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Stock-based Compensation Expense (Additional Information) (Details) $ in Millions | 3 Months Ended | 9 Months Ended
--- | --- | ---
Oct. 31, 2018 USD ($) | Oct. 31, 2017 USD ($) | Oct. 31, 2018 USD ($) period shares | Oct. 31, 2017 USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Allocated share-based compensation expense | $ 64.2 | $ 65.1 | $ 175.5 | $ 199.5
Market capitalization |  |  | 2,000.0 |
Restricted Stock Units (RSUs) and Performance Shares |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards vested in period, fair value |  |  | $ 355.1 | 332.8
Awards granted in period (shares) | shares |  |  | 1,784,600 |
Restricted Stock Units (RSUs) |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards granted in period (shares) | shares |  |  | 1,600,000 |
Allocated share-based compensation expense | 49.8 | 51.5 | $ 135.6 | 153.5
Performance Stock Unit |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards granted in period (shares) | shares |  |  | 200,000 |
Allocated share-based compensation expense | $ 7.5 | $ 7.1 | $ 19.9 | 27.7
Award vesting period |  |  | 3 years |
Employee Qualified Stock Purchase Plan 1998 ESP 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 |
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% |
Chief Executive Officer | Restricted Stock Units (RSUs) |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Allocated share-based compensation expense |  |  |  | 9.1
Chief Executive Officer | Performance Stock Unit |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Allocated share-based compensation expense |  |  |  | $ 7.5

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