To Students / ТР по Дискретной математике для ЗРЗ-319, ЗРП-319

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Задача 9. Дополнение графа, реберный граф

Для указанного графа построить его дополнение и реберный граф.

Задача 10. Остовное дерево минимального веса

Для графа G, заданного матрицей весов, построить минимальный по весу остов и

найти его вес.												0	x1	1 7					15 12 1 10 1 1
0	x1	1 10 1 5 1 1 14 1										0	x1	1 7					15 12 1 10 1 1
	N0	1		x1	x2	x3	x4	x5	x6	x7			N0	2			x1	x2 x3		x4	x5	x6	x7
B	x3			1	6	1	3 1 1				C B		x3			15 13				7	15 7			C
B				1		1				1 C		B							1				1 C
B	x2			10 1 6 2 4 8 1							C	B	x2			7 1 13 9					1 1 8			C
B	x5						1		1		C	B	x5							1		1		C
B	x5			1	4 1 6			1	5		C B		x5						15 9		1	10		C
B	x4			1				1		1 C B			x4			1 1					1		1 C
B	x4			5 2 3				6		3	C B		x4			12 9			7		9		11	C
B	x6			1	8 1		1	5	1	2	C B		x6			10			7		10	1	12	C
B	x7			1			1		1		C	B	x7					1		1		1		C
B	x7			14	1 1		3	1	2		C B		x7			1		8	1	11	1	12		C
@					1 1			1		1 A @						1			1		1		1 A
0	x1	1 10 11 1 14 1 12 1 0											x1	1 3					5	1 6		1 1 1
	N0	3		x1	x2	x3	x4	x5	x6	x7			N0	4			x1	x2 x3		x4	x5	x6	x7
B	x3			11 10		1	12 10		1	6	C B		x3			5 10				5	7	1	9	C
B						1			1		C	B							1			1		C
B	x2			10 1 10 9 1 1 7							C B		x2			3 1 10 6					8	1 4		C
B	x4			1	9 12		1	9 12			C B		x4			1		6	5		8	7		C
B	x5			1			1			1 C		B	x5			1			7	1			1 C
B	x5			14	1	10 9		1	11 12		C B		x5			6 8			7	8	1	9 11		C
B	x6				1			1			C	B	x6							7	1			C
B	x6			1 1 1			12 11				C B		x6			1 1 1				7	9			C
B	x7			1 1 1					1 1 C B				x7			1 1 1					11	1 1 C
B	x7			12 7 6			1	12 8			C B		x7			1		4	9		11			C
@							1			1 A		@				1				1		1 1 A
0	x1	1 8 1 10 13 1 11 1 0											x1	1 6					8	1 1 7 1 1
	N0	5		x1	x2	x3	x4	x5	x6	x7			N0	6			x1	x2 x3		x4	x5	x6	x7
B	x3			1	7	1 1		19 10 15			C B		x3			8 11				7	8	1	9	C
B				1		1 1					C	B							1			1		C
B	x2			8 1 7 8 1 15 1							C B		x2			6 1 11 12 9						1 5		C
B	x4			10 8		1 1		9	1	6	C B		x4			1		12 7			6	5 10		C
B	x5			13		1 1			1		C	B	x5			1		9	8	1		8		C
B	x5			13	1	19 9		1	8		C B		x5			1		9	8	6	1	8		C
B	x6				1			1		1 C		B	x6			1				5	1		1 C
B	x6			1	15 10		1	8	1	12	C B		x6			7		1 1		5	8	1	7	C
B	x7			1			1		1		C	B	x7					1 1				1		C
B	x7			11	1	15 6		1	12		C B		x7			1		5	9	10	1	7		C
@					1			1		1 A		@				1					1		1 A
0	x1	1 3 8 1 3 6 1 1 0											x1	1 9 10						15	1 1 11 1
	N0	7		x1	x2	x3	x4	x5	x6	x7			N0	8	x1			x2	x3	x4	x5	x6	x7
B	x3			8 7		1	4 6		1	10	C B		x3		10 14				1	10	9	1	6	C
B	x2					1			1		C	B	x2						1	12		1		C:
B	x2			3 1 7 6 1 1 4							C B		x2		9 1 14					12	1 8 15			C
B	x4			1	6 4		1	5 7			C B		x4		15 12				10	1	11	12		C
B				1	1		1	1		1 C		B			1 1					1	1		1 C
B	x6			6	1			1			C	B	x6		1 1					12	1			C
B	x6			6	1 1		7 8				C B		x6		1			8	1	12	12			C
B	x5			3	1 1				1 1 C B				x5		1				1			1 1 C
B	x5			3		6 5			8 9		C B		x5						9 11			12 11		C
@	x7			1	4 10		1	9	1 1 A @				x7		11 15				6	1	11	1 1 A
B	x7				4 10			9			C B		x7		11 15				6		11			C
0	N0 9		x1 x2 x3 x4 x5 x6 x7								1 0		N0 10				x1 x2 x3 x4 x5 x6 x7								1
	N0 9		x1 x2 x3 x4 x5 x6 x7										N0 10				x1 x2 x3 x4 x5 x6 x7
	x1		1 8 9 1 1 1 6										x1				1 8 4 9 1 6 1
B						1				1 C		B							1		1		1 C
B	x2		8 1 7 6 9 1 1									B	x2				8 1 11 6 10 1 8
B			1				1			1 C		B								1			1 C
B	x3		9 7				6 10 5				C B		x3				4 11			7		9		C
B	x5		1		9 10 8			1	4 5		C B		x5				1	10		5	1	7 6		C
B	x4		1		6 6			1			C	B	x4				1		1		1			C
B	x4				6 6			8 7			C B		x4				9 6 7				5 6			C
B	x6		1 1			5 7 4			1	6	C B		x6				6		9 6 7			1	8	C
B	x7		1 1						1		C	B	x7					1				1		C
B	x7		6		1 1 1			5 6			C B		x7				1	8			6 8			C
@					1 1 1					1 A @							1	1 1					1 A

