Just another update

Task/N-queens-problem/Mathematica/n-queens-problem-1.math

@@ -2,8 +2,8 @@ safe[q_List, n_] :=
  With[{l = Length@q},
   Length@Union@q == Length@Union[q + Range@l] ==
    Length@Union[q - Range@l] == l]
-nQueen[q_List:{}, n_] :=
+nQueen[q_List: {}, n_] :=
  If[safe[q, n],
-  If[Length[q] == n, q,
-   Cases[Flatten[{nQueen[Append[q, #], n]}, 2] & /@ Range[n],
-    Except[{Null} | {}]]], Null]
+  If[Length[q] == n, {q},
+   Cases[nQueen[Append[q, #], n] & /@ Range[n],
+    Except[{Null} | {}], {2}]], Null]

Task/N-queens-problem/Mathematica/n-queens-problem-4.math

@@ -0,0 +1,44 @@
+dispSol[sol_] := sol /. {1 -> "Q" , 0 -> "-"} // Grid
+
+solveNqueens[n_] :=
+ Module[{c, m, b, vars}, c = cqueens[n]; m = mqueens[n];
+  vars = mqueens2[n]; b = bqueens[Length[m]];
+  Partition[LinearProgramming[c, m, b, vars, Integers], n]]
+
+cqueens[n_] := Table[-1, {i, n^2}]
+
+bqueens[l_] := Table[{1, -1}, {i, l}]
+
+mqueens2[n_] := Table[{0, 1}, {i, n^2}]
+
+mqueens[n_] :=
+ Module[{t, t2, t3, t4}, t = mqueensh[n]; t2 = Append[t, mqueensv[n]];
+   t3 = Append[t2, mqueensd[n]]; t4 = Append[t3, mqueensdm[n]];
+  Partition[Flatten[t4], n^2]]
+
+mqueensh[n_] :=
+ Module[{t}, t = Table[0, {i, n}, {j, n^2}];
+  For[i = 1, i <= n, i++,
+   For[j = 1, j <= n, j++, t[[i, ((i - 1)*n) + j]] = 1]]; t]
+
+mqueensv[n_] :=
+ Module[{t}, t = Table[0, {i, n}, {j, n^2}];
+  For[i = 1, i <= n, i++,
+   For[j = 1, j <= n, j++, t[[j, ((i - 1)*n) + j]] = 1]]; t]
+
+mqueensd[n_] :=
+ Module[{t}, t = Table[0, {i, (2*n) - 1}, {j, n^2}];
+  For[k = 2, k <= 2 n, k++,
+   For[i = 1, i <= n, i++,
+    For[j = 1, j <= n, j++,
+     If[i + j == k, t[[k - 1, ((i - 1)*n) + j]] = 1]]]]; t]
+
+mqueensdm[n_] :=
+ Module[{t}, t = Table[0, {i, Sum[1, {i, 1 - n, n - 1}]}, {j, n^2}];
+  For[k = 1 - n, k <= n - 1, k++,
+   For[i = 1, i <= n, i++,
+    For[j = 1, j <= n, j++,
+     If[i == j - k, t[[k + n, ((i - 1)*n) + j]] = 1]]]]; t]
+
+
+solveNqueens[8] // dispSol