solve.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 410,
   "id": "dbbe99da-2378-4532-9044-460a42721f2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pysat.formula import CNF\n",
    "from pysat.solvers import Solver\n",
    "from sympy.logic.boolalg import Or, And, Not, to_cnf\n",
    "from sympy import symbols\n",
    "from pprint import pprint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "id": "ffe9b46e-c80f-449b-9c42-a1d7431c0724",
   "metadata": {},
   "outputs": [],
   "source": [
    "def flatten(s):\n",
    "    return [x for xs in s for x in xs]\n",
    "\n",
    "def len_flat(s):\n",
    "    return len(flatten(s))"
   ]
  },
  {
   "attachments": {
    "99ce6221-e7a2-4a0d-b6c3-ab47836d923b.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "4182cbb9-facd-487f-ad9e-088726034918",
   "metadata": {},
   "source": [
    "![Screenshot from 2024-11-22 09-25-20.png](attachment:99ce6221-e7a2-4a0d-b6c3-ab47836d923b.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "id": "5f88fef4-0b84-4a90-8e42-4364fb5739fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "rows = 15\n",
    "cols = 15\n",
    "cols_seqs = ((7,),(2,1,1,2),(2,5,2),(4,2,1),(1,1,1,1,3),(3,3,1,1),(1,2,4,2),(2,5,2,3),(2,1,1,2,1,1),(7,3,1),(1,1,3,1,1),(3,2,3,1),(1,5,1,1),(1,1,3),(3,))\n",
    "num_col_seqs = len_flat(cols_seqs)\n",
    "rows_seqs = ((6,),(3,1,2,3),(2,4,2,1),(1,2,2,4),(3,2,3,3),(1,1,1,1,1,1,1),(3,2,3,3),(1,2,2,1,2),(2,4,4),(2,1,3,1),(6,3),(1,1),(7,),(2,1),(8,))\n",
    "num_row_seqs = len_flat(rows_seqs)\n",
    "\n",
    "# The first variables, are for each of the col seqs, where do they start.\n",
    "# Then where do the rows seqs start. Lastly, whether each cell is black or white\n",
    "num_vars = rows * cols + num_col_seqs * rows + num_row_seqs * cols\n",
    "\n",
    "x = symbols(f\"x0:{num_vars}\")\n",
    "\n",
    "cols_seqs_index = 0\n",
    "rows_seqs_index = num_col_seqs * rows\n",
    "cells_index = num_col_seqs * rows + num_row_seqs * cols\n",
    "\n",
    "def cell_index(x, y):\n",
    "    return x * cols + y + cells_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "id": "5c638a53-386b-418a-a4f0-281b703e05d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "non_cnf_formula = And()\n",
    "for i in range(num_col_seqs):\n",
    "    non_cnf_formula &= Or(*[x[j] for j in range(i * rows, (i+1)*rows)])\n",
    "\n",
    "for i in range(num_row_seqs):\n",
    "    non_cnf_formula &= Or(*[x[j] for j in range(rows_seqs_index + i * cols, rows_seqs_index + (i+1)*cols)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "id": "0eba2ab7-4826-4823-9fea-fad0603d45e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now each seq starting from some index i, implies that the next sequence can't start from the \n",
    "# start of the column up to this index i, and can't start from index i forward the amount of the \n",
    "# sequence, and another 1 cell for spacing\n",
    "rule = And()\n",
    "var_index = 0\n",
    "for col_seqs in cols_seqs:\n",
    "    # The last seq in the column doesn't say anything on the next ones\n",
    "    for seq in col_seqs[:-1]:\n",
    "        # The var that the next seq is starting in row 0\n",
    "        next_seq_index = var_index + rows\n",
    "        for irow in range(rows):\n",
    "            # If the current seq starts at row <irow>, the next seq can't start from 0 to <irow + seq_length>\n",
    "            next_seq_can_start_from = min(irow + seq + 1, rows)\n",
    "            \n",
    "            rule &= And(*[x[var_index] >> ~x[next_seq_index + j] for j in range(0,next_seq_can_start_from)])\n",
    "            # The var that the seq <seqi> is starting in row <i> \n",
    "            var_index += 1\n",
