Goodwill and Other Intangible Assets, Net - Components of Other Intangible Assets (Details) - USD ($) $ in Millions	May 03, 2024	Oct. 31, 2023	May 05, 2023
Other Intangible Assets
Weighted-Average Useful Life in Years	13 years 7 months 6 days	13 years 3 months 18 days	13 years 4 months 24 days
Gross Carrying Amount	$ 458.6	$ 471.0	$ 465.1
Accumulated Amortization	(207.4)	(202.4)	(186.3)
Net	251.2	268.6	278.8
Indefinite-lived - trade names	271.5	271.5	289.6
Total other intangible assets, gross	730.1	742.5	754.7
Total other intangible assets, net	$ 522.7	$ 540.1	$ 568.4
Patents
Other Intangible Assets
Weighted-Average Useful Life in Years	9 years 10 months 24 days	9 years 10 months 24 days	9 years 10 months 24 days
Gross Carrying Amount	$ 18.2	$ 18.2	$ 18.2
Accumulated Amortization	(16.4)	(16.0)	(15.7)
Net	$ 1.8	$ 2.2	$ 2.5
Non-compete agreements
Other Intangible Assets
Weighted-Average Useful Life in Years		5 years 6 months	5 years 6 months
Gross Carrying Amount		$ 6.9	$ 6.9
Accumulated Amortization		(6.9)	(6.9)
Net		$ 0.0	$ 0.0
Customer-related
Other Intangible Assets
Weighted-Average Useful Life in Years	15 years 9 months 18 days	15 years 9 months 18 days	16 years
Gross Carrying Amount	$ 327.6	$ 327.5	$ 321.4
Accumulated Amortization	(118.7)	(106.7)	(95.8)
Net	$ 208.9	$ 220.8	$ 225.6
Developed technology
Other Intangible Assets
Weighted-Average Useful Life in Years	7 years 1 month 6 days	7 years 1 month 6 days	7 years 1 month 6 days
Gross Carrying Amount	$ 102.1	$ 102.0	$ 102.1
Accumulated Amortization	(67.9)	(63.1)	(58.4)
Net	$ 34.2	$ 38.9	$ 43.7
Trade names
Other Intangible Assets
Weighted-Average Useful Life in Years	13 years 8 months 12 days	13 years 8 months 12 days	13 years 8 months 12 days
Gross Carrying Amount	$ 10.7	$ 10.7	$ 10.8
Accumulated Amortization	(4.4)	(4.0)	(3.8)
Net	$ 6.3	$ 6.7	$ 7.0
Backlog and other
Other Intangible Assets
Weighted-Average Useful Life in Years		7 months 6 days	7 months 6 days
Gross Carrying Amount		$ 5.7	$ 5.7
Accumulated Amortization		(5.7)	(5.7)
Net		$ 0.0	$ 0.0