examples: add a simple sudoku solver

examples/sudoku.v

@@ -0,0 +1,97 @@
+fn main() {
+	mut grid := [
+		[0, 3, 0, 0, 7, 0, 0, 0, 0],
+		[0, 0, 0, 1, 3, 5, 0, 0, 0],
+		[0, 0, 1, 0, 0, 0, 0, 5, 0],
+		[1, 0, 0, 0, 6, 0, 0, 0, 3],
+		[4, 0, 0, 8, 0, 3, 0, 0, 1],
+		[7, 0, 0, 0, 2, 0, 0, 0, 6],
+		[0, 0, 0, 0, 0, 0, 2, 1, 0],
+		[0, 0, 0, 4, 1, 2, 0, 0, 5],
+		[0, 0, 0, 0, 0, 0, 0, 7, 4],
+	]
+	print_grid('Sudoku Puzzle:', grid)
+	println('Solving...')
+	if solve_sudoku(mut grid) {
+		print_grid('Solution:', grid)
+	} else {
+		println('No solution exists.')
+		exit(1)
+	}
+}
+
+// is_valid checks if placing `num` at grid[row][col] is valid
+fn is_valid(grid [][]int, row int, col int, num int) bool {
+	// check the row, if the number has been placed already:
+	for x := 0; x < 9; x++ {
+		if grid[row][x] == num {
+			return false
+		}
+	}
+	// check column
+	for x := 0; x < 9; x++ {
+		if grid[x][col] == num {
+			return false
+		}
+	}
+	// check 3x3 subgrid
+	start_row := row - row % 3
+	start_col := col - col % 3
+	for i := 0; i < 3; i++ {
+		for j := 0; j < 3; j++ {
+			if grid[i + start_row][j + start_col] == num {
+				return false
+			}
+		}
+	}
+	return true
+}
+
+// find_empty finds an empty cell (0) in the grid:
+fn find_empty(grid [][]int) ?(int, int) {
+	for i := 0; i < 9; i++ {
+		for j := 0; j < 9; j++ {
+			if grid[i][j] == 0 {
+				return i, j
+			}
+		}
+	}
+	return none
+}
+
+// solve_sudoku solves the Sudoku puzzle using backtracking
+fn solve_sudoku(mut grid [][]int) bool {
+	// If there is no empty cell, the puzzle is solved:
+	row, col := find_empty(grid) or { return true }
+	// Try placing all the digits in turn in the empty cell:
+	for num := 1; num <= 9; num++ {
+		if is_valid(grid, row, col, num) {
+			grid[row][col] = num
+			// Recursively try to solve the rest
+			if solve_sudoku(mut grid) {
+				return true
+			}
+			// We could not find a solution using this number,
+			// so backtrack and try another number instead:
+			grid[row][col] = 0
+		}
+	}
+	return false
+}
+
+// print_grid prints a labeled Sudoku grid
+fn print_grid(label string, grid [][]int) {
+	println(label)
+	for i := 0; i < 9; i++ {
+		if i % 3 == 0 && i != 0 {
+			println('- - - - - - - - - - - -')
+		}
+		for j := 0; j < 9; j++ {
+			if j % 3 == 0 && j != 0 {
+				print(' | ')
+			}
+			print('${grid[i][j]} ')
+		}
+		println('')
+	}
+}