"class":953,"line":1203},[951,1878,1787],{"emptyLinePlaceholder":1786},[951,1880,1881],{"class":953,"line":1217},[951,1882,1883],{"class":1062},"    \u002F\u002F static_assert 是静态断言；如果括号内表达式为 false 导致编译错误\n",[951,1885,1886,1889,1891,1894,1896,1898,1901,1903,1905,1908,1910,1912],{"class":953,"line":1232},[951,1887,1888],{"class":1019},"    static_assert",[951,1890,1135],{"class":965},[951,1892,1893],{"class":1019},"42",[951,1895,1851],{"class":965},[951,1897,1854],{"class":1019},[951,1899,1900],{"class":965}," ==",[951,1902,1809],{"class":961},[951,1904,1812],{"class":965},[951,1906,1907],{"class":961},"strong_ordering",[951,1909,1812],{"class":965},[951,1911,1706],{"class":1012},[951,1913,1914],{"class":965},");\n",[951,1916,1917,1919,1921,1924,1926,1928,1930,1932,1934,1937,1939,1942],{"class":953,"line":1249},[951,1918,1888],{"class":1019},[951,1920,1135],{"class":965},[951,1922,1923],{"class":1012},"NaN ",[951,1925,1132],{"class":965},[951,1927,1869],{"class":1019},[951,1929,1900],{"class":965},[951,1931,1809],{"class":961},[951,1933,1812],{"class":965},[951,1935,1936],{"class":961},"partial_ordering",[951,1938,1812],{"class":965},[951,1940,1941],{"class":1012},"unordered",[951,1943,1914],{"class":965},[951,1945,1946],{"class":953,"line":1263},[951,1947,1069],{"class":965},[1274,1949,1950],{"id":1950},"三路比较运算符重载",[918,1952,1953],{},"正如最初代码中展现的，可以在类中声明如下的预置三路比较函数：",[941,1955,1957],{"className":943,"code":1956,"language":945,"meta":946,"style":946},"struct S {\n    auto operator\u003C=>(const S&) const = default;\n    \u002F\u002F 或者\n    std::strong_ordering operator\u003C=>(const S&) const = default;\n    \u002F\u002F 或者\n    std::weak_ordering operator\u003C=>(const S&) const = default;\n    \u002F\u002F 或者\n    std::partial_ordering operator\u003C=>(const S&) const = default;\n};\n",[948,1958,1959,1968,1994,1999,2030,2034,2065,2069,2099],{"__ignoreMap":946},[951,1960,1961,1963,1966],{"class":953,"line":954},[951,1962,958],{"class":957},[951,1964,1965],{"class":961}," S",[951,1967,966],{"class":965},[951,1969,1970,1972,1974,1976,1978,1980,1982,1984,1986,1988,1990,1992],{"class":953,"line":969},[951,1971,1126],{"class":957},[951,1973,1129],{"class":1019},[951,1975,1132],{"class":961},[951,1977,1135],{"class":965},[951,1979,1138],{"class":957},[951,1981,1965],{"class":961},[951,1983,1143],{"class":957},[951,1985,1146],{"class":965},[951,1987,1149],{"class":957},[951,1989,1152],{"class":965},[951,1991,1155],{"class":1019},[951,1993,985],{"class":965},[951,1995,1996],{"class":953,"line":988},[951,1997,1998],{"class":1062},"    \u002F\u002F 或者\n",[951,2000,2001,2004,2006,2008,2010,2012,2014,2016,2018,2020,2022,2024,2026,2028],{"class":953,"line":994},[951,2002,2003],{"class":961},"    