ACM (UVa): 386


Data type:
Integer

Algorithm:
Use brute force method. I have used 4 nested loop
Continue ( A = 6 to 200) // most outer loop. Loop no: 1
Continue ( B = 2 to less than A) // Inner loop of 1. Loop no: 2
Continue ( C = B + 1 to less than A ) // Inner loop of 2.
Continue ( D = C + 1 to less than A) // most inner loop

Remember, A > D > C > B

// to avoid time limit exceed, pre-calculate all possible combination and then just print. For example: I wrote in C/C++
…………….

#include
#include

int main ()
{
double A, B, C, D, PA, PB, PC, PD;
//char K = 10;

freopen (“386out”, “w”, stdout);

for (A = 6; A <= 200; A++) { PA = pow (A, 3); for (D = 2; D < A; D++) { PD = pow (D, 3); for (C = D + 1; C < A; C++) { PC = pow (C, 3); for (B = C + 1; B < A; B++) { PB = pow (B, 3); if ( floor (PA) == (floor (PB) + floor (PC) + floor (PD)) ) printf("Cube = %0.lf, Triple = (%0.lf,%0.lf,%0.lf)\n", A, D, C, B); } } } } return 0; } /* Cube = 6, Triple = (3,4,5) Cube = 12, Triple = (6,8,10) Cube = 18, Triple = (2,12,16) Cube = 18, Triple = (9,12,15) Cube = 19, Triple = (3,10,18) Cube = 20, Triple = (7,14,17) Cube = 24, Triple = (12,16,20) Cube = 25, Triple = (4,17,22) Cube = 27, Triple = (3,18,24) Cube = 28, Triple = (18,19,21) Cube = 29, Triple = (11,15,27) Cube = 30, Triple = (15,20,25) Cube = 36, Triple = (4,24,32) Cube = 36, Triple = (18,24,30) Cube = 38, Triple = (6,20,36) Cube = 40, Triple = (14,28,34) Cube = 41, Triple = (2,17,40) Cube = 41, Triple = (6,32,33) Cube = 42, Triple = (21,28,35) Cube = 44, Triple = (16,23,41) Cube = 45, Triple = (5,30,40) Cube = 46, Triple = (3,36,37) Cube = 46, Triple = (27,30,37) Cube = 48, Triple = (24,32,40) Cube = 50, Triple = (8,34,44) Cube = 53, Triple = (29,34,44) Cube = 54, Triple = (6,36,48) Cube = 54, Triple = (12,19,53) Cube = 54, Triple = (27,36,45) Cube = 56, Triple = (36,38,42) Cube = 57, Triple = (9,30,54) Cube = 58, Triple = (15,42,49) Cube = 58, Triple = (22,30,54) Cube = 60, Triple = (21,42,51) Cube = 60, Triple = (30,40,50) Cube = 63, Triple = (7,42,56) Cube = 66, Triple = (33,44,55) Cube = 67, Triple = (22,51,54) Cube = 69, Triple = (36,38,61) Cube = 70, Triple = (7,54,57) Cube = 71, Triple = (14,23,70) Cube = 72, Triple = (8,48,64) Cube = 72, Triple = (34,39,65) Cube = 72, Triple = (36,48,60) Cube = 75, Triple = (12,51,66) Cube = 75, Triple = (38,43,66) Cube = 76, Triple = (12,40,72) Cube = 76, Triple = (31,33,72) Cube = 78, Triple = (39,52,65) Cube = 80, Triple = (28,56,68) Cube = 81, Triple = (9,54,72) Cube = 81, Triple = (25,48,74) Cube = 82, Triple = (4,34,80) Cube = 82, Triple = (12,64,66) Cube = 82, Triple = (19,60,69) Cube = 84, Triple = (28,53,75) Cube = 84, Triple = (42,56,70) Cube = 84, Triple = (54,57,63) Cube = 85, Triple = (50,61,64) Cube = 87, Triple = (20,54,79) Cube = 87, Triple = (26,55,78) Cube = 87, Triple = (33,45,81) Cube = 87, Triple = (38,48,79) Cube = 88, Triple = (21,43,84) Cube = 88, Triple = (25,31,86) Cube = 88, Triple = (32,46,82) Cube = 89, Triple = (17,40,86) Cube = 90, Triple = (10,60,80) Cube = 90, Triple = (25,38,87) Cube = 90, Triple = (45,60,75) Cube = 90, Triple = (58,59,69) Cube = 92, Triple = (6,72,74) Cube = 92, Triple = (54,60,74) Cube = 93, Triple = (32,54,85) Cube = 95, Triple = (15,50,90) Cube = 96, Triple = (19,53,90) Cube = 96, Triple = (48,64,80) Cube = 97, Triple = (45,69,79) Cube = 99, Triple = (11,66,88) Cube = 100, Triple = (16,68,88) Cube = 100, Triple = (35,70,85) Cube = 102, Triple = (51,68,85) Cube = 103, Triple = (12,31,102) Cube = 105, Triple = (33,70,92) Cube = 106, Triple = (58,68,88) Cube = 108, Triple = (12,72,96) Cube = 108, Triple = (13,51,104) Cube = 108, Triple = (15,82,89) Cube = 108, Triple = (24,38,106) Cube = 108, Triple = (54,72,90) Cube = 110, Triple = (29,75,96) Cube = 111, Triple = (16,47,108) Cube = 112, Triple = (72,76,84) Cube = 113, Triple = (50,74,97) Cube = 114, Triple = (18,60,108) Cube = 114, Triple = (57,76,95) Cube = 115, Triple = (3,34,114) Cube = 116, Triple = (23,86,97) Cube = 116, Triple = (30,84,98) Cube = 116, Triple = (44,60,108) Cube = 117, Triple = (13,78,104) Cube = 120, Triple = (9,55,116) Cube = 120, Triple = (42,84,102) Cube = 120, Triple = (60,80,100) Cube = 121, Triple = (49,84,102) Cube = 122, Triple = (19,92,101) Cube = 123, Triple = (6,51,120) Cube = 123, Triple = (18,96,99) Cube = 123, Triple = (44,51,118) Cube = 125, Triple = (20,85,110) Cube = 126, Triple = (14,84,112) Cube = 126, Triple = (23,94,105) Cube = 126, Triple = (63,84,105) Cube = 127, Triple = (13,65,121) Cube = 129, Triple = (38,57,124) Cube = 132, Triple = (5,76,123) Cube = 132, Triple = (48,69,123) Cube = 132, Triple = (66,88,110) Cube = 133, Triple = (21,70,126) Cube = 134, Triple = (44,102,108) Cube = 134, Triple = (86,95,97) Cube = 135, Triple = (15,90,120) Cube = 137, Triple = (44,73,128) Cube = 138, Triple = (9,108,111) Cube = 138, Triple = (69,92,115) Cube = 138, Triple = (72,76,122) Cube = 138, Triple = (81,90,111) Cube = 139, Triple = (94,96,99) Cube = 140, Triple = (14,108,114) Cube = 140, Triple = (49,98,119) Cube = 140, Triple = (90,95,105) Cube = 141, Triple = (72,85,122) Cube = 142, Triple = (28,46,140) Cube = 142, Triple = (31,64,137) Cube = 144, Triple = (16,96,128) Cube = 144, Triple = (68,78,130) Cube = 144, Triple = (72,96,120) Cube = 145, Triple = (12,81,136) Cube = 145, Triple = (55,75,135) Cube = 147, Triple = (22,75,140) Cube = 150, Triple = (24,102,132) Cube = 150, Triple = (71,73,138) Cube = 150, Triple = (75,100,125) Cube = 150, Triple = (76,86,132) Cube = 151, Triple = (46,47,148) Cube = 152, Triple = (24,80,144) Cube = 152, Triple = (62,66,144) Cube = 153, Triple = (17,102,136) Cube = 156, Triple = (65,87,142) Cube = 156, Triple = (78,104,130) Cube = 159, Triple = (3,121,131) Cube = 159, Triple = (87,102,132) Cube = 160, Triple = (56,112,136) Cube = 160, Triple = (69,123,124) Cube = 162, Triple = (18,108,144) Cube = 162, Triple = (36,57,159) Cube = 162, Triple = (50,96,148) Cube = 162, Triple = (59,93,148) Cube = 162, Triple = (81,108,135) Cube = 164, Triple = (8,68,160) Cube = 164, Triple = (24,128,132) Cube = 164, Triple = (38,120,138) Cube = 164, Triple = (69,99,146) Cube = 167, Triple = (12,86,159) Cube = 168, Triple = (56,106,150) Cube = 168, Triple = (84,112,140) Cube = 168, Triple = (108,114,126) Cube = 170, Triple = (96,107,141) Cube = 170, Triple = (100,122,128) Cube = 171, Triple = (19,114,152) Cube = 171, Triple = (27,90,162) Cube = 171, Triple = (54,80,163) Cube = 171, Triple = (107,108,136) Cube = 174, Triple = (40,108,158) Cube = 174, Triple = (45,126,147) Cube = 174, Triple = (47,97,162) Cube = 174, Triple = (52,110,156) Cube = 174, Triple = (66,90,162) Cube = 174, Triple = (76,96,158) Cube = 174, Triple = (87,116,145) Cube = 175, Triple = (28,119,154) Cube = 176, Triple = (25,92,167) Cube = 176, Triple = (42,86,168) Cube = 176, Triple = (50,62,172) Cube = 176, Triple = (64,92,164) Cube = 177, Triple = (48,137,142) Cube = 178, Triple = (34,80,172) Cube = 178, Triple = (48,133,147) Cube = 179, Triple = (17,57,177) Cube = 180, Triple = (20,120,160) Cube = 180, Triple = (50,76,174) Cube = 180, Triple = (63,126,153) Cube = 180, Triple = (90,120,150) Cube = 180, Triple = (116,118,138) Cube = 181, Triple = (108,109,150) Cube = 184, Triple = (12,144,148) Cube = 184, Triple = (108,120,148) Cube = 185, Triple = (57,68,180) Cube = 185, Triple = (68,113,166) Cube = 186, Triple = (18,121,167) Cube = 186, Triple = (64,108,170) Cube = 186, Triple = (93,124,155) Cube = 187, Triple = (58,131,160) Cube = 188, Triple = (115,122,149) Cube = 189, Triple = (21,46,188) Cube = 189, Triple = (21,126,168) Cube = 190, Triple = (30,100,180) Cube = 190, Triple = (56,133,163) Cube = 191, Triple = (39,146,156) Cube = 192, Triple = (34,123,173) Cube = 192, Triple = (38,106,180) Cube = 192, Triple = (96,128,160) Cube = 193, Triple = (25,68,190) Cube = 194, Triple = (90,138,158) Cube = 196, Triple = (126,133,147) Cube = 197, Triple = (53,58,194) Cube = 198, Triple = (22,132,176) Cube = 198, Triple = (27,46,197) Cube = 198, Triple = (73,135,170) Cube = 198, Triple = (99,132,165) Cube = 199, Triple = (6,127,180) Cube = 200, Triple = (32,136,176) Cube = 200, Triple = (70,140,170) */ [/sourcecode] ....................

// to avoid WA
“In these cases, the triples with the smaller b values should be listed first.” See the above example for Cube = 36

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