sudoku3 (1).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "from random import randint, choice\n",
    "import operator\n",
    "alphabets = 'ABCDEFGHI'\n",
    "digits = range(1,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_grid():\n",
    "    d = defaultdict()\n",
    "    for a in alphabets:\n",
    "        for ii in digits:\n",
    "            d[(a,ii)] = 0            \n",
    "    return d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def peer_grid2(gn):\n",
    "    e = defaultdict(lambda: defaultdict(list))\n",
    "    matrix_step = [ (a, ii) for a in ('ABC', 'DEF', 'GHI') for ii in ('123', '456', '789') ]\n",
    "    matrix2 = defaultdict(int)\n",
    "    for i, t in enumerate(matrix_step):\n",
    "        matrix2[t] = i + 1\n",
    "    for k in gn:\n",
    "        e[k]['prow'] = [ (k[0], i) for i in digits if i != k[1] ]\n",
    "        e[k]['pcol'] = [ (a, k[1]) for a in alphabets if a != k[0] ]\n",
    "        for key in matrix2:\n",
    "            if k[0] in key[0] and str(k[1]) in key[1]:\n",
    "                    squarelist = [ (a, int(b)) for a in key[0] for b in key[1] if (a, int(b)) != k]\n",
    "                    e[k]['psquares'] = [s for s in squarelist ]\n",
    "    return e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def values_grid2(gn):\n",
    "    d = defaultdict(int)\n",
    "    for k in gn:\n",
    "        if gn[k] != 0:\n",
    "            d[k] = gn[k]\n",
    "        if gn[k] == 0:\n",
    "            d[k] = [ i for i in digits ]\n",
    "    return d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eliminate2(gn, pn, vn, r, c):\n",
    "    peers = []\n",
    "#     print(gn[(r, c)])\n",
    "    if type(gn[(r, c)]) == int and gn[(r, c)] != 0:\n",
    "        for k in pn[(r, c)]:\n",
    "            for char in pn[(r, c)][k]:\n",
    "                peers.append(char)\n",
    "    for peer in peers:\n",
    "#             print(peer)\n",
    "#             print(vn[peer])\n",
    "        if type(vn[peer]) == list:\n",
    "            if gn[(r, c)] in vn[peer] and len(vn[peer]) != 1:\n",
    "                vn[peer].remove(gn[(r, c)])\n",
    "                if len(vn[peer]) == 1:\n",
    "                    vn[peer] = vn[peer][0]\n",
    "                    eliminate2(gn, pn, vn, peer[0], peer[1])\n",
    "    return vn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bullseye2(gn, pn, vn, r, c):\n",
    "    nlist = [ vn[vv] for vv in pn[(r, c)]['prow'] ]\n",
    "    nlist2 = [ vn[vv] for vv in pn[(r, c)]['pcol'] ]\n",
    "    nlist3 = [ vn[vv] for vv in pn[(r, c)]['psquares'] ]\n",
    "    num2 = [ n for n in digits if n not in nlist and n not in nlist2 and n not in nlist3]\n",
    "    if len(num2) == 1: vn[[(r, c)]] = num2\n",
    "#     print(nlist, nlist2, nlist3, num2)\n",
    "    eliminate2(gn, pn, vn, r, c)\n",
    "    return vn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def constraint_prop2(gn, pn, vn, r, c):\n",
    "    vn = eliminate2(gn, pn, vn, r, c)\n",
    "    vn = bullseye2(gn, pn, vn, r, c)\n",
    "    return vn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def search2(gn, pn, vn):\n",
    "    working = defaultdict(int)\n",
    "    working = { k: len(v) for k, v in vn if type(v) == list }\n",
    "    ordering = sorted(working, key=working.get)\n",
    "    for k in ordering:\n",
    "        n1, n2 = k[0], k[1]\n",
    "#         print(vn[k])\n",
    "        if type(vn[k]) == list:\n",
    "            start = 0\n",
    "            if start <= len(vn[k]):\n",
    "                n3 = vn[k][start]\n",
    "                square_check = [ k for k in pn[k]['psquares'] if gn[k] != pn[k] ]\n",
    "                c = all(gn[k] != n3 for k in square_check)\n",
    "                while r_c_check(vn, n1, n2, n3) is True and c is False:\n",
    "                    start += 1\n",
