September 2017 Update

Task/N-queens-problem/Stata/n-queens-problem-1.stata

@@ -0,0 +1,60 @@
+mata
+real matrix queens(real scalar n) {
+	real scalar i, j, k, p, q
+	real rowvector a, s, u, v
+	real matrix m
+	
+	m = J(0, n, .)
+	a = 1..n
+	s = J(1, n, 0)
+	u = J(1, 2*n-1, 1)
+	v = J(1, 2*n-1, 1)
+	i = j = 1
+L1:	k = a[j]
+	a[j] = a[i]
+	a[i] = k
+	p = i-k+n
+	q = i+k-1
+	if (u[p] & v[q]) {
+		s[i++] = j
+		u[p] = v[q] = 0
+		if (i > n) {
+			m = m\a
+			goto L3
+		}
+		j = i
+		goto L1
+	}
+L2:	if (++j <= n) goto L1
+	while (--j > i) {
+		k = a[i]
+		a[i] = a[j]
+		a[j] = k
+	}
+L3:	if (--i == 0) return(m)
+	p = i-a[i]+n
+	q = i+a[i]-1
+	j = s[i]
+	u[p] = v[q] = 1
+	goto L2
+}
+
+a = queens(8)
+e = I(8)
+1:/e[a[1,.],.]
+       1   2   3   4   5   6   7   8
+    +---------------------------------+
+  1 |  1   .   .   .   .   .   .   .  |
+  2 |  .   .   .   .   1   .   .   .  |
+  3 |  .   .   .   .   .   .   .   1  |
+  4 |  .   .   .   .   .   1   .   .  |
+  5 |  .   .   1   .   .   .   .   .  |
+  6 |  .   .   .   .   .   .   1   .  |
+  7 |  .   1   .   .   .   .   .   .  |
+  8 |  .   .   .   1   .   .   .   .  |
+    +---------------------------------+
+
+
+rows(a)
+  92
+end

Task/N-queens-problem/Stata/n-queens-problem-2.stata

@@ -0,0 +1,4 @@
+clear
+mata: a=queens(8)
+getmata (a*)=a
+save queens, replace

Task/N-queens-problem/Stata/n-queens-problem-3.stata

@@ -0,0 +1,58 @@
+mata
+real matrix queens(real scalar n) {
+	real rowvector a, u, v
+	real matrix m
+	
+	a = 1..n
+	u = J(1, 2*n-1, 1)
+	v = J(1, 2*n-1, 1)
+	m = J(0, n, .)
+	queens_aux(n, 1, a, u, v, m)
+	return(m)
+}
+
+void queens_aux(real scalar n, real scalar i, real rowvector a,
+	real rowvector u, real rowvector v, real matrix m) {
+	
+	real scalar j, k, s
+	
+	if (i > n) {
+		m = m\a
+	} else {
+		for (k = i; k <= n; k++) {
+			j = a[k]
+			p = i+j-1
+			q = i-j+n
+			if (u[p] & v[q]) {
+				u[p] = v[q] = 0
+				s = a[i]
+				a[i] = a[k]
+				a[k] = s
+				queens_aux(n, i+1, a, u, v, m)
+				u[p] = v[q] = 1
+				s = a[i]
+				a[i] = a[k]
+				a[k] = s
+			}
+		}
+	}
+}
+
+a = queens(8)
+e = I(8)
+1:/e[a[1,.],.]
+       1   2   3   4   5   6   7   8
+    +---------------------------------+
+  1 |  1   .   .   .   .   .   .   .  |
+  2 |  .   .   .   .   1   .   .   .  |
+  3 |  .   .   .   .   .   .   .   1  |
+  4 |  .   .   .   .   .   1   .   .  |
+  5 |  .   .   1   .   .   .   .   .  |
+  6 |  .   .   .   .   .   .   1   .  |
+  7 |  .   1   .   .   .   .   .   .  |
+  8 |  .   .   .   1   .   .   .   .  |
+    +---------------------------------+
+
+rows(a)
+  92
+end