0	x1		1 10 1 5					1 6 1 1					0		x1		1 5 11 14 1 1 87								1
	N0 11			x1	x2	x3	x4	x5	x6	x7					N0 12			x1	x2	x3	x4	x5	x6	x
B				1		1				1 C			B							1				1 C
B	x2			10	1 6 1			4 1 5			C B				x2			5 1 5 7				1 1 8			C
	x4			5 1		3		3	1	5					x4			14 7 4				7	1	11
B	x3				6		1					C		B		x3			11 5			1			C
B							3	1 2			C B										4	8 6			C
B	x5			1	4	1 3		1	4 2		C B				x5			1 1		8 7		1		3 5		C
B	x6					2					C		B		x6					6				6	C
B				6				4			C B							1 1				3	1		C
B	x7				1		1		2	1 1 C B						x7						1			C
B				1	5	1	5				C B							8 8		1	11 5 6				C
@									1 1 A				@												1 A
0	x1		1 6 5 1 8 1 10 1 0												x1		1 5 8 1 1 8 1 1
	N0 13	x1			x2	x3	x4	x5	x6	x7					N0 14	x1			x2	x3	x4	x5	x6	x7
B	x3		5 9			1	8 9		1	11	C B				x3		8 7			1	4 7 7			1 C
B											C		B											1 C
B	x2		6 1 9 7 6 1 1								C B				x2		5 1 7 10 1 8								C
	x4		1		7 8		1	5 6							x4		1		10 4		1	6 9 4
B	x5									1 C			B		x5								3 5		C
B			8 6 9 5					1	7 9		C B						1 1			7 6		1			C
B	x6										C		B		x6									6	C
B			1 1 1				6		7			C B					8 8 7 9 3						1		C
B							1		1 1 C				B					1 1 1								C
@	x7		10		1	11		9	1 1 A @						x7		4 5 6					1 A
B											C B														C
0	x1		1 6			5 1 10 9 1 1							0		x1		1 7 8 1 6 1 4								1
	N0 15			x1	x2	x3	x4	x5	x6	x7					N0 16			x1	x2	x3	x4	x5	x6	x7
B						1			1		C		B							1		1		1 C
B	x2			6 1 4 5				3 1 6			C B				x2			7 1 8 1 5 10 1							C
	x4			1	5	6		3 6							x4			1 1		6		3 9 4
B	x3						1		7		1 C			B		x3						1		3		C
B				5 4			6			8	C B							8 8			6				C
B	x5			10	3	7 3		1	8 7		C B				x5			6 5		1	3	1	8 7		C
B	x6			9			6			5	C		B		x6										C
B					1 1			8	1		C B							1	10 3 9			8			C
B	x7										C		B		x7						4	7	1 1 C
B				1	6	8		7 5			C B							4	1 1						C
@							1				1 A @													1 1 A
0	N0 17			x1 x2 x3 x4 x5 x6 x7								1	0		N0 18			x1 x2 x3 x4 x5 x6 x7								1

