Backtracking approach : 1392

- : - 2 . . .

/57 - : - 3 . .

. n . n nn . .

/57 ( ) - : - 4 ( preorder) . . .

/57 - : - 5 . . . . .

/57 (State Space) - : - 6 ( ) () . n n=4 . : 4444

/57 - : - 7 . .

/57 - : - 8

/57 - : - 9

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n (n=4) - : - 10/57 n (n=4) - : - 11

/57 n - : - 12 . n . col(i) i . : col(i) = col(k) : |col(i)-col(k)| = |i-k|

/57 n - : - 13

/57 - : - 14 . :1 n 1 n2 2 ... nn n1+n+n2+n3++nn = (nn+1-1)/n-1 n=8 19173961 . . .1+n+n(n-1)+n(n-1)(n-2)+.+n! n=8 109601

/57 ... - : - 15 3 1: 2:

/57 - : - 16 n wi () W . n W .

/57 - : - 17 w1 w1 . . wi wi wi 0 .

/57 (n=3 W=6) - : - 18

/57 - : - 19 i wi+1 . weight i : weight + wi+1 > W . total : weight + total < W . weight = W . ./57 (n=4 W=13) - : - 20

/57 - : - 21

/57 - : - 22 W . ( : : ). . :

/57 - : - 23 weight i : weight W . : pi/wi . (bound). profit . bound totweight profit weight . bound totweight W . bound .

/57 ... - : - 24 i k W :

maxprofit . bound maxprofit i .

/57 - : - 25

/57

- : - 261) (0,0)Profit = 0$Weight = 0Maxprofit = 0$

totweight = 7Bound = 115$ : (weight maxprofit)/57 - : - 27

/57

- : - 282) (1,1)Profit = 40$Weight = 2Maxprofit = 0$ 40$

totweight = 7Bound = 115$ : (weight maxprofit)/57 - : - 29

/57

- : - 303) (2,1)Profit = 70$Weight = 7Maxprofit = 40$ 70$

totweight = 7Bound = 115$ : (weight maxprofit)/57 - : - 31

/57 - : - 324) (3,1)Profit = 120$Weight = 17 : (weight > 16)Maxprofit = 70$ (2,1)/57 - : - 33

/57 - : - 345) (3,2)Profit = 70$Weight = 7Maxprofit = 70$

totweight = 7 + 5 = 12Bound = 70+ 10 = 80$ : (weight maxprofit)/57 - : - 35

/57 - : - 366) (4,1)Profit = 80$Weight = 12Maxprofit = 70$ 80$ Bound = 80$ : (bound maxprofit) (3,2)/57 - : - 37

/57 - : - 387) (4,2)Profit = 70$Weight = 7Maxprofit = 80$ Bound = 70$ : (bound maxprofit) (1,1)/57 - : - 39

/57 - : - 408) (2,2)Profit = 40$Weight = 2Maxprofit = 80$totweight = 2 + 10 = 12Bound = 40$ + 50$ + (16-12) 2$ = 98$ : (weight maxprofit)/57 - : - 41

/57 - : - 429) (3,3)Profit = 90$Weight = 12Maxprofit = 80$ 90$totweight = 12Bound = 90$ + (16-12) 2$ = 98$ : (weight maxprofit)/57 - : - 43

/57 - : - 4410) (4,3)Profit = 100$Weight = 17Maxprofit = 90$ : (weight 16) maxprofit . (3,3)/57 - : - 45

/57 - : - 4611) (4,4)Profit = 90$Weight = 12Maxprofit = 90$ Bound = 90$ : (bound maxprofit) (2,2)

/57 - : - 47

/57 - : - 4812) (3,4)Profit = 40$Weight = 2Maxprofit = 90$totweight = 2 + 5 = 7Bound = 40$ + 10$ = 50$ : (bound maxprofit) (0,0)

/57 - : - 49

/57 - : - 5013) (1,2)Profit = 0$Weight = 0Maxprofit = 90$totweight = 0+ 5 + 10 = 15Bound = 0$ + 30$ + 50$ +(16-15) 2$ = 82$ : (bound maxprofit) (0,0) . .

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/57

- : - 54/57 - : - 55

/57 - : - 56 : O (minimum (2 , nW)) (2n) .

. . (1974) ./57 ( //) - : - 57 C++ C# Java . C++ C# Java .

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