Solving Integer Systems of Inequalities and Equalities in Multiple Solutions of One Run--Another Illustration, Second Edition

Jsun Yui Wong

The computer program listed below seeks to solve simultaneously the following complete set of only the first four expressions in Basumatary [11; this comes from a comment in [11]]:

a + b + c = 4,

9 <= a + 2b + 3c <= 12,

c >=2,

b + c >=3.

These are used in the following line 196 through line 345, which include all the given equalities and inequalities shown above.

One notes the new line 193, which is 193 REM IF X(1) < 0## THEN 1670.

0 DEFDBL A-Z

1 DEFINT I, J, K

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(44), J44(44), PN(22), NN(22)

85 FOR JJJJ = -32000 TO 32000

89 RANDOMIZE JJJJ

90 M = -3D+30

111 FOR J44 = 1 TO 3

112 A(J44) = FIX(RND * 9)

113 NEXT J44

128 FOR I = 1 TO 5000

129 FOR KKQQ = 1 TO 3

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

139 FOR IPP = 1 TO FIX(1 + RND * 2)

140 B = 1 + FIX(RND * 2)

144 IF RND < .5 THEN 160 ELSE GOTO 167

160 R = (1 - RND * 2) * A(B)

164 X(B) = A(B) + (RND ^ (RND * 15)) * R

165 GOTO 168

167 IF RND < .5 THEN X(B) = A(B) - FIX(RND * 3) ELSE X(B) = A(B) + FIX(RND * 3)

168 NEXT IPP

180 FOR J44 = 1 TO 3

181 X(J44) = INT(X(J44))

182 NEXT J44

193 REM IF X(1) < 0## THEN 1670

196 IF X(3) < 2# THEN 1670

199 IF X(2) + X(3) < 3## THEN 1670

201 IF X(1) + 2 * X(2) + 3 * X(3) - 9 < 0## THEN 1670

204 IF X(1) + 2 * X(2) + 3 * X(3) - 12 > 0## THEN 1670

345 PD1 = -ABS(-4 + X(1) + X(2) + X(3))

466 P = PD1

1111 IF P <= M THEN 1670

1452 M = P

1454 FOR KLX = 1 TO 3

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1670 NEXT I

1777 IF M < -99999.01 THEN 1999

1904 PRINT A(1), A(2), A(3), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [102]. Its output of one run through JJJJ= -31106 is shown below:

0 0 4 0 -31998

1 1 2 0 -31996

1 1 2 0 -31988

0 0 4 0 -31986

1 -2 5 0 -31984

0 0 4 0 -31981

1 0 3 0 -31978

1 0 3 0 -31977

0 0 4 0 -31976

0 1 3 0 -31971

1 1 2 0 -31970

0 2 2 0 -31968

1 1 2 0 -31966

0 1 3 0 -31954

1 -1 4 0 -31950

.

.

.

-1 3 2 0 -31912

.

.

.

-1 2 3 0 -31613

.

.

.

-2 4 2 0 -31106

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with Processor Intel Pentium CPU G620@ 2.60GHz, 4.00 GB of RAM (3.89 GB usable), 64-bit Operating System, and QB64v1000-win [102], the wall-clock time (**not CPU time**) for obtaining the output through JJJJ = -31106 was 5 seconds, counting from "Starting program...".

**Acknowledgement**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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