	x1			1 12 10 1 11 1 18											x1			1 5 4 11 1 6 1
B						1			1		C		B							1 1			1		C
B	x2			12	1 13 14 1 1 7						C B				x2			5 1 8 9				1 9 1			C
	x4			1	14 9			15 14							x4			11 9		1 1 1			5 3
B	x3				13		1		13		1 C			B		x3			4 8					7	C
B				10			9			16	C B											5			C
B	x5			11		13 15			15 14		C B				x5			1 1		5	1 1		7 8		C
B	x6				1			1			C		B		x6									6	C
B				1 1 1			14		15			C B						6 9		1	5	7	1		C
B	x7							14	1 1 C B							x7										C
B				18	7	16					C B							1 1		7 3		8 6			C
@							1			1 1 A				@											1 A
0	N0 19			x1 x2 x			x4 x5 x6 x7					1	0		N0 20			x1 x2 x3 x4 x5 x6 x7								1

						3
	x1			1 8		9	1 10 1 1								x1			1 11 5 8				1 8 1
B						1				1 C				B							1 1			1		C
B	x2			8 1 6 5				9 1 7			C		B		x2			11 1 6 13 1 10 1							C
				1			1														1 1
B	x3			9 6			11			7 12			C B				x3			5 6				7		9	C
B	x5			10	9	7 3		1	4		C B				x5			1 1		7 3		1	9 7		C
B	x4				5	11				1 C			B		x4										C
B								3 5 4			C B							8 13				3 5 8			C
B	x6			1		12 5		4	1	9	C B				x6			8 10		1	5	9			C
B	x7				1		4				C		B		x7							7	1 1 C
B				1	7	1		1	9		C B							1 1		9 8					C
@										1 A @													1 1 A

0	x1	1 1 11 1 8							1 10 1 0								x1			1 1 1 10 11 1 67								1
	N0 21	x1	x2	x3	x4		x5			x6		x7					N0	22	x1		x2		x3	x4	x5	x6	x
B	x3	11	1 1 1					6	4 3					C B			x3			1 1 1				3 3		1	8	C
B			1 1 1						8 1					C B						1 1 1						1		C
B	x2	1 1 1 12 5							8 1					C B			x2							12 10 5 1				C
B	x4	1	12	1 1				5		1		7		C B			x4			10 12 3				1	6	1	7	C
B	x5	1		1 1						1				C		B	x5							1		1		C
B	x5	8 5 6 5					1			7 4				C B			x5			11 10 3 6					1	9		C
B		1					1							C		B									1		1 C
B	x7	1			1 1 1 C B												x7			1 1 1 1								C
B	x7	10	1	3 7 4										C B			x7			6	1		8 7		1	11		C
@	x6		1					7		1 1 A						@	x6				1				1		1 A
B	x6		8 4					7						C B			x6				5				9		11	C
0	x1	1 1 12 10 14 1 1 1 0															x1			1 3 8 12 7 1 16 1
	N0 23	x1	x2	x3	x4		x5			x6		x7					N0	24	x1		x2		x3	x4	x5	x6	x7
B	x3	12	12	1	7 6				8					C B			x3			8 4			1	5 7 11				C
B				1								1 C				B							1				1 C
B	x2	1 1 12 1 5							1 7					C B			x2			3 1 4 1 9 1 1								C
B	x4	10	1	7	1			4	9 9					C B			x4			12	1		5	1	10 6 4			C
B	x5	14	1		1					8				C		B	x5				1			1		5		C
B	x5	14	5 6 4				1			8				C B			x5			7 9 7 10					1	5		C
B	x6						1					1 C				B	x6								1		1 C
B	x6	1	1	8 9 8						1		7		C B			x6			1 1			11 6 5			1	5	C
B	x7	1	1		9					1				C		B	x7			1 1				4		1		C
B	x7	1	7	1	9		1			7				C B			x7			16	1 1			4	1	5		C
@		1		1	0		1					1 A @									1 1				1		1 A
					0		x1			1 1 7 1 1 11 1 1
						N0			25		x1		x2		x3	x4	x5	x6		x7
					B		x3				7		1 1			5	6	1		10		C	:
					B		x2						1 1				8	1		1		C	:
					B		x2				1 1 1 17						8	15		1		C
					B		x4				1		17		5	1	12	5		3		C
					B						1					1	1					C
					B		x6				1		15			5	1					C
					B		x6				11		15		1	5	4					C
					B		x5							8	1	12		1 1 C
					B		x5							8	6	12		4		9		C
					@		x7				1 1				10	3	9	1 1 A
					B		x7								10	3	9					C