    "    if col_seqs:\n",
    "        # The last seq can't be in the last cells in the col\n",
    "        last_seq = col_seqs[-1]\n",
    "        rule &= And(*[~x[var_index + j] for j in range(rows-last_seq+1, rows)])\n",
    "        # Advance to the var in the next col\n",
    "        var_index += rows\n",
    "\n",
    "non_cnf_formula &= rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "id": "852e85de-f35f-41bc-b923-7f712c3fbddb",
   "metadata": {},
   "outputs": [],
   "source": [
    "rule = And()\n",
    "for row_seqs in rows_seqs:\n",
    "    # The last seq in the column doesn't say anything on the next ones\n",
    "    for seq in row_seqs[:-1]:\n",
    "        # The var that the next seq is starting in col 0\n",
    "        next_seq_index = var_index + cols\n",
    "        for icol in range(cols):\n",
    "            # If the current seq starts at col <icol>, the next seq can't start from 0 to <icol + seq_length>\n",
    "            next_seq_can_start_from = min(icol + seq + 1, cols)\n",
    "            \n",
    "            rule &= And(*[x[var_index] >> ~x[next_seq_index + j] for j in range(0,next_seq_can_start_from)])\n",
    "            # The var that the seq <seqi> is starting in col <i> \n",
    "            var_index += 1\n",
    "    if row_seqs:\n",
    "        # The last seq can't be in the last cells in the row\n",
    "        last_seq = row_seqs[-1]\n",
    "        rule &= And(*[~x[var_index + j] for j in range(cols-last_seq+1, cols)])\n",
    "        # Advance to the var in the next col\n",
    "        var_index += cols\n",
    "\n",
    "non_cnf_formula &= rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "id": "053386a5-d86f-41dd-89af-74b9f5e7b61b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# rule A - Column sequences starting are implying cells are black, and one empty cell\n",
    "rule = And()\n",
    "var_index = 0\n",
    "for icol, col_seqs in enumerate(cols_seqs):\n",
    "    for seq in col_seqs:\n",
    "        for irow in range(rows):\n",
    "            if (irow + seq > rows):\n",
    "                # The sequence cannot start here, it doesn't have enough space\n",
    "                var_index += 1\n",
    "                continue\n",
    "            # Current seq starts at <irow>. This implies cells are black/white\n",
    "            rule &= x[var_index] >> And(*[x[cell_index(y, icol)] for y in range(irow, irow+seq)])\n",
    "            if (irow+seq < rows):\n",
    "                # Add a space cell after the seq\n",
    "                rule &= x[var_index] >> ~x[cell_index(irow + seq, icol)]\n",
    "            var_index += 1\n",
    "\n",
    "non_cnf_formula &= rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "id": "9607f426-0636-451d-b4d7-b097a95f818a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# rule B - Row sequences starting are implying cells are black, and one empty cell\n",
    "rule = And()\n",
    "var_index = rows_seqs_index\n",
    "for irow, row_seqs in enumerate(rows_seqs):\n",
    "    for seq in row_seqs:\n",
    "        for icol in range(cols):\n",
    "            if (icol + seq > cols):\n",
    "                # The sequence cannot start here, it doesn't have enough space\n",
    "                var_index += 1\n",
    "                continue\n",
    "            # Current seq starts at <icol>. This implies cells are black/white\n",
    "            rule &= x[var_index] >> And(*[x[cell_index(irow, y)] for y in range(icol, icol+seq)])\n",
    "            if (icol+seq < cols):\n",
    "                # Add a space cell after the seq\n",
    "                rule &= x[var_index] >> ~x[cell_index(irow, icol + seq)]\n",
    "            var_index += 1\n",