std",[951,2005,1812],{"class":965},[951,2007,1907],{"class":961},[951,2009,1129],{"class":1019},[951,2011,1132],{"class":961},[951,2013,1135],{"class":965},[951,2015,1138],{"class":957},[951,2017,1965],{"class":961},[951,2019,1143],{"class":957},[951,2021,1146],{"class":965},[951,2023,1149],{"class":957},[951,2025,1152],{"class":965},[951,2027,1155],{"class":1019},[951,2029,985],{"class":965},[951,2031,2032],{"class":953,"line":1009},[951,2033,1998],{"class":1062},[951,2035,2036,2038,2040,2043,2045,2047,2049,2051,2053,2055,2057,2059,2061,2063],{"class":953,"line":1030},[951,2037,2003],{"class":961},[951,2039,1812],{"class":965},[951,2041,2042],{"class":961},"weak_ordering",[951,2044,1129],{"class":1019},[951,2046,1132],{"class":961},[951,2048,1135],{"class":965},[951,2050,1138],{"class":957},[951,2052,1965],{"class":961},[951,2054,1143],{"class":957},[951,2056,1146],{"class":965},[951,2058,1149],{"class":957},[951,2060,1152],{"class":965},[951,2062,1155],{"class":1019},[951,2064,985],{"class":965},[951,2066,2067],{"class":953,"line":1047},[951,2068,1998],{"class":1062},[951,2070,2071,2073,2075,2077,2079,2081,2083,2085,2087,2089,2091,2093,2095,2097],{"class":953,"line":1066},[951,2072,2003],{"class":961},[951,2074,1812],{"class":965},[951,2076,1936],{"class":961},[951,2078,1129],{"class":1019},[951,2080,1132],{"class":961},[951,2082,1135],{"class":965},[951,2084,1138],{"class":957},[951,2086,1965],{"class":961},[951,2088,1143],{"class":957},[951,2090,1146],{"class":965},[951,2092,1149],{"class":957},[951,2094,1152],{"class":965},[951,2096,1155],{"class":1019},[951,2098,985],{"class":965},[951,2100,2101],{"class":953,"line":1188},[951,2102,991],{"class":965},[918,2104,2105,2106,2109,2110,2112],{},"这四种声明方式的区别仅在于函数返回值。它决定了整个结构体上的序关系是全序、弱序还是预序。如果使用 ",[948,2107,2108],{},"auto"," 作为返回值类型，编译器会根据该类的成员、基类自动使用最严格的序关系。除了一些极端情形，一般用 ",[948,2111,2108],{}," 就足够了。",[918,2114,2115],{},"当使用预置的三路比较运算符重载时，编译器会生成类似这样的代码：",[941,2117,2119],{"className":943,"code":2118,"language":945,"meta":946,"style":946},"#include \u003Ccompare>\nstruct S {\n    \u002F\u002F 假设这里有三个成员 a b c…\n    int a;\n    double b;\n    int c;\n\n    \u002F\u002F 下为编译器生成的预置三路比较\n    \u002F\u002F 由于包含浮点数成员，所以是 std::partial_ordering\n    std::partial_ordering operator\u003C=>(const S& rhs) const {\n        constexpr auto EQUAL{std::partial_ordering::equivalent};\n        if (auto cmp{a \u003C=> rhs.a}; cmp != EQUAL) return cmp;\n        if (auto cmp{b \u003C=> rhs.b}; cmp != EQUAL) return cmp;\n        return c \u003C=> rhs.c;\n    }\n};\nint main() {\n    S a{1, 2.0, 3};\n    S b{1, 3.0, 2};\n    a \u003C=> b; \u002F\u002F std::partial_ordering::less\n    a > b; \u002F\u002F false\n}\n",[948,2120,2121,2132,2140,2145,2153,2162,2171,2175,2180,2185,2215,2241,2285,2323,2342,2348,2353,2364,2385,2406,2420,2433],{"__ignoreMap":946},[951,2122,2123,2125,2127,2129],{"class":953,"line":954},[951,2124,1083],{"class":1082},[951,2126,1086],{"class":965},[951,2128,1090],{"class":1089},[951,2130,2131],{"class":965},">\n",[951,2133,2134,2136,2138],{"class":953,"line":969},[951,2135,958],{"class":957},[951,2137,1965],{"class":961},[951,2139,966],{"class":965},[951,2141,2142],{"class":953,"line":988},[951,2143,2144],{"class":1062},"    \u002F\u002F 假设这里有三个成员 a b c…\n",[951,2146,2147,2149,2151],{"class":953,"line":994},[951,2148,972],{"class":957},[951,2150,1241],{"class":975},[951,2152,985],{"class":965},[951,2154,2155,2158,2160],{"class":953,"line":1009},[951,2156,2157],{"class":957},"    