Data update

Task/N-queens-problem/C/n-queens-problem-1.c

@@ -1,31 +1,87 @@
 #include <stdio.h>
 #include <stdlib.h>
+#include <stdbool.h>
 
-int count = 0;
-void solve(int n, int col, int *hist)
-{
-	if (col == n) {
-		printf("\nNo. %d\n-----\n", ++count);
-		for (int i = 0; i < n; i++, putchar('\n'))
-			for (int j = 0; j < n; j++)
-				putchar(j == hist[i] ? 'Q' : ((i + j) & 1) ? ' ' : '.');
+// In column order, print out the given positions in chess notation.
+// For example, when N = 8, the first solution printed is:
+// "a1 b5 c8 d6 e3 f7 g2 h4"
+static void print_positions(int x[], const size_t n) {
+	static const char alphabet[] = "abcdefghijklmnopqrstuvwxyz";
 
-		return;
+	// There are only 26 letters in the ASCII alphabet, so
+	// so don't bother with chess notation above 26.
+	if (n <= 26) {
+		for (size_t i = 0; i < n; ++i)
+			printf("%c%u ", alphabet[i], x[i] + 1);
+	} else {
+		for (size_t i = 0; i < n; ++i)
+			printf("%u ", x[i] + 1);
 	}
+    putchar('\n');
+}
 
-#	define attack(i, j) (hist[j] == i || abs(hist[j] - i) == col - j)
-	for (int i = 0, j = 0; i < n; i++) {
-		for (j = 0; j < col && !attack(i, j); j++);
-		if (j < col) continue;
+// Print all solutions to the N queens problem, holding the results in
+// the intermediate array x, and with the auxiliary boolean arrays a, b, and c.
+// x and a are both N elements long, while b and c are 2*N-1 elements long.
+// It is assumed that these arrays are zeroed before this routine is called.
+static void queens(int x[], bool a[], bool b[], bool c[], const size_t n) {
+	size_t col, row = 0;
 
-		hist[col] = i;
-		solve(n, col + 1, hist);
+advance_row:
+	if (row >= n) {
+		print_positions(x, n);
+		goto backtrack;
+	}
+	col = 0;
+try_column:
+	if (!a[col] && !b[col+row-1] && !c[col-row+n]) {
+		a[col] = true;
+		b[col+row-1] = true;
+		c[col-row+n] = true;
+		x[row] = col;
+		row++;
+		goto advance_row;
+	}
+try_again:
+	if (col < n-1) {
+		col++;
+		goto try_column;
+	}
+backtrack:
+	if (row != 0) {
+		--row;
+		col = x[row];
+		c[col-row+n] = false;
+		b[col+row-1] = false;
+		a[col] = false;
+		goto try_again;
 	}
 }
 
-int main(int n, char **argv)
-{
-	if (n <= 1 || (n = atoi(argv[1])) <= 0) n = 8;
-	int hist[n];
-	solve(n, 0, hist);
+static void *calloc_wrapper(size_t count, size_t bytesize) {
+	void *r;
+	if ((r = calloc(count, bytesize)) == NULL) {
+		exit(EXIT_FAILURE);
+	}
+	return r;
+}
+
+int main(int argc, char **argv) {
+	bool *a, *b, *c;
+	int n, *x;
+	
+	if (argc != 2 || (n = atoi(argv[1])) <= 0) {
+		printf("%s: specify a natural number argument\n", argv[0]);
+		return 1;
+	}
+
+	x = calloc_wrapper(n, sizeof(x[0]));
+	a = calloc_wrapper(n, sizeof(a[0]));
+	b = calloc_wrapper((2 * n - 1), sizeof(b[0]));
+	c = calloc_wrapper((2 * n - 1), sizeof(c[0]));
+
+	queens(x, a, b, c, n);
+
+	// Don't bother freeing before exiting.
+	return 0;
 }