Ìîäåëü ôîðìàëüíîãî äîêàçàòåëüñòâà êîíêðåòíîñòè ïðîãðàììû - ÷àñòü 4

                                                                

                                                                                                   i < N

                                                               

                      **

                                                                 í³                       T’(i)>T’(i+1)  

                                                               

                                                                                    Èçìåíèòü

                                                                               T( è) íà  T(è+1)

                                               

                                                 

                                                                                        *                                                                                               

                                                                                        M = true

                     Ðèñ.7.1.   Ñõåìà ñîðòèðîâêè   ýëåìåíòîâ ìàññèâà Ò'

 òî÷êå ñ äâóìÿ çâåçäî÷êàìè âûïîëíåíû âñå âîçìîæíûå îïåðàöèè îáìåíà ìåñòàìè ïàð ñìåæíûõ ýëåìåíòîâ ìàññèâà T' çà îäèí ïðîõîä ÷åðåç T', òî åñòü îïåðàòîð îáìåíà  ðàáîòàë îäèí èëè áîëüøå ðàç. Îäíàêî ïóçûðüêîâàÿ ñîðòèðîâêà íå äàåò ãàðàíòèè, ÷òî äîñòèãíóòî óïîðÿäî÷åíèå çà îäèí ïðîõîä ïî ìàññèâó T', ïîñêîëüêó ïîñëå î÷åðåäíîãî îáìåíà èíäåêñ  i óâåëè÷èâàåòñÿ íà 1 íåçàâèñèìî îò òîãî, êàê ñîîòíîñèòñÿ íîâûé ýëåìåíò T '( i)  ñ ïðåäøåñòâóþùèì ýëåìåíòîì T '(i – 1).

 Â ýòîé òî÷êå òàêæå ñïðàâåäëèâîå óòâåðæäåíèå:

$ i , åñëè   i < N  òî T' ( i) < T' ( i + 1).

×àñòü àëãîðèòìà, îáîçíà÷åííàÿ òî÷êîé ñ äâóìÿ çâåçäî÷êàìè âûïîëíÿåòñÿ äî òåõ ïîð, ïîêà íå áóäåò óïîðÿäî÷åí âåñü ìàññèâ, òî åñòü íå áóäåò âûïîëíÿòüñÿ óñëîâèå (â) óòâåðæäåíèÿ Àånd äëÿ âñåõ ýëåìåíòîâ ìàññèâà T':

"i,  åñëè   i < N  òî T' (i) <  T' (i+ 1).

Ñîäåðæàíèå  Íàçàä  Âïåðåä

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