double",[951,2159,1056],{"class":975},[951,2161,985],{"class":965},[951,2163,2164,2166,2169],{"class":953,"line":1030},[951,2165,972],{"class":957},[951,2167,2168],{"class":975}," c",[951,2170,985],{"class":965},[951,2172,2173],{"class":953,"line":1047},[951,2174,1787],{"emptyLinePlaceholder":1786},[951,2176,2177],{"class":953,"line":1066},[951,2178,2179],{"class":1062},"    \u002F\u002F 下为编译器生成的预置三路比较\n",[951,2181,2182],{"class":953,"line":1188},[951,2183,2184],{"class":1062},"    \u002F\u002F 由于包含浮点数成员，所以是 std::partial_ordering\n",[951,2186,2187,2189,2191,2193,2195,2197,2199,2201,2203,2205,2209,2211,2213],{"class":953,"line":1203},[951,2188,2003],{"class":961},[951,2190,1812],{"class":965},[951,2192,1936],{"class":961},[951,2194,1129],{"class":1019},[951,2196,1132],{"class":961},[951,2198,1135],{"class":965},[951,2200,1138],{"class":957},[951,2202,1965],{"class":961},[951,2204,1143],{"class":957},[951,2206,2208],{"class":2207},"sHdIc"," rhs",[951,2210,1146],{"class":965},[951,2212,1149],{"class":957},[951,2214,966],{"class":965},[951,2216,2217,2220,2223,2226,2228,2231,2233,2235,2237,2239],{"class":953,"line":1217},[951,2218,2219],{"class":957},"        constexpr",[951,2221,2222],{"class":957}," auto",[951,2224,2225],{"class":975}," EQUAL",[951,2227,1016],{"class":965},[951,2229,2230],{"class":961},"std",[951,2232,1812],{"class":965},[951,2234,1936],{"class":961},[951,2236,1812],{"class":965},[951,2238,1706],{"class":975},[951,2240,991],{"class":965},[951,2242,2243,2246,2249,2251,2254,2256,2258,2261,2263,2266,2268,2271,2273,2275,2277,2280,2283],{"class":953,"line":1232},[951,2244,2245],{"class":1082},"        if",[951,2247,2248],{"class":965}," (",[951,2250,2108],{"class":957},[951,2252,2253],{"class":975}," cmp{a ",[951,2255,1132],{"class":965},[951,2257,2208],{"class":1012},[951,2259,2260],{"class":965},".",[951,2262,1378],{"class":1012},[951,2264,2265],{"class":975},"}",[951,2267,1059],{"class":965},[951,2269,2270],{"class":975}," cmp ",[951,2272,1254],{"class":965},[951,2274,2225],{"class":975},[951,2276,1146],{"class":965},[951,2278,2279],{"class":1082}," return",[951,2281,2282],{"class":975}," cmp",[951,2284,985],{"class":965},[951,2286,2287,2289,2291,2293,2296,2298,2300,2302,2305,2307,2309,2311,2313,2315,2317,2319,2321],{"class":953,"line":1249},[951,2288,2245],{"class":1082},[951,2290,2248],{"class":965},[951,2292,2108],{"class":957},[951,2294,2295],{"class":975}," cmp{b ",[951,2297,1132],{"class":965},[951,2299,2208],{"class":1012},[951,2301,2260],{"class":965},[951,2303,2304],{"class":1012},"b",[951,2306,2265],{"class":975},[951,2308,1059],{"class":965},[951,2310,2270],{"class":975},[951,2312,1254],{"class":965},[951,2314,2225],{"class":975},[951,2316,1146],{"class":965},[951,2318,2279],{"class":1082},[951,2320,2282],{"class":975},[951,2322,985],{"class":965},[951,2324,2325,2328,2331,2333,2335,2337,2340],{"class":953,"line":1263},[951,2326,2327],{"class":1082},"        return",[951,2329,2330],{"class":975}," c ",[951,2332,1132],{"class":965},[951,2334,2208],{"class":1012},[951,2336,2260],{"class":965},[951,2338,2339],{"class":1012},"c",[951,2341,985],{"class":965},[951,2343,2345],{"class":953,"line":2344},15,[951,2346,2347],{"class":965},"    }\n",[951,2349,2351],{"class":953,"line":2350},16,[951,2352,991],{"class":965},[951,2354,2356,2358,2360,2362],{"class":953,"line":2355},17,[951,2357,997],{"class":957},[951,2359,1001],{"class":1000},[951,2361,1004],{"class":965},[951,2363,966],{"class":965},[951,2365,2367,2370,2372,2374,2376,2379,2381,2383],{"class":953,"line":2366},18,[951,2368,2369],{"class":1012},"    S a",[951,2371,1016],{"class":965},[951,2373,1020],{"class":1019},[951,2375,979],{"class":965},[951,2377,2378],{"class":1019}," 2.0",[951,2380,979],{"class":965},[951,2382,1042],{"class":1019},[951,2384,991],{"class":965},[951,2386,2388,2391,2393,2395,2397,2400,2402,2404],{"class":953,"line":2387},19,[951,2389,2390],{"class":1012},"    S b",[951,2392,1016],{"class":965},[951,2394,1020],{"class":1019},[951,2396,979],{"class":965},[951,2398,2399],{"class":1019}," 3.0",[951,2401,979],{"class":965},[951,2403,1025],{"class":1019},[951,2405,991],{"class":965},[951,2407,2409,2411,2413,2415,2417],{"class":953,"line":2408},20,[951,2410,1050],{"class":1012},[951,2412,1132],{"class":965},[951,2414,1056],{"class":1012},[951,2416,1059],{"class":965},[951,2418,2419],{"class":1062}," \u002F\u002F std::partial_ordering::less\n",[951,2421,2423,2425,2427,2429,2431],{"class":953,"line":2422},21,[951,2424,1050],{"class":1012},[951,2426,1093],{"class":965},[951,2428,1056],{"class":1012},[951,2430,1059],{"class":965},[951,2432,1214],{"class":1062},[951,2434,2436],{"class":953,"line":2435},22,[951,2437,1069],{"class":965},[918,2439,2440],{},"用人话说就是：先三路比较第一个成员，如果比较结果不是 $\\tt equal$ 就直接返回它；否则比较第二个成员，如果不是 $\\tt equal$ 就直接返回它；然后再比较第三个成员……这样一直比较到成员列表中的最后一个数据成员。也可以形象地解释为按照成员列表“字典序”比较。",[918,2442,2443],{},"这种比较方式是很常用的；你可以通过调整成员列表的顺序来控制比较方法。如果你不想这样做，你也可以像这样手动提供三路比较：",[941,2445,2447],{"className":943,"code":2446,"language":945,"meta":946,"style":946},"#include \u003Ccompare>\nstruct S {\n    int a;\n    double b;\n    int c;\n\n    std::partial_ordering operator\u003C=>(const S& rhs) const {\n        \u002F\u002F 这次，先比较 c 后比较 b\n        if (auto cmp{a \u003C=> rhs.a}; cmp != 0) return cmp;\n        if (auto cmp{c \u003C=> rhs.c}; cmp != 0) return cmp;\n        return b \u003C=> rhs.b;\n    }\n};\nint main() {\n    S a{1, 2.0, 3};\n    S b{1, 3.0, 2};\n    a \u003C=> b; \u002F\u002F std::partial_ordering::greater\n    a > b; \u002F\u002F true\n}\n",[948,2448,2449,2459,2467,2475,2483,2491,2495,2523,2528,2565,2602,2619,2623,2627,2637,2655,2673,2686,2698],{"__ignoreMap":946},[951,2450,2451,2453,2455,2457],{"class":953,"line":954},[951,2452,1083],{"class":1082},[951,2454,1086],{"class":965},[951,2456,1090],{"class":1089},[951,2458,2131],{"class":965},[951,2460,2461,2463,2465],{"class":953,"line":969},[951,2462,958],{"class":957},[951,2464,1965],{"class":961},[951,2466,966],{"class":965},[951,2468,2469,2471,2473],{"class":953,"line":988},[951,2470,972],{"class":957},[951,2472,1241],{"class":975},[951,2474,985],{"class":965},[951,2476,2477,2479,2481],{"class":953,"line":994},[951,2478,2157],{"class":957},[951,2480,1056],{"class":975},[951,2482,985],{"class":965},[951,2484,2485,2487,2489],{"class