Segment and Geographic Information - Financial Information by Reportable Segment (Details) - USD ($) $ in Millions	3 Months Ended								12 Months Ended
	Oct. 31, 2019	Jul. 31, 2019	Apr. 30, 2019	Jan. 31, 2019	Oct. 31, 2018	Jul. 31, 2018	Apr. 30, 2018	Jan. 31, 2018	Oct. 31, 2019	Oct. 31, 2018	Oct. 31, 2017
Revenues
Revenues	$ 1,648.0	$ 1,647.9	$ 1,594.7	$ 1,607.9	$ 1,648.8	$ 1,624.3	$ 1,580.8	$ 1,588.3	$ 6,498.6	$ 6,442.2	$ 5,453.6
Operating profit (loss)
Operating profit (loss)									208.3	138.6	101.9
Income from unconsolidated affiliates									3.0	3.2	4.2
Interest expense									(51.1)	(54.1)	(19.2)
Income from continuing operations before income taxes									160.2	87.7	86.9
Depreciation and amortization
Depreciation and amortization									107.4	112.5	70.1
Operating Segments
Revenues
Revenues									6,626.3
Corporate
Operating profit (loss)
Operating profit (loss)									(159.0)	(168.8)	(189.0)
Depreciation and amortization
Depreciation and amortization									13.9	12.4	11.8
Segment Reconciling Items
Operating profit (loss)
Adjustment for tax deductions for energy efficient government buildings, included in Technical Solutions									0.1	(2.8)	(1.9)
Income from unconsolidated affiliates									(3.0)	(3.2)	(4.1)
Business & Industry | Operating Segments
Revenues
Revenues									3,251.4	3,268.4	2,939.4
Operating profit (loss)
Operating profit (loss)									182.3	157.9	146.6
Depreciation and amortization
Depreciation and amortization									21.3	23.6	17.4
Aviation | Operating Segments
Revenues
Revenues									1,017.3	1,038.7	1,003.0
Operating profit (loss)
Operating profit (loss)									21.1	23.2	23.0
Depreciation and amortization
Depreciation and amortization									11.9	13.1	13.4
Technology & Manufacturing | Operating Segments
Revenues
Revenues									917.0	925.4	698.1
Operating profit (loss)
Operating profit (loss)									72.5	67.4	48.6
Depreciation and amortization
Depreciation and amortization									14.3	15.6	6.4
Education | Operating Segments
Revenues
Revenues									847.4	856.7	368.8
Operating profit (loss)
Operating profit (loss)									39.0	44.1	17.4
Depreciation and amortization
Depreciation and amortization									37.3	37.5	8.4
Technical Solutions | Operating Segments
Revenues
Revenues									593.2	500.1	473.4
Operating profit (loss)
Operating profit (loss)									55.4	21.8	39.4
Depreciation and amortization
Depreciation and amortization									8.6	10.2	12.5
Government Services | Operating Segments
Revenues
Revenues									0.0	0.0	86.5
Operating profit (loss)
Operating profit (loss)									(0.1)	(0.8)	21.8
Elimination of inter-segment revenues | Operating Segments
Revenues
Revenues									$ (127.7)	$ (147.1)	$ (115.7)