Stock-based Compensation Expense (Additional Information) (Details) $ in Millions	3 Months Ended
Apr. 30, 2019 USD ($) period shares	Apr. 30, 2018 USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Compensation cost related to non-vested stock options	$ 58.5
Market capitalization	2,000.0
Allocated share-based compensation expense	$ 75.2	$ 54.4
Expected dividend yield	0.00%
Stock Options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Compensation cost related to non-vested stock options, weighted average period of recognition	2 years 7 months 6 days
Restricted Stock Units (RSUs) and Performance Shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Awards vested in period, fair value	$ 50.3	96.2
Awards granted in period (shares) \| shares	904,800
Restricted Stock Units (RSUs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Awards granted in period (shares) \| shares	700,000
Allocated share-based compensation expense	$ 54.4	41.7
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	$ 6.5	$ 6.5
Award vesting period	3 years
Expected dividend yield	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	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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Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Volatility, Market Capitalization

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Represents the expense recognized during the period arising from equity-based compensation arrangements (for example, shares of stock, unit, stock options or other equity instruments) with employees, directors and certain consultants qualifying for treatment as employees.

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Weighted average period over which unrecognized compensation is expected to be recognized for equity-based compensation plans, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Unrecognized cost of unvested options awarded to employees as compensation.

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Fair value of share-based awards for which the grantee gained the right by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash.

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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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