Stock-based Compensation Expense (Additional Information) (Details) $ in Millions	3 Months Ended
Apr. 30, 2020 USD ($) period shares	Apr. 30, 2019 USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Allocated share-based compensation expense	$ 98.2	$ 75.2
Settlement of liability-classified restricted stock units	28.7	0.0
Market capitalization	$ 2,000.0
Expected dividend yield (in percentage)	0.00%
Restricted Stock Units (RSUs) and Performance Shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Awards vested in period, fair value	$ 111.4	50.3
Awards granted in period (shares) \| shares	775,400
Restricted Stock Units (RSUs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Awards granted in period (shares) \| shares	500,000
Allocated share-based compensation expense	$ 76.9	54.4
Performance Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Awards granted in period (shares) \| shares	300,000
Allocated share-based compensation expense	$ 7.4	$ 6.5
Award vesting period	3 years
Expected dividend yield (in percentage)	0.00%	0.00%
1998 Employee Qualified Stock Purchase Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Employee stock purchase plan maximum percentage of compensation to purchase shares by eligible participants	15.00%
Employee stock purchase plan minimum percentage of common stock fair value defined to purchase shares by eligible participants	85.00%
Employee stock purchase plan, number of exercise periods \| period	4
Employee stock purchase plan, term of exercise period	6 months
Employee stock purchase plan, term of offering period	24 months
Expected dividend yield (in percentage)	0.00%	0.00%
Share-based Compensation Award, Tranche One \| Performance Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
PSU annual vesting percentage	33.33%
Share-based Compensation Award, Tranche Two \| Performance Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
PSU annual vesting percentage	33.33%
Share-based Compensation Award, Tranche Three \| Performance Stock Unit
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
PSU annual vesting percentage	33.33%

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Employee Stock Purchase Plan, Minimum Percentage of Common Stock Fair Value Defined to Purchase Shares By Eligible Participants

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Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

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The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term.

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