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Stock-based Compensation Expense (Additional Information) (Details) $ in Millions | 3 Months Ended
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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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