# Here we use the and/or operators of the Python interface to create a
# new optimization problem.
#
# (C) Fair Isaac Corp., 1983-2020
# Solve a simple SAT problem by finding the solution with the fewest
# True variables that satisfy all clauses
import xpress as xp
p = xp.problem()
N = 10
k = 5
x = [xp.var(vartype=xp.binary) for _ in range(N)]
p = xp.problem(x)
# Creates a continuous list despite the 2 step in range()
y_and = [xp.var(vartype=xp.binary) for i in range(0, N-1, 2)]
y_or = [xp.var(vartype=xp.binary) for i in range(N-k)]
p.addVariable(y_and, y_or)
p.addgencons([xp.gencons_and] * (N//2) + [xp.gencons_or] * (N-k),
y_and + y_or, # two list of resultants
[2*i for i in range(N // 2)] + # colstart is the list [0, 2, 4...] for the AND constraint
[2 * (N // 2) + k*i for i in range(N-k)], # ... and then the list [0, k, 2*k...] displaced by 2N
x[:2 * (N//2)] + # consider all original variables in this order
[x[i+j] for j in range(k) for i in range(N-k)]) # and then variables [0..k-1, 1..k, 2..k+1, ...]
# Set time limit to 20 seconds
p.controls.maxtime = -20
p.solve()
print("solution: x = ", p.getSolution())
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