    "\n",
    "non_cnf_formula &= rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "id": "e35b4017-e216-48d9-884e-54d3dc5d2289",
   "metadata": {},
   "outputs": [],
   "source": [
    "# rule A - empty spaces before the first seq every col\n",
    "rule = And()\n",
    "var_index = 0\n",
    "for icol, col_seqs in enumerate(cols_seqs):\n",
    "    first_seq = col_seqs[0]\n",
    "    for irow in range(1, rows):\n",
    "        # The seq starting at irow, implies that the previous cells are empty \n",
    "        rule &= x[var_index+irow] >> And(*[~x[cell_index(i, icol)] for i in range(0,irow)])\n",
    "    var_index += len(col_seqs) * rows\n",
    "\n",
    "non_cnf_formula &= rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "id": "9fa794ac-4acc-440c-9a4a-9fbc6da0b88e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# rule B - empty spaces before the first seq every col\n",
    "rule = And()\n",
    "var_index = rows_seqs_index\n",
    "for irow, row_seqs in enumerate(rows_seqs):\n",
    "    first_seq = row_seqs[0]\n",
    "    for icol in range(1, cols):\n",
    "        # The seq starting at icol, implies that the previous cells are empty \n",
    "        rule &= x[var_index+icol] >> And(*[~x[cell_index(irow, i)] for i in range(0,icol)])\n",
    "    var_index += len(row_seqs) * cols\n",
    "\n",
    "non_cnf_formula &= rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "id": "7c680333-d426-4717-8046-d0878b198911",
   "metadata": {},
   "outputs": [],
   "source": [
    "# rule A - empty spaces after the last seq every col\n",
    "rule = And()\n",
    "var_index = 0\n",
    "for icol, col_seqs in enumerate(cols_seqs):\n",
    "    last_seq = col_seqs[-1]\n",
    "    var_index += len(col_seqs) * rows - rows\n",
    "    for irow in range(0, rows - last_seq):\n",
    "        # The seq starting at irow, implies that the previous cells are empty \n",
    "        rule &= x[var_index+irow] >> And(*[~x[cell_index(i, icol)] for i in range(irow+last_seq,rows)])\n",
    "    var_index += rows\n",
    "\n",
    "non_cnf_formula &= rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "id": "d6cd9fa9-1d68-4959-b8a8-12396d46d63b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# rule B - empty spaces after the last seq every row\n",
    "rule = And()\n",
    "var_index = rows_seqs_index\n",
    "for irow, row_seqs in enumerate(rows_seqs):\n",
    "    last_seq = row_seqs[-1]\n",
    "    var_index += len(row_seqs) * cols - cols\n",
    "    for icol in range(0, cols - last_seq):\n",
    "        # The seq starting at icol, implies that the previous cells are empty \n",
    "        # print(irow,icol,var_index+icol,cell_index(irow,icol+last_seq))\n",
    "        rule &= x[var_index+icol] >> And(*[~x[cell_index(irow, i)] for i in range(icol+last_seq,cols)])\n",
    "    var_index += cols\n",
    "\n",
    "non_cnf_formula &= rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 422,
   "id": "e424b6df-ddb0-4463-8a0e-a6c644f20064",
   "metadata": {},
   "outputs": [],
   "source": [
    "# rule A - Fill empty spaces in between each 2 sequences\n",
    "rule = And()\n",
    "var_index = 0\n",
    "for icol, col_seqs in enumerate(cols_seqs):\n",
    "    for iseq, seq in enumerate(col_seqs[:-1]):\n",
    "        next_var_index = var_index + rows\n",
    "\n",
    "        for seq_start_row in range(rows):\n",
    "            for next_var_row in range(seq_start_row + seq + 2, rows):\n",
    "                var_start_index = var_index + seq_start_row\n",
    "                next_var_start_index = next_var_index + next_var_row\n",
    "                rule &= And(x[var_start_index] & x[next_var_start_index]) >> And(*[~x[cell_index(row, icol)] for row in range(seq_start_row+seq, next_var_row)])\n",
