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079: n-Queens Completion Problem and Excluded Diagonals n-Queens Problem

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language ESSENCE' 1.0
given      n : int(1..)
letting    AMOUNT_QUEENS be domain int(0..n-1)
find       q1: matrix indexed by [ AMOUNT_QUEENS ] of int(0..n-1)
find       q2: matrix indexed by [ AMOUNT_QUEENS ] of int(-(n-1)..n-1)
find       q3: matrix indexed by [ AMOUNT_QUEENS ] of int(0..(n-1)*2)
given      numdiff : int(0..)
given      numsum : int(0..)
given      diffdiags : matrix indexed by [ int(1..numdiff) ] of int(-(n-1)..n-1)
given      sumdiags : matrix indexed by [ int(1..numsum) ] of int(0..(n-1)*2)
 
$ Tables to connect q2 and q3 to q1 instead of sum constraints.
 
such that  allDiff(q1),
           allDiff(q2),
           allDiff(q3),
            
         $ diagonals
           forAll i : AMOUNT_QUEENS . (
               table([q2[i], q1[i]], [[a,a+i] | a : int(-(n-1)..n-1), a+i>=0, a+i<n])  /\
               table([q3[i], q1[i]], [[a,a-i] | a : int(0..(n-1)*2), a-i>=0, a-i<n])
           ),
 
           forAll i : int(1..numdiff) .
        forAll j : AMOUNT_QUEENS .
            q2[j] != diffdiags[i],
 
           forAll i : int(1..numsum) .
        forAll j : AMOUNT_QUEENS .
            q3[j] != sumdiags[i],
            
        true