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Stock-based Compensation Expense (Additional Information) (Details) $ in Millions | 3 Months Ended | 9 Months Ended
--- | --- | ---
Oct. 31, 2019 USD ($) shares | Oct. 31, 2018 USD ($) shares | Oct. 31, 2019 USD ($) period shares | Oct. 31, 2018 USD ($)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Compensation cost related to non-vested stock options | $ 35.9 |  | $ 35.9 |
Allocated share-based compensation expense | $ 94.0 | $ 64.2 | 257.4 | $ 175.5
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 2 months 12 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 |  |  | $ 277.3 | 355.1
Awards granted in period (shares) | shares |  |  | 2,812,300 |
Restricted Stock Units (RSUs) |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards granted in period (shares) | shares |  |  | 2,200,000 |
Allocated share-based compensation expense | $ 73.8 | $ 49.8 | $ 192.4 | 135.6
RSU based upon stock closing price |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards granted in period (shares) | shares |  |  | 300,000 |
Performance Stock Unit |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |
Awards granted in period (shares) | shares | 0 | 0 | 300,000 |
Allocated share-based compensation expense | $ 6.4 | $ 7.5 | $ 18.6 | $ 19.9
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% | 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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