    "        var_index += rows\n",
    "    var_index += rows\n",
    "\n",
    "non_cnf_formula &= rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "id": "7666b5e2-d819-42bd-b4bb-76bd5e1f4be0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# rule B - Fill empty spaces in between each 2 sequences in rows\n",
    "# For some reason I see that this was never needed in any of the griddlers I've tested. I'm not sure why\n",
    "# Since it's the heaviest rule, I rather avoid it if it's not necessary. I'll add it if I see a puzzle which needs it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 424,
   "id": "942f7164-2c45-4c6a-82e9-58d7793ac365",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert to CNF\n",
    "cnf_formula = to_cnf(non_cnf_formula)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 425,
   "id": "019aa0d7-0392-4efd-b614-d8bc6143aabe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sympy_to_pysat(cnf_expr, mapping):\n",
    "    def traverse(expr):\n",
    "        if isinstance(expr, And):\n",
    "            return [traverse(arg) for arg in expr.args]\n",
    "        elif isinstance(expr, Or):\n",
    "            return [traverse(arg) for arg in expr.args]\n",
    "        elif isinstance(expr, Not):\n",
    "            return -mapping[expr.args[0]]\n",
    "        else:  # It's a variable\n",
    "            return mapping[expr]\n",
    "    \n",
    "    # Flatten the AND clauses into a list of lists\n",
    "    return [clause if isinstance(clause, list) else [clause] for clause in traverse(cnf_expr)]\n",
    "\n",
    "# Convert to pysat format\n",
    "variable_mapping = {var: idx + 1 for idx, var in enumerate(x)}\n",
    "pysat_cnf = sympy_to_pysat(cnf_formula, variable_mapping)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "id": "8166f7cd-5fa1-4454-8a5b-93ee4f53478e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "formula is satisfiable\n"
     ]
    }
   ],
   "source": [
    "# create a satisfiable CNF formula \"(-x1 ∨ x2) ∧ (-x1 ∨ -x2)\":\n",
    "cnf = CNF(from_clauses=pysat_cnf)\n",
    "\n",
    "# create a SAT solver for this formula:\n",
    "with Solver(bootstrap_with=cnf) as solver:\n",
    "    # 1.1 call the solver for this formula:\n",
    "    print('formula is', f'{\"s\" if solver.solve() else \"uns\"}atisfiable')\n",
    "\n",
    "    # 1.2 the formula is satisfiable and so has a model:\n",
    "\n",
    "    solution = [x - 1 if x > 0 else x + 1 for x in solver.get_model()]\n",
    "    # print('and the model is:', solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 427,
   "id": "42f040b6-2768-4687-bcc6-ab25c66341ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_ _ X X X X X X _ _ _ _ _ _ _ \n",
      "_ X X X _ X _ X X _ X X X _ _ \n",
      "X X _ X X X X _ X X _ X _ _ _ \n",
      "X _ X X _ _ X X _ X X X X _ _ \n",
      "X X X _ X X _ X X X _ _ X X X \n",
      "X _ X _ _ X _ X _ X _ _ X _ X \n",
      "X X X _ X X _ X X X _ _ X X X \n",
      "X _ X X _ _ X X _ X _ X X _ _ \n",
      "X X _ X X X X _ X X X X _ _ _ \n",
      "_ X X _ X _ X X X _ X _ _ _ _ \n",
      "_ _ X X X X X X _ X X X _ _ _ \n",
      "_ _ _ _ _ _ _ _ _ X _ X _ _ _ \n",
      "_ _ _ _ _ _ _ X X X X X X X _ \n",
      "_ _ _ _ _ _ X X _ _ _ _ _ X _ \n",
      "_ _ _ _ _ _ X X X X X X X X _ \n"
     ]
    }
   ],
   "source": [
    "d = solution[cells_index:]\n",
    "for i in range(rows):\n",
    "    for j in range(cols):\n",
    "        val = d[i*cols+j]\n",
    "        sign = val > 0\n",
    "        print(\"X\" if sign else \"_\", end=\" \")\n",
    "        # print(val, end=\" \")\n",
    "    print()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}