":953,"line":1009},[951,2486,972],{"class":957},[951,2488,2168],{"class":975},[951,2490,985],{"class":965},[951,2492,2493],{"class":953,"line":1030},[951,2494,1787],{"emptyLinePlaceholder":1786},[951,2496,2497,2499,2501,2503,2505,2507,2509,2511,2513,2515,2517,2519,2521],{"class":953,"line":1047},[951,2498,2003],{"class":961},[951,2500,1812],{"class":965},[951,2502,1936],{"class":961},[951,2504,1129],{"class":1019},[951,2506,1132],{"class":961},[951,2508,1135],{"class":965},[951,2510,1138],{"class":957},[951,2512,1965],{"class":961},[951,2514,1143],{"class":957},[951,2516,2208],{"class":2207},[951,2518,1146],{"class":965},[951,2520,1149],{"class":957},[951,2522,966],{"class":965},[951,2524,2525],{"class":953,"line":1066},[951,2526,2527],{"class":1062},"        \u002F\u002F 这次，先比较 c 后比较 b\n",[951,2529,2530,2532,2534,2536,2538,2540,2542,2544,2546,2548,2550,2552,2554,2557,2559,2561,2563],{"class":953,"line":1188},[951,2531,2245],{"class":1082},[951,2533,2248],{"class":965},[951,2535,2108],{"class":957},[951,2537,2253],{"class":975},[951,2539,1132],{"class":965},[951,2541,2208],{"class":1012},[951,2543,2260],{"class":965},[951,2545,1378],{"class":1012},[951,2547,2265],{"class":975},[951,2549,1059],{"class":965},[951,2551,2270],{"class":975},[951,2553,1254],{"class":965},[951,2555,2556],{"class":1019}," 0",[951,2558,1146],{"class":965},[951,2560,2279],{"class":1082},[951,2562,2282],{"class":975},[951,2564,985],{"class":965},[951,2566,2567,2569,2571,2573,2576,2578,2580,2582,2584,2586,2588,2590,2592,2594,2596,2598,2600],{"class":953,"line":1203},[951,2568,2245],{"class":1082},[951,2570,2248],{"class":965},[951,2572,2108],{"class":957},[951,2574,2575],{"class":975}," cmp{c ",[951,2577,1132],{"class":965},[951,2579,2208],{"class":1012},[951,2581,2260],{"class":965},[951,2583,2339],{"class":1012},[951,2585,2265],{"class":975},[951,2587,1059],{"class":965},[951,2589,2270],{"class":975},[951,2591,1254],{"class":965},[951,2593,2556],{"class":1019},[951,2595,1146],{"class":965},[951,2597,2279],{"class":1082},[951,2599,2282],{"class":975},[951,2601,985],{"class":965},[951,2603,2604,2606,2609,2611,2613,2615,2617],{"class":953,"line":1217},[951,2605,2327],{"class":1082},[951,2607,2608],{"class":975}," b ",[951,2610,1132],{"class":965},[951,2612,2208],{"class":1012},[951,2614,2260],{"class":965},[951,2616,2304],{"class":1012},[951,2618,985],{"class":965},[951,2620,2621],{"class":953,"line":1232},[951,2622,2347],{"class":965},[951,2624,2625],{"class":953,"line":1249},[951,2626,991],{"class":965},[951,2628,2629,2631,2633,2635],{"class":953,"line":1263},[951,2630,997],{"class":957},[951,2632,1001],{"class":1000},[951,2634,1004],{"class":965},[951,2636,966],{"class":965},[951,2638,2639,2641,2643,2645,2647,2649,2651,2653],{"class":953,"line":2344},[951,2640,2369],{"class":1012},[951,2642,1016],{"class":965},[951,2644,1020],{"class":1019},[951,2646,979],{"class":965},[951,2648,2378],{"class":1019},[951,2650,979],{"class":965},[951,2652,1042],{"class":1019},[951,2654,991],{"class":965},[951,2656,2657,2659,2661,2663,2665,2667,2669,2671],{"class":953,"line":2350},[951,2658,2390],{"class":1012},[951,2660,1016],{"class":965},[951,2662,1020],{"class":1019},[951,2664,979],{"class":965},[951,2666,2399],{"class":1019},[951,2668,979],{"class":965},[951,2670,1025],{"class":1019},[951,2672,991],{"class":965},[951,2674,2675,2677,2679,2681,2683],{"class":953,"line":2355},[951,2676,1050],{"class":1012},[951,2678,1132],{"class":965},[951,2680,1056],{"class":1012},[951,2682,1059],{"class":965},[951,2684,2685],{"class":1062}," \u002F\u002F