bitsets for fast checking if a number fits (slower)

src/main.rs

@@ -1,55 +1,123 @@
+use std::time::Instant;
+
+#[derive(Copy, Clone, Debug)]
+struct Bitset {
+    set: u16,
+}
+
+impl Bitset {
+    pub fn new() -> Self {
+        Self { set: 0 }
+    }
+
+    #[inline(always)]
+    fn get(&self, nr: usize) -> bool {
+        self.set & (1 << nr) != 0
+    }
+
+    #[inline(always)]
+    fn set(&mut self, nr: usize) {
+        self.set |= 1 << nr;
+    }
+
+    #[inline(always)]
+    fn unset(&mut self, nr: usize) {
+        self.set &= !(1 << nr);
+    }
+}
+
+const BLOCK_SIZE: usize = 4;
+//const MAX_BLOCK_SIZE: usize = 10;
+
 struct SField {
     field: Vec<usize>,
     fixed: Vec<usize>,
     size: usize,
-    block_size: usize,
     pos: usize,
     pos_last_placed: usize,
     num_fields: usize,
     possible_values: Vec<Vec<usize>>,
+
+    // For each row/col/block we create a bitset that represents the numbers
+    // that are already in that row, col or block.
+    // This way we can check very fast if a nr fits into a specific field or not.
+    rows: [Bitset; BLOCK_SIZE * BLOCK_SIZE],
+    cols: [Bitset; BLOCK_SIZE * BLOCK_SIZE],
+    blocks: [Bitset; BLOCK_SIZE * BLOCK_SIZE],
+}
+
+#[inline(always)]
+fn xy_to_pos(x: usize, y: usize, size: usize) -> usize {
+    y * size + x
+}
+
+#[inline(always)]
+fn pos_to_xy_blocknr(pos: usize, size: usize) -> (usize, usize, usize) {
+    let x = pos % size;
+    let y = pos / size;
+
+    let block_x = x / BLOCK_SIZE;
+    let block_y = y / BLOCK_SIZE;
+
+    let block_nr = block_y * BLOCK_SIZE + block_x;
+
+    (x, y, block_nr)
 }
 
 impl SField {
-    pub fn new(block_size: usize) -> SField {
+    pub fn new() -> SField {
-        let size = block_size * block_size;
+        const SIZE: usize = BLOCK_SIZE * BLOCK_SIZE;
 
         // EMPTY FIELD
         // let field = vec![0; size * size];
 
-        // BLOCK_SIZE 4
+        #[rustfmt::skip]
-        // #[rustfmt::skip]
+        let field = match BLOCK_SIZE {
-        // let field = vec![
+            4 => vec![
-        //     0,15,0,0,0,0,11,4,0,5,0,0,0,0,12,8,
+                0usize,15,0,0,0,0,11,4,0,5,0,0,0,0,12,8,
-        //     12,0,0,9,0,1,0,5,0,0,8,15,0,0,0,13,
+                12,0,0,9,0,1,0,5,0,0,8,15,0,0,0,13,
-        //     0,0,3,0,0,10,13,0,0,11,4,0,15,0,6,0,
+                0,0,3,0,0,10,13,0,0,11,4,0,15,0,6,0,
-        //     13,10,0,11,0,0,0,14,0,3,2,0,0,9,0,0,
+                13,10,0,11,0,0,0,14,0,3,2,0,0,9,0,0,
-        //     0,0,15,10,8,0,0,0,0,0,14,0,0,6,2,0,
+                0,0,15,10,8,0,0,0,0,0,14,0,0,6,2,0,
-        //     0,0,14,0,0,0,6,0,0,0,0,0,1,0,0,0,
+                0,0,14,0,0,0,6,0,0,0,0,0,1,0,0,0,
-        //     0,11,0,8,3,0,15,1,6,0,0,0,0,0,0,7,
+                0,11,0,8,3,0,15,1,6,0,0,0,0,0,0,7,
-        //     0,6,0,7,0,0,0,0,8,13,0,0,10,0,0,0,
+                0,6,0,7,0,0,0,0,8,13,0,0,10,0,0,0,
-        //     0,14,0,2,0,0,0,0,3,0,5,0,11,15,9,0,
+                0,14,0,2,0,0,0,0,3,0,5,0,11,15,9,0,
-        //     0,0,0,12,11,0,2,0,0,0,0,0,0,0,0,0,
+                0,0,0,12,11,0,2,0,0,0,0,0,0,0,0,0,
-        //     0,8,0,0,6,14,1,0,13,15,0,0,0,0,0,10,
+                0,8,0,0,6,14,1,0,13,15,0,0,0,0,0,10,
-        //     10,0,0,3,9,0,7,0,0,1,0,0,13,12,8,0,
+                10,0,0,3,9,0,7,0,0,1,0,0,13,12,8,0,
-        //     7,0,0,0,0,0,14,0,0,0,0,0,0,0,0,9,
+                7,0,0,0,0,0,14,0,0,0,0,0,0,0,0,9,
-        //     0,3,0,14,0,0,9,6,0,0,0,0,0,4,0,0,
+                0,3,0,14,0,0,9,6,0,0,0,0,0,4,0,0,
-        //     0,4,6,0,0,7,0,0,0,0,0,0,0,0,0,0,
+                0,4,6,0,0,7,0,0,0,0,0,0,0,0,0,0,
-        //     5,2,0,0,0,4,10,15,1,0,3,0,0,0,7,0,
+                5,2,0,0,0,4,10,15,1,0,3,0,0,0,7,0,
-        // ];
+            ],
+            3 => vec![
+                0,0,0,0,0,0,0,0,9,
+                0,0,0,0,8,9,0,2,0,
+                0,0,0,0,2,0,4,0,0,
+                0,0,4,0,6,0,0,0,8,
+                0,0,0,5,0,0,0,0,0,
+                0,6,5,0,0,2,0,7,4,
+                0,3,0,0,0,5,0,4,0,
+                0,0,1,8,0,0,0,0,0,
+                0,0,8,2,0,0,0,6,0,
+            ],
+            _ => panic!("Unsupported block size. Only 3 and 4 is ok for now.")
+        };
 
         // MANY SOLUTIONS
-        #[rustfmt::skip]
+        // #[rustfmt::skip]
-        let field = vec![
+        // let field = vec![
-            0,0,0,0,0,0,0,0,9,
+        //     0,0,0,0,0,0,0,0,9,
-            0,0,0,0,8,9,0,2,0,
+        //     0,0,0,0,8,9,0,2,0,
-            0,0,0,0,2,0,4,0,0,
+        //     0,0,0,0,2,0,4,0,0,
-            0,0,4,0,6,0,0,0,8,
+        //     0,0,4,0,6,0,0,0,8,
-            0,0,0,5,0,0,0,0,0,
+        //     0,0,0,5,0,0,0,0,0,
-            0,6,5,0,0,2,0,7,4,
+        //     0,6,5,0,0,2,0,7,4,
-            0,3,0,0,0,5,0,4,0,
+        //     0,3,0,0,0,5,0,4,0,
-            0,0,1,8,0,0,0,0,0,
+        //     0,0,1,8,0,0,0,0,0,
-            0,0,8,2,0,0,0,6,0,
+        //     0,0,8,2,0,0,0,6,0,
-        ];
+        // ];
 
         // HARD
         // #[rustfmt::skip]
@@ -79,7 +147,7 @@ impl SField {
         //     7,3,6,0,2,0,0,0,0,
         // ];
 
-        let mut fixed = Vec::with_capacity(size * size);
+        let mut fixed = Vec::with_capacity(SIZE * SIZE);
         field.iter().for_each(|e| {
             if *e == 0 {
                 fixed.push(0);
@@ -88,15 +156,82 @@ impl SField {
             }
         });
 
