024: Langford's number problem

"""
PyCSP3 Model (see pycsp.org)

Examples:
  python LangfordNumber.py
  python LangfordNumber.py -data=[3,10]
"""

from pycsp3 import *

k, n = data or (3, 12)  # k is the number of occurrences for a value -- n is the number of values

# x[i][j] is the position in the sequence of the ith occurrence of j+1
x = VarArray(size=[k, n], dom=range(k * n))

satisfy(
    # all positions of the sequence must be set
    AllDifferent(x),

    # there are j numbers between two occurrences of j
    [x[i + 1][j] == x[i][j] + j + 2 for i in range(k - 1) for j in range(n)]
)