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Computation of Earnings Per Common Share - Narratives (Details) - $ / shares
6 Months Ended
Jan. 27, 2018
Jan. 26, 2019
Jul. 28, 2018
Apr. 28, 2018
Jul. 29, 2017
Jul. 30, 2016
Sep. 15, 2015
Shares used in computing earnings per common share:              
Adoption of accounting principled effect on diluted shares 177,575            
Weighted average stock price (usd per share) $ 106.11   $ 99.27 $ 110.46      
Convertible Note Hedge              
Shares used in computing earnings per common share:              
Debt instrument, convertible, conversion price (per share)   $ 96.89         $ 96.89
0.75% Convertible Senior Notes Due 2021              
Shares used in computing earnings per common share:              
Debt, interest rate (in percent) 0.75% 0.75%     0.75% 0.75%  
Debt instrument, convertible, conversion price (per share)             96.89
Class of warrant or right, exercise price of warrants or rights (per warrant)   $ 130.43         $ 130.43