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// a = 1/2 Rational b(3, 5); // b = 3/5 Rational c = a * b; // c Ϊ 3/10 ÆÚÍûÒѾ´æÔÚÒ»¸öֵΪ 3/10 µÄÓÐÀíÊýÊDz»ÏÖʵµÄ¡£Èç¹ûoperator* Ò»¶¨Òª ·µ»ØÕâÑùÒ»¸öÊýµÄÒýÓ㬾ͱØÐë×Ô¼º´´½¨Õâ¸öÊýµÄ¶ÔÏó¡£ Ò»¸öº¯ÊýÖ»ÄÜÓÐÁ½ÖÖ·½·¨´´½¨Ò»¸öжÔÏó£ºÔÚ¶ÑÕ»Àï»òÔÚ¶ÑÉÏ¡£ÔÚ¶ÑÕ»Àï ´´½¨¶ÔÏóʱ°éËæ×ÅÒ»¸ö¾Ö²¿±äÁ¿µÄ¶¨Ò壬²ÉÓÃÕâÖÖ·½·¨£¬¾ÍÒªÕâÑùдoperator*£º // д´Ëº¯ÊýµÄµÚÒ»¸ö´íÎó·½·¨ inline const Rational& operator*(const Rational& lhs, const Rational& rhs) { Rational result(lhs.n * rhs.n, lhs.d * rhs.d); return result; } Õâ¸ö·½·¨Ó¦¸Ã±»·ñ¾ö£¬ÒòΪÎÒÃǵÄÄ¿±êÊDZÜÃâ¹¹Ô캯Êý±»µ÷Ó㬵« result ±ØÐëÒªÏóÆäËü¶ÔÏóÒ»Ñù±»¹¹Ôì¡£ÁíÍ⣬Õâ¸öº¯Êý»¹ÓÐÁíÍâÒ»¸ö¸üÑÏÖØµÄÎÊÌ⣬ Ëü·µ»ØµÄÊÇÒ»¸ö¾Ö²¿¶ÔÏóµÄÒýÓ㬹ØÓÚÕâ¸ö´íÎó£¬Ìõ¿î31 ½øÐÐÁËÉîÈëµÄÌÖÂÛ¡£ ÄÇô£¬ÔÚ¶ÑÉÏ´´½¨Ò»¸ö¶ÔÏóÈ»ºó·µ»ØËüµÄÒýÓÃÄØ£¿»ùÓڶѵĶÔÏóÊÇͨ¹ýʹ ÓÃnew ²úÉúµÄ£¬ËùÒÔÓ¦¸ÃÕâÑùдoperator*£º // д´Ëº¯ÊýµÄµÚ¶þ¸ö´íÎó·½·¨ inline const Rational& operator*(const Rational& lhs, const Rational& rhs) { Rational *result = new Rational(lhs.n * rhs.n, lhs.d * rhs.d); return *result; } Ê×ÏÈ£¬Ä㻹Êǵøºµ£¹¹Ô캯Êýµ÷ÓõĿªÏú£¬ÒòΪ new ·ÖÅäµÄÄÚ´æÊÇͨ¹ýµ÷ ÓÃÒ»¸öÊʵ±µÄ¹¹Ô캯ÊýÀ´³õʼ»¯µÄ£¨¼ûÌõ¿î5 ºÍM8£©¡£ÁíÍ⣬»¹ÓÐÒ»¸öÎÊÌ⣺ ˽«¸ºÔðÓÃdelete À´É¾³ýµônew Éú³ÉµÄ¶ÔÏóÄØ£¿ ʵ¼ÊÉÏ£¬Õâ¾ø¶ÔÊÇÒ»¸öÄÚ´æÐ¹Â©¡£¼´Ê¹¿ÉÒÔ˵·þ operator*µÄµ÷ÓÃÕßȥȡº¯ Êý·µ»ØÖµµØÖ·£¬È»ºóÓÃdelete ȥɾ³ýËü£¨¾ø¶Ô²»¿ÉÄÜ¡ª¡ªÌõ¿î31 չʾÁËÕâÑù µÄ´úÂë»áÊÇʲôÑùµÄ£©£¬µ«Ò»Ð©¸´Ôӵıí´ïʽ»á²úÉúûÓÐÃû×ÖµÄÁÙʱֵ£¬³ÌÐòÔ± ÊDz»¿ÉÄܵõ½µÄ¡£ÀýÈ磺 Rational w, x, y, z; w = x * y * z; Á½¸ö¶Ô operator*µÄµ÷Óö¼²úÉúÁËûÓÐÃû×ÖµÄÁÙʱֵ£¬³ÌÐòÔ±ÎÞ·¨¿´µ½£¬Òò ¶øÎÞ·¨É¾³ý¡££¨ÔٴβμûÌõ¿î31£© Ò²Ðí£¬Äã»áÏëÄã±ÈÒ»°ãµÄÐÜ¡ª¡ª»òÒ»°ãµÄ³ÌÐòÔ±¡ª¡ªÒª´ÏÃ÷£»Ò²Ðí£¬Äã×¢ Òâµ½ÔÚ¶ÑÕ»ºÍ¶ÑÉÏ´´½¨¶ÔÏóµÄ·½·¨±ÜÃâ²»Á˶Թ¹Ô캯ÊýµÄµ÷Óã»Ò²Ðí£¬ÄãÏëÆð ÁËÎÒÃÇ×î³õµÄÄ¿±êÊÇΪÁ˱ÜÃâÕâÖÖ¶Ô¹¹Ô캯ÊýµÄµ÷Óã»Ò²Ðí£¬ÄãÓиö°ì·¨¿ÉÒÔ Ö»ÓÃÒ»¸ö¹¹Ô캯ÊýÀ´¸ãµàÒ»ÇУ»Ò²Ðí£¬ÄãµÄÑÛǰ³öÏÖÁËÕâÑùÒ»¶Î´úÂ룺operator* ·µ»ØÒ»¸ö¡°ÔÚº¯ÊýÄÚ²¿¶¨ÒåµÄ¾²Ì¬Rational ¶ÔÏó¡±µÄÒýÓ㺠// д´Ëº¯ÊýµÄµÚÈý¸ö´íÎó·½·¨ inline const Rational& operator*(const Rational& lhs, const Rational& rhs) { static Rational result; // ½«Òª×÷ΪÒýÓ÷µ»ØµÄ // ¾²Ì¬¶ÔÏó lhs ºÍrhs Ïà³Ë£¬½á¹û·Å½øresult£» return result; } Õâ¸ö·½·¨¿´ÆðÀ´ºÃÏóÓÐÏ·£¬ËäÈ»ÔÚʵ¼ÊʵÏÖÉÏÃæµÄα´úÂëʱÄã»á·¢ÏÖ£¬²» µ÷ÓÃÒ»¸öRational ¹¹Ô캯ÊýÊDz»¿ÉÄܸø³öresult µÄÕýÈ·ÖµµÄ£¬¶ø±ÜÃâÕâÑùµÄµ÷ ÓÃÕýÊÇÎÒÃÇҪ̸ÂÛµÄÖ÷Ìâ¡£¾ÍËãÄãʵÏÖÁËÉÏÃæµÄα´úÂ룬µ«£¬ÄãÔÙ´ÏÃ÷Ò²²»ÄÜ ×îÖÕÍì¾ÈÕâ¸ö²»ÐÒµÄÉè¼Æ¡£ ÏëÖªµÀΪʲô£¬¿´¿´ÏÂÃæÕâ¶ÎдµÃºÜºÏÀíµÄÓû§´úÂ룺 bool operator==(const Rational& lhs, // Rationals µÄoperator== const Rational& rhs); // Rational a, b, c, d; ... if ((a * b) == (c * d)) { ´¦ÀíÏàµÈµÄÇé¿ö; } else { ´¦Àí²»ÏàµÈµÄÇé¿ö; } ¿´³öÀ´ÁËÂð£¿((a*b) == (c*d)) »áÓÀԶΪtrue£¬²»¹Üa£¬b£¬c ºÍd ÊÇʲôֵ£¡ Óõȼ۵ĺ¯ÊýÐÎÊ½ÖØÐ´ÉÏÃæµÄÏàµÈÅжÏÓï¾ä¾ÍºÜÈÝÒ×Ã÷°×·¢ÉúÕâÒ»¿É¶ñÐРΪµÄÔÒòÁË£º if (operator==(operator*(a, b), operator*(c, d))) ×¢Òâµ± operator==±»µ÷ÓÃʱ£¬×ÜÓÐÁ½¸öoperator*¸Õ±»µ÷Óã¬Ã¿¸öµ÷Ó÷µ»Ø operator*ÄÚ²¿µÄ¾²Ì¬Rational ¶ÔÏóµÄÒýÓá£ÓÚÊÇ£¬ÉÏÃæµÄÓï¾äʵ¼ÊÉÏÊÇÇëÇó operator==¶Ô¡°operator*ÄÚ²¿µÄ¾²Ì¬Rational ¶ÔÏóµÄÖµ¡±ºÍ¡°operator*ÄÚ²¿µÄ ¾²Ì¬Rational ¶ÔÏóµÄÖµ¡±½øÐбȽϣ¬ÕâÑùµÄ±È½Ï²»ÏàµÈ²Å¹ÖÄØ£¡ ÐÒÔ˵ϰ£¬ÎÒÒÔÉϵÄ˵Ã÷Ó¦¸Ã×ãÒÔ˵·þÄ㣺Ïë¡°ÔÚÏóoperator*ÕâÑùµÄº¯Êý Àï·µ»ØÒ»¸öÒýÓá±Êµ¼ÊÉÏÊÇÔÚÀË·Ñʱ¼ä¡£µ«ÎÒûÓ×Öɵ½»áÏàÐÅÐÒÔË×Ü»á¹âÁÙ×Ô ¼º¡£Ò»Ð©ÈË¡ª¡ªÄãÃÇÖªµÀÕâЩÈËÊÇָˡª¡ª´Ë¿Ì»áÔÚÏ룬¡°ßí£¬ÉÏÃæÄǸö·½·¨£¬ Èç¹ûÒ»¸ö¾²Ì¬±äÁ¿²»¹»Óã¬Ò²Ðí¿ÉÒÔÓÃÒ»¸ö¾²Ì¬Êý×é⋯⋯¡± Çë¾Í´Ë´òס£¡ÎÒÃÇÄѵÀ»¹Ã»Êܹ»Â𣿠ÎÒ²»ÄÜÈÃ×Ô¼ºÐ´Ò»¶ÎʾÀý´úÂëÀ´Ì«¸ßÕâ¸öÉè¼Æ£¬ÒòΪ¼´Ê¹Ö»±§ÓÐÉÏÃæÕâÖÖ Ïë·¨¶¼×ãÒÔÁîÈ˸е½ÐßÀ¢¡£Ê×ÏÈ£¬Äã±ØÐëÑ¡ÔñÒ»¸ön£¬Ö¸¶¨Êý×éµÄ´óС¡£Èç¹û n ̫С£¬¾Í»áûµØ·½´¢´æº¯Êý·µ»ØÖµ£¬ÕâºÍÎÒÃÇÇ°Ãæ·ñ¶¨µÄÄǸö¡°²ÉÓõ¥¸ö¾² ̬±äÁ¿µÄÉè¼Æ¡±Ïà±ÈûÓÐʲô¸Ä½ø¡£Èç¹ûn Ì«´ó£¬¾Í»á½µµÍ³ÌÐòµÄÐÔÄÜ£¬ÒòΪ º¯ÊýµÚÒ»´Î±»µ÷ÓÃʱÊý×éÖÐÿ¸ö¶ÔÏó¶¼Òª±»´´½¨¡£Õâ»á´øÀ´n ¸ö¹¹Ô캯ÊýºÍn ¸öÎö¹¹º¯ÊýµÄ¿ªÏú£¬¼´Ê¹Õâ¸öº¯ÊýÖ»±»µ÷ÓÃÒ»´Î¡£Èç¹û˵"optimization"£¨×îÓÅ »¯£© ÊÇÖ¸Ìá¸ßÈí¼þµÄÐÔÄܵĹý³Ì£¬ ÄÇ Ã´ ÏÖ ÔÚ Õâ ÖÖ ×ö ·¨ ¼ò Ö± ¿É ÒÔ ³Æ Ϊ "pessimization"£¨×î²î»¯£©¡£×îºó£¬ÏëÏëÔõô°ÑÐèÒªµÄÖµ·Åµ½Êý×éµÄ¶ÔÏóÖÐÒÔ¼° ÐèÒª¶à´óµÄ¿ªÏú£¿ÔÚ¶ÔÏó¼ä´«ÖµµÄ×îÖ±½ÓµÄ·½·¨ÊÇͨ¹ý¸³Öµ£¬µ«¸³ÖµµÄ¿ªÏúÓÖ Óжà´óÄØ£¿Ò»°ãÀ´Ëµ£¬ËüÏ൱ÓÚµ÷ÓÃÒ»¸öÎö¹¹º¯Êý£¨´Ý»Ù¾ÉÖµ£©ÔÙ¼ÓÉϵ÷ÓÃÒ» ¸ö¹¹Ô캯Êý£¨¿½±´ÐÂÖµ£©¡£µ«ÎÒÃÇÏÖÔÚµÄÄ¿±êÕýÊÇΪÁ˱ÜÃâ¹¹ÔìºÍÎö¹¹µÄ¿ªÏú°¡£¡ Ãæ¶ÔÏÖʵ°É£ºÕâ¸ö·½·¨Ò²¾ø¶Ô²»ÄÜÑ¡ÓᣠËùÒÔ£¬Ð´Ò»¸ö±ØÐë·µ»ØÒ»¸öжÔÏóµÄº¯ÊýµÄÕýÈ··½·¨¾ÍÊÇÈÃÕâ¸öº¯Êý·µ»Ø Ò»¸öжÔÏó¡£¶ÔÓÚRational µÄoperator*À´Ëµ£¬ÕâÒâζ×ÅÒª²»¾ÍÊÇÏÂÃæµÄ´úÂ루¾Í ÊÇ×î³õ¿´µ½µÄÄǶδúÂ룩£¬Òª²»¾ÍÊDZ¾ÖÊÉϺÍËüµÈ¼ÛµÄ´úÂ룺 inline const Rational operator*(const Rational& lhs, const Rational& rhs) { return Rational(lhs.n * rhs.n, lhs.d * rhs.d); } µÄÈ·£¬Õâ»áµ¼Ö¡°operator*µÄ·µ»ØÖµ¹¹ÔìºÍÎö¹¹Ê±´øÀ´µÄ¿ªÏú¡±£¬µ«¹é¸ù ½áµ×ËüÖ»ÊÇÓÃСµÄ´ú¼Û»»À´ÕýÈ·µÄ³ÌÐòÔËÐÐÐÐΪ¶øÒÑ¡£¿öÇÒ£¬ÄãËùµ£ÐĵĿªÏú »¹ÓпÉÄÜÓÀÔ¶²»»á³öÏÖ£ººÍËùÓгÌÐòÉè¼ÆÓïÑÔÒ»Ñù£¬C++ÔÊÐí±àÒëÆ÷µÄÉè¼ÆÕß ²ÉÓÃһЩÓÅ»¯´ëÊ©À´Ìá¸ßËùÉú³ÉµÄ´úÂëµÄÐÔÄÜ£¬ËùÒÔ£¬ÔÚÓÐЩ³¡ºÏ£¬operator* µÄ·µ»ØÖµ»á±»°²È«µØ³ýÈ¥£¨¼ûÌõ¿îM20£©¡£µ±±àÒëÆ÷²ÉÓÃÁËÕâÖÖÓÅ»¯Ê±£¨µ±Ç° ´ó²¿·Ö±àÒëÆ÷Õâô×ö£©£¬³ÌÐòºÍÒÔǰһÑù¼ÌÐø¹¤×÷£¬Ö»²»¹ýÊÇÔËÐÐËٶȱÈÄãÔ¤¼Æ µÄÒª¿ì¶øÒÑ¡£ ÒÔÉÏÌÖÂÛ¿ÉÒÔ¹é½áΪ£ºµ±ÐèÒªÔÚ·µ»ØÒýÓúͷµ»Ø¶ÔÏó¼ä×ö¾ö¶¨Ê±£¬ÄãµÄÖ° ÔðÊÇÑ¡Ôñ¿ÉÒÔÍê³ÉÕýÈ·¹¦ÄܵÄÄǸö¡£ÖÁÓÚÔõôÈÃÕâ¸öÑ¡ÔñËù²úÉúµÄ´ú¼Û¾¡¿ÉÄÜ µÄС£¬ÄÇÊDZàÒëÆ÷µÄÉú²úÉÌÈ¥ÏëµÄÊ¡£ |
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