Задача 11. Кратчайшие пути в графе. Алгоритм Дейкстры

По заданной матрице весов графа найти величину минимального пути и сам путь от вершины x1 до вершины x6 или x7 по алгоритму Дейкстры.

0	x1	1 5 10				13	1 1		1	0	x1	1 11			1 14		15	1 1
	N0	1	x1	x2	x3	x4	x5	x6			N0	2	x1	x2	x3	x4	x5	x6
B	x3		1 1 1			5 3 6			C B		x3		1 1		1 1			13	C
B			1 1 1					1	C B				1 1 1 1 1					1	C
B	x2		1 1 8 9 13					1	C B		x2				13			1
B			1 1 1 1						C B				1			1 1 C
B	x4		1 1 1 1 1					10	C B		x4		1	7 11		1 1			C
B	x4						8	10	C B		x4			7 11			9		C
B	x6								C	B	x6								C
@	x5		1 1 1 1 1 1 A @								x5		1 1 1 1 1 1 A
B	x5							9	C B		x5			11 10				14	C
0	x1	1 5 8 7 18						1	1	0	x1	1 6 8 11 10						1 1
	N0	3	x1	x2	x3	x4	x5	x6			N0	4	x1	x2	x3	x4	x5	x6
B			1 1 1 1 1					1	C B				1 1						C
B	x2		1 1		11	1 1		1	C B		x2		1 1 1 9 7 15						C
B	x3		1 1			1 1		17	C B		x3			8		7 14		11	C
B	x4		1	10 12		1	6		C B		x4		1 1 1 1				6 7		C
B	x5		1	7 8		1		1 C B			x5		1 1 1 1					9	C
B	x5		1	7 8		1 1		11	C B		x5		1 1 1 1 1					9	C
B	x6		1			1 1			C B		x6		1 1 1 1 1						C
B	x6								C	B	x6								C
@			1 1 1 1 1 1 A @										1 1 1 1 1 1 A

