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Stock-based Compensation Expense (Additional Information) (Details) $ in Millions | 3 Months Ended | 6 Months Ended
--- | --- | ---
Jul. 31, 2019 USD ($) | Jul. 31, 2018 USD ($) | Jul. 31, 2019 USD ($) period shares | Jul. 31, 2018 USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Compensation cost related to non-vested stock options | $ 42.3 |  | $ 42.3 |
Allocated share-based compensation expense | $ 88.2 | $ 56.9 | 163.4 | $ 111.3
Market capitalization |  |  | $ 2,000.0 |
Expected dividend yield (in percentage) |  |  | 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 3 months 18 days |  | 2 years 4 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 |  |  | $ 84.3 | 133.7
Awards granted in period (shares) | shares |  |  | 1,349,000.0 |
Restricted Stock Units (RSUs) |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards granted in period (shares) | shares |  |  | 800,000 |
Allocated share-based compensation expense | $ 58.9 | 44.1 | $ 113.3 | 85.8
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 | $ 11.0 | $ 5.9 | $ 17.5 | $ 12.4
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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