+        // create bitsets
+        // rows
+        let mut bit_rows = [Bitset::new(); SIZE];
+        for row_nr in 0..SIZE {
+            let mut row = [0; SIZE];
+            for count in 0..SIZE {
+                row[count] = field[xy_to_pos(count, row_nr, SIZE)];
+            }
+
+            row.into_iter()
+                .filter(|val| *val != 0)
+                .for_each(|val| bit_rows[row_nr].set(val - 1));
+        }
+
+        // cols
+        let mut bit_cols = [Bitset::new(); SIZE];
+        for col_nr in 0..SIZE {
+            let mut col = [0; SIZE];
+            for count in 0..SIZE {
+                col[count] = field[xy_to_pos(col_nr, count, SIZE)];
+            }
+
+            col.into_iter()
+                .filter(|val| *val != 0)
+                .for_each(|val| bit_cols[col_nr].set(val - 1));
+        }
+
+        // blocks
+        let mut bit_blocks = [Bitset::new(); SIZE];
+
+        for block_nr in 0..SIZE {
+            let block_start_x = block_nr * BLOCK_SIZE % SIZE;
+            let block_start_y = block_nr * BLOCK_SIZE / SIZE * BLOCK_SIZE;
+
+            let mut block = [0; SIZE];
+            for count in 0..SIZE {
+                let block_offset_x = count % BLOCK_SIZE;
+                let block_offset_y = count / BLOCK_SIZE;
+
+                let field_x = block_start_x + block_offset_x;
+                let field_y = block_start_y + block_offset_y;
+
+                //dbg!(
+                //block_nr,
+                //block_start_x,
+                //block_start_y,
+                //block_offset_x,
+                //block_offset_y,
+                //field_x,
+                //field_y,
+                //);
+
+                block[count] = field[xy_to_pos(field_x, field_y, SIZE)];
+            }
+
+            block
+                .into_iter()
+                .filter(|x| *x != 0)
+                .for_each(|x| bit_blocks[block_nr].set(x - 1));
+        }
+
+        //dbg!(bit_rows);
+        //dbg!(bit_cols);
+        //dbg!(bit_blocks);
+
         SField {
             field,
             fixed,
-            size,
+            size: SIZE,
-            block_size,
             pos: 0,
             pos_last_placed: 0,
-            num_fields: size * size,
+            num_fields: SIZE * SIZE,
-            possible_values: vec![vec![]; size * size],
+            possible_values: vec![vec![]; SIZE * SIZE],
+            rows: bit_rows,
+            cols: bit_cols,
+            blocks: bit_blocks,
         }
     }
 
@@ -122,24 +257,29 @@ impl SField {
         let mut found_solution = false;
         let mut num_solutions = 0;
 
-        //let mut loop_count = 0;
+        let mut loop_count = 0;
+        let mut last_loop_count = 0;
+        let mut now = Instant::now();
         loop {
             //std::thread::sleep_ms(30);
             //self.print_clear();
             //self.print();
-            //loop_count += 1;
+            loop_count += 1;
-            //if loop_count % 1000000 == 0 {
+            if now.elapsed().as_millis() >= 1000 {
-            //self.print_clear();
+                now = Instant::now();
-            //self.print();
+                self.print_clear();
-            //}
+                self.print();
+                println!("{} loops/s", loop_count - last_loop_count);
+                last_loop_count = loop_count;
+            }
             if self.is_end() {
                 found_solution = true;
                 num_solutions += 1;
-                if num_solutions % 100 == 0 {
+                //if num_solutions % 100 == 0 {
-                    self.print_clear();
+                //self.print_clear();
-                    println!("Solutions: {}", num_solutions);
+                //println!("Solutions: {}", num_solutions);
-                    self.print();
+                //self.print();
-                }
+                //}
 
                 if self.is_fixed() {
                     continue;
@@ -283,8 +423,9 @@ impl SField {
                 continue;
             }
 
-            if self.ok(*nr) {
+            let nr = *nr;
-                self.set(*nr);
+            if self.ok(nr) {
+                self.set(nr);
                 return true;
             }
         }
@@ -298,14 +439,11 @@ impl SField {
 
     #[inline(always)]
     fn ok(&self, nr: usize) -> bool {
-        self.block_ok(nr) && self.row_ok(nr) && self.col_ok(nr)
+        //self.block_ok(nr) && self.row_ok(nr) && self.col_ok(nr)
-    }
 
-    #[inline(always)]
+        let (x, y, block_nr) = pos_to_xy_blocknr(self.pos, self.size);
-    fn _pos_to_xy(&self) -> (usize, usize) {
+
-        let y = self.pos / self.size;
+        !self.rows[y].get(nr - 1) && !self.cols[x].get(nr - 1) && !self.blocks[block_nr].get(nr - 1)
-        let x = self.pos % self.size;
-        (x + 1, y + 1)
     }
 
