sudoku: backtracking: add exhaustive solver

meson.build

@@ -9,6 +9,7 @@ project(
 )
 
 sources = [
+  'src/backtracking.c',
   'src/constraints.c',
   'src/main.c',
   'src/solver/last_remaining.c',

src/backtracking.c

@@ -0,0 +1,36 @@
+#include "backtracking.h"
+
+#include <stddef.h>
+
+#include "constraints.h"
+#include "sudoku.h"
+
+static bool try_at(struct sudoku *grid, size_t i, size_t j, int n) {
+    grid->grid[i][j] = n;
+    return !(line_violation(grid, i, j) || column_violation(grid, i, j)
+             || square_violation(grid, i, j));
+}
+
+bool solve_backtracking(struct sudoku *grid) {
+    if (!grid)
+        return false;
+
+    for (size_t i = 0; i < 9; ++i) {
+        for (size_t j = 0; j < 9; ++j) {
+            if (grid->grid[i][j] != 0)
+                continue;
+
+            for (int n = 1; n <= 9; ++n) {
+                if (!try_at(grid, i, j, n))
+                    continue;
+                if (solve_backtracking(grid))
+                    return true;
+            }
+
+            grid->grid[i][j] = 0;
+            return false;
+        }
+    }
+
+    return true;
+}

src/backtracking.h

@@ -0,0 +1,10 @@
+#ifndef BACKTRACKING_H
+#define BACKTRACKING_H
+
+#include <stdbool.h>
+
+struct sudoku;
+
+bool solve_backtracking(struct sudoku *grid);
+
+#endif /* !BACKTRACKING_H */