		N0 5								x1 x2 x3 x4 x5 x6 x7																						0								x		x				x					x


0																											1				N 6						x1											x5				6
				x1						1 1 11 15 7 1 1																					N 6						x1			2		3				4		x5				6
				x1						1 1 11 15 7 1 1																					x1									5		6				9								C
B				x2						1 1									14		18						C B				x3						1			3						3 4 16								C
				x2							1 1 1								14		18			1				0			x2						1									3		1 1						1
B				x4							1 1 1													1			C		B		x2						1					1				3					14			C
B				x4						1 9											11 16						C		B								1					1												C
B				x3						1 9						13 7 11 22											C										1 1 1 1																	C
B				x5						1 1 1 1 1											8 23						C B				x4						1 1 1 1 1														4			C
B				x5						1 1 1 1 1											8 23						C B				x5						1 1 1 1 1														8			C
B				x6						1 1 1 1 1														19			C B				x5						1 1 1									3		1			8			C
B				x6						1 1 1 1 1 1														19			C B				x6						1 1 1											1						C
B										1 1 1 1 1 1																	C B				x6																							C
B				x7																							C	@									1 1 1 1 1 1 A
@										1 1 1 1 1 1 1 A
		0				x1					1 7 9 1 11 1														1			0			x1				1 7 15 1 14 1 1
					N0				7		x1	x2			x3			x4		x5		x6								N0 8				x1				x2		x3				x4			x5		x6
		B				x3					1		6		1				5 6						C B						x3				1 1 1									19			1		21			C
		B									1				1							1 C B													1 1 1												1					C
		B				x2						1 1 6 1 13													C			B			x2				1 1 7 16 1 1																	C
		B				x4					1 1 1 1 1											7			C			B			x4				1 1 1 1 1														17			C
		B				x5					1 1 1 1 1											8			C B						x5				1 1 1 1 1														18			C
		B				x5					1		4		1				6	1		8			C B						x5				1			13 14 15									1		18			C
		B				x6					1				1					1					C			B			x6				1												1					C
		B				x6																			C			B			x6																					C
		@									1 1 1 1 1 1 A @																								1 1 1 1 1 1 A
			x1					1			10 12																0	x1					1 7 19 20 1 15 1 1
0			0																			1						N0		10		x1 x2								x3		x4				x5		x6			x7
0	N 9							1					x3			1 1 1						1						x2														11				6
	N 9						x x2						x3			x4			x5		x6						B																											C
B			x3					1 1											1								B	x3					1 1 1									6 9						1			16			C
B			x3					1 1 1 1											10				C B					x4					1 1 1															1						C:
B			x2					1 1 1 1													1 C B							x4																				8 13 C
B			x2										11			9					19		C B																												1			C
B			x5					1 1 1													6		C B					x5					1 1 1 1 1															5 15						C
B			x5										13								6		C B										1 1 1 1 1																					C
B			x4										13						11 10				C B										1 1 1 1 1																					C
B			x6					1 1 1 1 1															C B					x6					1 1 1 1 1 1																		14			C
B			x6																				C B										1 1 1 1 1 1																					C
@								1 1 1 1 1 1 A																			B	x7																										C
																											@						1 1 1 1 1 1 1 A
	B		N0 11								x1 x2 x3 x4 x5 x6																			N0 12						x1 x2 x3 x4 x5 x6																	C
			N0 11								x1 x2 x3 x4 x5 x6																			N0 12						x1 x2 x3 x4 x5 x6
						x3					1		2						1 3 11							C B					x3					1 1									5 6 15
	0					x1					1 7 2 1 13 1															1 0					x1					1 10 11 6 1 1																	1
	B										1				1										C			B								1 1 1																	C
	B					x2						1 1 1 6 1													C			B			x2											13 8 11 17											C
	B					x4					1 1 1 1 1											5			C			B			x4					1 1 1 1												7					C
	B					x5					1 1 1 1 1											5			C B						x5					1 1 1 1														1 C
	B					x5					1 1 1								3	1		5			C B						x5					1 1 1 1 1															9		C
	B					x6					1 1 1									1					C B						x6					1 1 1 1 1																	C
	B					x6																			C			B			x6																						C
	@										1 1 1 1 1 1 A @																										1 1 1 1 1 1 A
	0					x1					1 6 1 9 12 1														1 0						x1				1 4 9 8 1 1 1
			N0 13								x1	x2			x3			x4		x5		x6								N0		14				x1			x2			x3			x4			x5		x6
	B					x3					1 1 1 1 1											6			C B						x3					1 1 1 1															3		C
	B										1 1 1 1 1														C B											1 1 1 1 1														1			C
	B					x2					1 1 6 1 1 1														C			B			x2											2								1
	B					x5					1		7 5					1				10			C			B			x5					1			2					1						1 C
	B					x5					1		7 5					1 1				10			C B						x5					1			2		1 1 1										3		C
	B					x4					1		4 8					1 1							C B						x4					1					1 1 1												C
	B					x4							4 8								6 14				C B						x4								2 4									6					C
	B					x6																			C			B			x6																						C
	@										1 1 1 1 1 1 A @																										1 1 1 1 1 1 A
	N0 15									x1 x2 x3 x4 x5 x6 x7																		0				0						1													1 1


0			x2											7 1 4 9 1													1					x2								x				5 9 6
																															N 16							x1		x			x x4					x5				x6
			x1							1 5 1 10 8 12 1																														2				3
			x1							1 5 1 10 8 12 1																						x1								6				9		13 12						15 C
B										1 1 1									1								C B					x3															6					15 C
B			x3							1 1							5				6 11						C											1 1													1				C
B			x5							1 1 1 1 1 1																	C B					x4						1 1 1 1											8 9						C
B			x5											6							13 21						C B											1 1 1 1																	C
B			x4																					14			C B											1 1 1 1																	C
B			x6							1 1 1 1															9		C B					x5						1 1 1 1 1														8			C
B			x6							1 1 1							8		1 1						9		C B					x6						1 1 1 1 1																	C
B										1 1 1									1 1								C B					x6																							C
B			x7																								C	@										1 1 1 1 1 1 A
@										1 1 1 1 1 1 1 A

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