     #[inline(always)]
@@ -327,26 +465,48 @@ impl SField {
 
     #[inline(always)]
     fn set(&mut self, nr: usize) {
-        self.field[self.pos] = nr;
+        let old = unsafe { self.field.get_unchecked_mut(self.pos) };
+
+        // if another number > 0 was in that cell, we need to remove that number from our bitsets
+        if *old > 0 {
+            let (x, y, block_nr) = pos_to_xy_blocknr(self.pos, self.size);
+            self.rows[y].unset(*old - 1);
+            self.cols[x].unset(*old - 1);
+            self.blocks[block_nr].unset(*old - 1);
+        }
+
+        // add new nr to our bitsets if it is a meaningful (> 0) number
+        if nr > 0 {
+            let (x, y, block_nr) = pos_to_xy_blocknr(self.pos, self.size);
+            self.rows[y].set(nr - 1);
+            self.cols[x].set(nr - 1);
+            self.blocks[block_nr].set(nr - 1);
+        }
+
+        // write the new number into the field
+        *old = nr;
+
+        // remember the last placed position for debugging purposes
         self.pos_last_placed = self.pos;
     }
 
+    /*
     #[inline(always)]
-    fn get_row(&self, row: &mut [usize; 9]) {
+    fn get_row(&self, row: &mut [usize]) {
         for (idx, row_elem) in row.iter_mut().enumerate() {
             *row_elem = self.get_field_at_pos((self.pos / self.size) * self.size + idx);
         }
     }
 
     #[inline(always)]
-    fn get_col(&self, col: &mut [usize; 9]) {
+    fn get_col(&self, col: &mut [usize]) {
         for (idx, col_elem) in col.iter_mut().enumerate() {
             *col_elem = self.get_field_at_pos(idx * self.size + self.pos % self.size);
         }
     }
 
     #[inline(always)]
-    fn get_block(&self, block: &mut [usize; 9]) {
+    fn get_block(&self, block: &mut [usize]) {
         let block_start_row = self.pos / self.size / self.block_size * self.block_size;
         let block_start_col = self.pos % self.size / self.block_size * self.block_size;
 
@@ -360,24 +520,25 @@ impl SField {
 
     #[inline(always)]
     fn block_ok(&self, nr: usize) -> bool {
-        let mut block = [0; 9];
+        let mut block = [0; MAX_BLOCK_SIZE * MAX_BLOCK_SIZE];
-        self.get_block(&mut block);
+        self.get_block(&mut block[0..self.size]);
         !block.contains(&nr)
     }
 
     #[inline(always)]
     fn row_ok(&self, nr: usize) -> bool {
-        let mut row = [0; 9];
+        let mut row = [0; MAX_BLOCK_SIZE * MAX_BLOCK_SIZE];
-        self.get_row(&mut row);
+        self.get_row(&mut row[0..self.size]);
         !row.contains(&nr)
     }
 
     #[inline(always)]
     fn col_ok(&self, nr: usize) -> bool {
-        let mut col = [0; 9];
+        let mut col = [0; MAX_BLOCK_SIZE * MAX_BLOCK_SIZE];
-        self.get_col(&mut col);
+        self.get_col(&mut col[0..self.size]);
         !col.contains(&nr)
     }
+    */
 
     #[inline(always)]
     fn next(&mut self) -> bool {
@@ -385,6 +546,7 @@ impl SField {
             return false;
         }
 
+        //println!("next {} -> {}", self.pos, self.pos + 1);
         self.pos += 1;
         true
     }
@@ -401,14 +563,16 @@ impl SField {
 
     #[inline(always)]
     fn solve(&mut self) {
+        let now = Instant::now();
         if !self.solve_backtracking() {
             println!("there is no solution.");
         }
+        println!("took {:.3}s", now.elapsed().as_secs_f64());
     }
 }
 
 fn run() -> Result<(), String> {
-    let mut field = SField::new(3);
+    let mut field = SField::new();
 
     field.build_possible_values_db();