01 knapsack using backtracking

Backtracking Technique ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Outline of Backtracking Approach ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1 2 3 5 7 11 4 6 8 9 10

N-Queens Problem ,[object Object],[object Object],[object Object],Q Q Q Q 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

N-Queens Problem: DFS ,[object Object]

N-Queens Problem: DFS (Same Col/Row x) ,[object Object],X 1 =1 X 2 =2 3 4 4 3 4 3 4 2 3 2 3 2 2 4 3 2 3 4 1 4 1 3 2 4 1 3 4 1 2 4 3 2 1 2 3 4 (x 1 , x 2 , x 3 , x 4 )=(2, 4, 1, 3) ,[object Object],[object Object],[object Object]

N-Queens Problem: Backtracking ,[object Object],[object Object],[object Object],[object Object],Q (i, col(i)) Q (k, col(k)) Q (i,col(i)) Q (k,col(k))

N-Queens Problem: Backtracking ,[object Object]

N-Queens Problem ,[object Object],[object Object],[object Object],[object Object],#Nodes Checked DFS (n n ) #Nodes Checked DFS (same col/row X) (n!) #Nodes Checked Backtracking 341 19,173,961 9.73 ⅹ10 12 1.20ⅹ 10 16 24 40,320 4.79 ⅹ10 8 8.72ⅹ 10 10 61 15,721 1.01 ⅹ10 7 3.78ⅹ 10 8 4 8 12 14 n

Graph Coloring ,[object Object],[object Object],[object Object],[object Object],V 1 V 2 V 4 V 3 2-coloring X 3-coloring O

Graph Coloring ,[object Object],[object Object],[object Object],start 1 2 3 2 1 3 2 1 3 2 1 3 X X X X X

Hamiltonian Circuits Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Hamiltonian Circuits Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],HC : X (Eg) V 1 V 2 V 6 V 5 V 3 V 7 V 4 V 8 V 1 V 2 V 5 V 3 V 4

Sum-of-Subsets Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],A w 1 w 2 w 3 w 2 w 3 w 3 w 3 O O O O O O O {w 1 ,w 2 }

Sum-of-Subsets Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],ⅹ 12 7 3 9 7 8 13 4 0 0 3 3 0 4 5 0 0 4 5 5 6 0 0 0 0 ⅹ ⅹ : 0+5+6=11<13 ⅹ ⅹ : 9+6=15>13 ⅹ ⅹ w1=3 w2=4 w3=5 w4=6 0 4 3 7

0-1 Knapsack Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],x 1 =1 x 2 =1 x 3 =1 x 4 =1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 x 2 =1

Branch-and-Bound ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Breadth First Search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],BFS of a graph BFS of a tree 1 2 3 4 5 6 7 8 9 1 2 5 6 7 8 9 3 4 10 11 12 13 14 15

0-1 Knapsack Problem ,[object Object],[object Object],0 0 115 40 2 115 0 0 82 70 7 115 40 2 98 120 17 0 70 7 80 80 12 80 70 7 70 90 12 98 40 2 50 100 17 0 90 12 90 30 5 82 80 15 82 30 5 40 0 0 60 p1=40 , w1=2 p2=30 , w2=5 p3=50 , w3=10 p4=10 , w4=5

0-1 Knapsack Problem ,[object Object],[object Object],[object Object],0 0 115 40 2 115 0 0 82 70 7 115 40 2 98 120 17 0 70 7 80 80 12 80 70 7 70 90 12 98 40 2 50 100 17 0 90 12 90 30 5 82 80 15 82 30 5 40 0 0 60 p1=40 , w1=2 p2=30 , w2=5 p3=50 , w3=10 p4=10 , w4=5

0-1 Knapsack Problem ,[object Object],0 0 115 40 2 115 0 0 82 70 7 115 40 2 98 120 17 0 70 7 80 90 12 98 40 2 50 100 17 0 p1=40 , w1=2 p2=30 , w2=5 p3=50 , w3=10 p4=10 , w4=5 90 12 90

01 knapsack using backtracking

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (20)

Andere mochten auch

Andere mochten auch (9)

Ähnlich wie 01 knapsack using backtracking

Ähnlich wie 01 knapsack using backtracking (20)

Kürzlich hochgeladen

Kürzlich hochgeladen (20)

01 knapsack using backtracking