std::partial_ordering::greater\n",[951,2687,2688,2690,2692,2694,2696],{"class":953,"line":2366},[951,2689,1050],{"class":1012},[951,2691,1093],{"class":965},[951,2693,1056],{"class":1012},[951,2695,1059],{"class":965},[951,2697,1246],{"class":1062},[951,2699,2700],{"class":953,"line":2387},[951,2701,1069],{"class":965},[918,2703,2704,2705,2708,2709,2711,2712,2715],{},"但如果只是调换成员比较顺序的话，可以通过 ",[948,2706,2707],{},"std::tie"," 来简化。",[948,2710,2707],{}," 可以生成定义了三路比较的 ",[948,2713,2714],{},"std::tuple"," 类型：",[941,2717,2719],{"className":943,"code":2718,"language":945,"meta":946,"style":946},"#include \u003Ccompare>\nstruct S {\n    int a;\n    double b;\n    int c;\n\n    std::partial_ordering operator\u003C=>(const S& rhs) const {\n        return std::tie(a, c, b) \u003C=> std::tie(rhs.a, rhs.c, rhs.b);\n    }\n};\nint main() {\n    S a{1, 2.0, 3};\n    S b{1, 3.0, 2};\n    a \u003C=> b; \u002F\u002F std::partial_ordering::greater\n    a > b; \u002F\u002F true\n}\n",[948,2720,2721,2731,2739,2747,2755,2763,2767,2795,2855,2859,2863,2873,2891,2909,2921,2933],{"__ignoreMap":946},[951,2722,2723,2725,2727,2729],{"class":953,"line":954},[951,2724,1083],{"class":1082},[951,2726,1086],{"class":965},[951,2728,1090],{"class":1089},[951,2730,2131],{"class":965},[951,2732,2733,2735,2737],{"class":953,"line":969},[951,2734,958],{"class":957},[951,2736,1965],{"class":961},[951,2738,966],{"class":965},[951,2740,2741,2743,2745],{"class":953,"line":988},[951,2742,972],{"class":957},[951,2744,1241],{"class":975},[951,2746,985],{"class":965},[951,2748,2749,2751,2753],{"class":953,"line":994},[951,2750,2157],{"class":957},[951,2752,1056],{"class":975},[951,2754,985],{"class":965},[951,2756,2757,2759,2761],{"class":953,"line":1009},[951,2758,972],{"class":957},[951,2760,2168],{"class":975},[951,2762,985],{"class":965},[951,2764,2765],{"class":953,"line":1030},[951,2766,1787],{"emptyLinePlaceholder":1786},[951,2768,2769,2771,2773,2775,2777,2779,2781,2783,2785,2787,2789,2791,2793],{"class":953,"line":1047},[951,2770,2003],{"class":961},[951,2772,1812],{"class":965},[951,2774,1936],{"class":961},[951,2776,1129],{"class":1019},[951,2778,1132],{"class":961},[951,2780,1135],{"class":965},[951,2782,1138],{"class":957},[951,2784,1965],{"class":961},[951,2786,1143],{"class":957},[951,2788,2208],{"class":2207},[951,2790,1146],{"class":965},[951,2792,1149],{"class":957},[951,2794,966],{"class":965},[951,2796,2797,2799,2801,2803,2806,2808,2810,2812,2814,2816,2818,2820,2822,2824,2826,2828,2830,2833,2835,2837,2839,2841,2843,2845,2847,2849,2851,2853],{"class":953,"line":1066},[951,2798,2327],{"class":1082},[951,2800,1809],{"class":961},[951,2802,1812],{"class":965},[951,2804,2805],