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. 2021 May 12;23(5):598. doi: 10.3390/e23050598

Table 7.

Related parameters of five classic 0-1 knapsack problems.

No. D Parameter (w, p, C) Opt
k 1 10 w = (95,4,60,32,23,72,80,62,65,46);
p = (55,10,47,5,4,50,8,61,85,87);
C = 269		 295
k 2 20 w = (92,4,43,83,84,68,92,82,6,44,32,18,56,83,25,96,70,48,14,58);
p = (44,46,90,72,91,40,75,35,8,54,78,40,77,15,61,17,75,29,75,63);
C = 878		 1024
k 3 50 w = (80,82,85,70,72,70,66,50,55,25,50,55,40,48,59,32,22,60,30, 32,40,38,35,32,25,28,30,22,50,30,45,30,60,50,20,65,20,25,30, 10,20,25,15,10,10,10,4,4,2,1);
p = (220,208,198,192,180,180,165,162,160,158,155,130,125, 122,120,118,115,110,105,101,100,100,98,96,95,90,88,82,80,77,75,7,72,70,69,66,65,63,60,58,56,50,30,20,15, 0,8,5,3,1);
C = 1000		 3103
k 4 80 w = (40, 27,5,21,51, 16, 42, 18, 52, 28, 57, 34, 44, 43,52,55,53,42, 47, 56,57,44, 16,2, 12, 9, 40, 23, 56, 3, 39,16, 54, 36, 52,5,53, 48, 23, 47, 41, 49, 22, 42, 10, 16, 53, 58, 40, 1,43,56,40,32,44,35, 37, 45, 52, 56, 40, 2, 23,49, 50, 26, 11,35, 32, 34, 58, 6, 52,26,31, 23, 4, 52, 53, 19);
p = (199,194,193,191,189,178,174,169,164,164,161,158,157, 154,152,152,149,142,131,125,124,124,124,122,119,116,114,113,111,110,109,100,97,94,91,82,82,81,80,80,80,79,77,76,74, 72, 71, 70, 69,68, 65, 65, 61, 56, 55, 54, 53, 47, 47, 46, 41, 36, 34, 32, 32,30, 29, 29, 26, 25, 23, 22, 20, 11, 10, 9,5,4,3, 1);
C = 1173 		5183
k 5 100 w = (54, 95, 36, 18,4, 71,83, 16, 27, 84, 88, 45, 94, 64, 14, 80, 4, 23, 75, 36, 90, 20, 77, 32, 58, 6, 14, 86, 84, 59,71, 21, 30, 22, 96, 49, 81, 48, 37, 28, 6, 84,19,55,88,38,51,52,79,55,70,53,64,99,61,86,1,64,32,60,42,45,34,22,49,37,33,1,78,43,85,24,96,32,99,57,23,8,10,74,59,89,95,40,46,65,6,89,84,83,6,19,45, 59, 26, 13, 8, 26, 5, 9);
p = (297, 295, 293, 292, 291, 289, 284, 284, 283, 283, 281, 280, 279, 277, 276, 275, 273,264, 260, 257, 250, 236, 236, 235, 235, 233, 232, 232, 228, 218, 217, 214, 211, 208, 205, 204, 203, 201, 196, 194,193, 193, 192, 191, 190, 187, 187, 184, 184, 184, 181, 179, 176, 173, 172, 171, 160, 128, 123, 114, 113, 107, 105,101, 100, 100, 99, 98, 97, 94, 94, 93, 91, 80, 74, 73, 72, 63, 63, 62, 61, 60, 56, 53, 52, 50, 48, 46, 40, 40, 35, 28, 22,22, 18, 15, 12,11, 6,5);
C = 3818;		 15,170