    "                if r_c_check(vn, n1, n2, n3) is False and c is True:\n",
    "                    vn[k] = n3\n",
    "                    vn = constraint_prop2(gn, pn, vn, n1, n2)\n",
    "                    start = 0\n",
    "    return vn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_init(gn, pn, numinit):\n",
    "    count = 0\n",
    "    while count <= numinit:\n",
    "        n1, n2, n3 = choice(alphabets), randint(1,9), randint(1,9)\n",
    "        if count == 0:\n",
    "            gn[(n1, n2)] = n3\n",
    "            count += 1\n",
    "        if count > 0:\n",
    "            if r_c_check(gn, n1, n2, n3) is False:\n",
    "                square_check = [ k for k in pn[(n1, n2)]['psquares'] if gn[k] != pn[k] ]\n",
    "                if all(gn[k] != n3 for k in square_check):\n",
    "                    gn[(n1, n2)] = n3\n",
    "                    count += 1\n",
    "            else:\n",
    "                pass  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def r_c_check(gn, r, c, num):\n",
    "    for i in digits:\n",
    "        if gn[(r, i)] == num:\n",
    "            return True\n",
    "            break\n",
    "    for a in alphabets:\n",
    "        if gn[(a, c)] == num:\n",
    "            return True\n",
    "            break\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_grid(gn):\n",
    "    for a in alphabets:\n",
    "        print('  -----------------------------------\\n',\n",
    "            '| {} | {} | {} | {} | {} | {} | {} | {} | {} |'.format(gn[(a, 1)], \n",
    "            gn[(a, 2)],\n",
    "            gn[(a, 3)],\n",
    "            gn[(a, 4)],\n",
    "            gn[(a, 5)],\n",
    "            gn[(a, 6)],\n",
    "            gn[(a, 7)],\n",
    "            gn[(a, 8)],\n",
    "            gn[(a, 9)]))\n",
    "        if a == 'I':\n",
    "            print('  -----------------------------------')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def input_grid(gn, x, y, num):\n",
    "    gn[(x, y)].update(num)\n",
    "    return gn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def whole_check(gn):\n",
    "    for k in gn:\n",
    "        if type(gn[k]) == list:\n",
    "#         if gn[k] == 0:\n",
    "            return True\n",
    "            break\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solver2(gn, pn, vn):\n",
    "#     while whole_check(vn) is True:\n",
    "#             vn = search(vn)\n",
    "    for i in range(1,10000):\n",
    "        for k in vn:\n",
    "            vn = constraint_prop2(gn, pn, vn, k[0], k[1])\n",
    "            vn = search2(gn, pn, vn)\n",
    "    return vn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sudoku():\n",
    "    d1 = init_grid()\n",
    "    d2 = peer_grid2(d1)\n",
    "    random_init(d1, d2, 17)\n",
    "    d3 = values_grid2(d1)\n",
    "    return d1, d2, d3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1, d2, d3 = sudoku()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  -----------------------------------\n",
      " | 0 | 0 | 0 | 2 | 0 | 9 | 0 | 3 | 0 |\n",
      "  -----------------------------------\n",
      " | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 | 0 |\n",
      "  -----------------------------------\n",
      " | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n",
      "  -----------------------------------\n",
      " | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 6 |\n",
      "  -----------------------------------\n",
      " | 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n",
      "  -----------------------------------\n",
      " | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 9 | 0 |\n",
      "  -----------------------------------\n",
      " | 8 | 9 | 7 | 0 | 0 | 0 | 0 | 0 | 0 |\n",
      "  -----------------------------------\n",
      " | 3 | 0 | 0 | 9 | 0 | 0 | 0 | 0 | 8 |\n",