{"class":1000},"tie",[951,2807,1135],{"class":965},[951,2809,1378],{"class":975},[951,2811,979],{"class":965},[951,2813,2168],{"class":975},[951,2815,979],{"class":965},[951,2817,1056],{"class":975},[951,2819,1146],{"class":965},[951,2821,1851],{"class":965},[951,2823,1809],{"class":961},[951,2825,1812],{"class":965},[951,2827,2805],{"class":1000},[951,2829,1135],{"class":965},[951,2831,2832],{"class":1012},"rhs",[951,2834,2260],{"class":965},[951,2836,1378],{"class":1012},[951,2838,979],{"class":965},[951,2840,2208],{"class":1012},[951,2842,2260],{"class":965},[951,2844,2339],{"class":1012},[951,2846,979],{"class":965},[951,2848,2208],{"class":1012},[951,2850,2260],{"class":965},[951,2852,2304],{"class":1012},[951,2854,1914],{"class":965},[951,2856,2857],{"class":953,"line":1188},[951,2858,2347],{"class":965},[951,2860,2861],{"class":953,"line":1203},[951,2862,991],{"class":965},[951,2864,2865,2867,2869,2871],{"class":953,"line":1217},[951,2866,997],{"class":957},[951,2868,1001],{"class":1000},[951,2870,1004],{"class":965},[951,2872,966],{"class":965},[951,2874,2875,2877,2879,2881,2883,2885,2887,2889],{"class":953,"line":1232},[951,2876,2369],{"class":1012},[951,2878,1016],{"class":965},[951,2880,1020],{"class":1019},[951,2882,979],{"class":965},[951,2884,2378],{"class":1019},[951,2886,979],{"class":965},[951,2888,1042],{"class":1019},[951,2890,991],{"class":965},[951,2892,2893,2895,2897,2899,2901,2903,2905,2907],{"class":953,"line":1249},[951,2894,2390],{"class":1012},[951,2896,1016],{"class":965},[951,2898,1020],{"class":1019},[951,2900,979],{"class":965},[951,2902,2399],{"class":1019},[951,2904,979],{"class":965},[951,2906,1025],{"class":1019},[951,2908,991],{"class":965},[951,2910,2911,2913,2915,2917,2919],{"class":953,"line":1263},[951,2912,1050],{"class":1012},[951,2914,1132],{"class":965},[951,2916,1056],{"class":1012},[951,2918,1059],{"class":965},[951,2920,2685],{"class":1062},[951,2922,2923,2925,2927,2929,2931],{"class":953,"line":2344},[951,2924,1050],{"class":1012},[951,2926,1093],{"class":965},[951,2928,1056],{"class":1012},[951,2930,1059],{"class":965},[951,2932,1246],{"class":1062},[951,2934,2935],{"class":953,"line":2350},[951,2936,1069],{"class":965},[1274,2938,2939],{"id":2939},"预置等于运算符",[918,2941,2942,2943,1448,2945,2947,2948,2950,2951,1356],{},"用三路比较导出等于、不等于运算符会出现一个小小的问题：存在性能损失。举一个字符串的例子，判断两个字符串相等与否可以先判断它们的长度是否相同：如果不同的话，那两个字符串肯定不相等。但如果用三路比较，就必须每个字符遍历一遍。因此，C++ 不会将 ",[948,2944,1053],{},[948,2946,1254],{}," 两个运算符通过 ",[948,2949,1132],{}," 实现。取而代之的，C++ 引入了新的",[1476,2952,2939],{},[941,2954,2956],{"className":943,"code":2955,"language":945,"meta":946,"style":946},"#include \u003Ccompare>\nstruct S {\n    int a;\n    double b;\n    int c;\n\n    auto operator\u003C=>(const S&) const = default;\n    \u002F\u002F 看下面\n    bool operator==(const S&) const = default;\n};\n",[948,2957,2958,2968,2976,2984,2992,3000,3004,3030,3035,3062],{"__ignoreMap":946},[951,2959,2960,2962,2964,2966],{"class":953,"line":954},[951,2961,1083],{"class":1082},[951,2963,1086],{"class":965},[951,2965,1090],{"class":1089},[951,2967,2131],{"class":965},[951,2969,2970,2972,2974],{"class":953,"line":969},[951,2971,958],{"class":957},[951,2973,1965],{"class":961},[951,2975,966],{"class":965},[951,2977,2978,2980,2982],{"class":953,"line":988},[951,2979,972],{"class":957},[951,2981,1241],{"class":975},[951,2983,985],{"class":965},[951,2985,2986,2988,2990],{"class":953,"line":994},[951,2987,2157],{"class":957},[951,2989,1056],{"class":975},[951,2991,985],{"class":965},[951,2993,2994,2996,2998],{"class":953,"line":1009},[951,2995,972],{"class":957},[951,2997,2168],{"class":975},[951,2999,985],{"class":965},[951,3001,3002],{"class":953,"line":1030},[951,3003,1787],{"emptyLinePlaceholder":1786},[951,3005,3006,3008,3010,3012,3014,3016,3018,3020,3022,3024,3026,3028],{"class":953,"line":1047},[951,3007,1126],{"class":957},[951,3009,1129],{"class":1019},[951,3011,1132],{"class":961},[951,3013,1135],{"class":965},[951,3015,1138],{"class":957},[951,3017,1965],{"class":961},[951,3019,1143],{"class":957},[951,3021,1146],{"class":965},[951,3023,1149],{"class":957},[951,3025,1152],{"class":965},[951,3027,1155],{"class":1019},[951,3029,985],{"class":965},[951,3031,3032],{"class":953,"line":1066},[951,3033,3034],{"class":1062},"    \u002F\u002F 看下面\n",[951,3036,3037,3040,3042,3044,3046,3048,3050,3052,3054,3056,3058,3060],{"class":953,"line":1188},[951,3038,3039],{"class":957},"    bool",[951,3041,1129],{"class":1019},[951,3043,1053],{"class":961},[951,3045,1135],{"class":965},[951,3047,1138],{"class":957},[951,3049,1965],{"class":961},[951,3051,1143],{"class":957},[951,3053,1146],{"class":965},[951,3055,1149],{"class":957},[951,3057,1152],{"class":965},[951,3059,1155],{"class":1019},[951,3061,985],{"class":965},[951,3063,3064],{"class":953,"line":1203},[951,3065,991],{"class":965},[918,3067,3068,3069,3072,3073,3075,3076,3078,3079,3081,3082,3084,3085,3087,3088,3090,3091,3093,3094,3096],{},"使用预置等于运算符时，会生成一个简单的等于运算符重载定义。其内容就是，按成员列表从上到下依次用 ",[948,3070,3071],{},"operator=="," 比较每个成员，在首个不等的地方返回 ",[948,3074,1320],{}," 或最终返回 ",[948,3077,1316],{},"。此外，",[948,3080,1254],{}," 运算符可以通过 ",[948,3083,1053],{}," 运算符导出，即仅定义 ",[948,3086,3071],{}," 就可以使用 ",[948,3089,1254],{}," 运算符。在实践上，你可以使用预置的 ",[948,3092,1271],{}," 和一个自定义的、有优化的 ",[948,3095,3071],{},"：这样既减少了代码长度，又最大程度的提高性能。",[918,3098,3099,3100,3102,3103,3105,3106,3108,3109,3111,3112,3114,3115,1448,3117,3119],{},"此外，如果你的 ",[948,3101,1271],{}," 是预置的话，编译器也会帮你预置一个 ",[948,3104,3071],{},"：这样仅仅一个 ",[948,3107,1271],{}," 就能处理好全部七个比较运算符，非常方便。但如果 ",[948,3110,1271],{}," 是自定义的的话，就需要手动指明 ",[948,3113,3071],{},"（预置或者自己定义），否则 ",[948,3116,1053],{},[948,3118,1254],{}," 运算符无法使用。",[1505,3121,3122],{},"html pre.shiki code .spNyl, html code.shiki .spNyl{--shiki-light:#9C3EDA;--shiki-default:#C792EA;--shiki-dark:#C792EA}html pre.shiki code .sBMFI, html code.shiki .sBMFI{--shiki-light:#E2931D;--shiki-default:#FFCB6B;--shiki-dark:#FFCB6B}html pre.shiki code .sMK4o, html code.shiki .sMK4o{--shiki-light:#39ADB5;--shiki-default:#89DDFF;--shiki-dark:#89DDFF}html pre.shiki code .swJcz, html code.shiki .swJcz{--shiki-light:#E53935;--shiki-default:#F07178;--shiki-dark:#F07178}html pre.shiki code .s2Zo4, html code.shiki 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