      "  -----------------------------------\n",
      " | 0 | 0 | 0 | 0 | 3 | 0 | 6 | 0 | 0 |\n",
      "  -----------------------------------\n"
     ]
    }
   ],
   "source": [
    "print_grid(d1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "defaultdict(<function peer_grid2.<locals>.<lambda> at 0x000001C579858BF8>, {('A', 1): defaultdict(<class 'list'>, {'prow': [('A', 2), ('A', 3), ('A', 4), ('A', 5), ('A', 6), ('A', 7), ('A', 8), ('A', 9)], 'pcol': [('B', 1), ('C', 1), ('D', 1), ('E', 1), ('F', 1), ('G', 1), ('H', 1), ('I', 1)], 'psquares': [('A', 2), ('A', 3), ('B', 1), ('B', 2), ('B', 3), ('C', 1), ('C', 2), ('C', 3)]}), ('A', 2): defaultdict(<class 'list'>, {'prow': [('A', 1), ('A', 3), ('A', 4), ('A', 5), ('A', 6), ('A', 7), ('A', 8), ('A', 9)], 'pcol': [('B', 2), ('C', 2), ('D', 2), ('E', 2), ('F', 2), ('G', 2), ('H', 2), ('I', 2)], 'psquares': [('A', 1), ('A', 3), ('B', 1), ('B', 2), ('B', 3), ('C', 1), ('C', 2), ('C', 3)]}), ('A', 3): defaultdict(<class 'list'>, {'prow': [('A', 1), ('A', 2), ('A', 4), ('A', 5), ('A', 6), ('A', 7), ('A', 8), ('A', 9)], 'pcol': [('B', 3), ('C', 3), ('D', 3), ('E', 3), ('F', 3), ('G', 3), ('H', 3), ('I', 3)], 'psquares': [('A', 1), ('A', 2), ('B', 1), ('B', 2), ('B', 3), ('C', 1), ('C', 2), ('C', 3)]}), ('A', 4): defaultdict(<class 'list'>, {'prow': [('A', 1), ('A', 2), ('A', 3), ('A', 5), ('A', 6), ('A', 7), ('A', 8), ('A', 9)], 'pcol': [('B', 4), ('C', 4), ('D', 4), ('E', 4), ('F', 4), ('G', 4), ('H', 4), ('I', 4)], 'psquares': [('A', 5), ('A', 6), ('B', 4), ('B', 5), ('B', 6), ('C', 4), ('C', 5), ('C', 6)]}), ('A', 5): defaultdict(<class 'list'>, {'prow': [('A', 1), ('A', 2), ('A', 3), ('A', 4), ('A', 6), ('A', 7), ('A', 8), ('A', 9)], 'pcol': [('B', 5), ('C', 5), ('D', 5), ('E', 5), ('F', 5), ('G', 5), ('H', 5), ('I', 5)], 'psquares': [('A', 4), ('A', 6), ('B', 4), ('B', 5), ('B', 6), ('C', 4), ('C', 5), ('C', 6)]}), ('A', 6): defaultdict(<class 'list'>, {'prow': [('A', 1), ('A', 2), ('A', 3), ('A', 4), ('A', 5), ('A', 7), ('A', 8), ('A', 9)], 'pcol': [('B', 6), ('C', 6), ('D', 6), ('E', 6), ('F', 6), ('G', 6), ('H', 6), ('I', 6)], 'psquares': [('A', 4), ('A', 5), ('B', 4), ('B', 5), ('B', 6), ('C', 4), ('C', 5), ('C', 6)]}), ('A', 7): defaultdict(<class 'list'>, {'prow': [('A', 1), ('A', 2), ('A', 3), ('A', 4), ('A', 5), ('A', 6), ('A', 8), ('A', 9)], 'pcol': [('B', 7), ('C', 7), ('D', 7), ('E', 7), ('F', 7), ('G', 7), ('H', 7), ('I', 7)], 'psquares': [('A', 8), ('A', 9), ('B', 7), ('B', 8), ('B', 9), ('C', 7), ('C', 8), ('C', 9)]}), ('A', 8): defaultdict(<class 'list'>, {'prow': [('A', 1), ('A', 2), ('A', 3), ('A', 4), ('A', 5), ('A', 6), ('A', 7), ('A', 9)], 'pcol': [('B', 8), ('C', 8), ('D', 8), ('E', 8), ('F', 8), ('G', 8), ('H', 8), ('I', 8)], 'psquares': [('A', 7), ('A', 9), ('B', 7), ('B', 8), ('B', 9), ('C', 7), ('C', 8), ('C', 9)]}), ('A', 9): defaultdict(<class 'list'>, {'prow': [('A', 1), ('A', 2), ('A', 3), ('A', 4), ('A', 5), ('A', 6), ('A', 7), ('A', 8)], 'pcol': [('B', 9), ('C', 9), ('D', 9), ('E', 9), ('F', 9), ('G', 9), ('H', 9), ('I', 9)], 'psquares': [('A', 7), ('A', 8), ('B', 7), ('B', 8), ('B', 9), ('C', 7), ('C', 8), ('C', 9)]}), ('B', 1): defaultdict(<class 'list'>, {'prow': [('B', 2), ('B', 3), ('B', 4), ('B', 5), ('B', 6), ('B', 7), ('B', 8), ('B', 9)], 'pcol': [('A', 1), ('C', 1), ('D', 1), ('E', 1), ('F', 1), ('G', 1), ('H', 1), ('I', 1)], 'psquares': [('A', 1), ('A', 2), ('A', 3), ('B', 2), ('B', 3), ('C', 1), ('C', 2), ('C', 3)]}), ('B', 2): defaultdict(<class 'list'>, {'prow': [('B', 1), ('B', 3), ('B', 4), ('B', 5), ('B', 6), ('B', 7), ('B', 8), ('B', 9)], 'pcol': [('A', 2), ('C', 2), ('D', 2), ('E', 2), ('F', 2), ('G', 2), ('H', 2), ('I', 2)], 'psquares': [('A', 1), ('A', 2), ('A', 3), ('B', 1), ('B', 3), ('C', 1), ('C', 2), ('C', 3)]}), ('B', 3): defaultdict(<class 'list'>, {'prow': [('B', 1), ('B', 2), ('B', 4), ('B', 5), ('B', 6), ('B', 7), ('B', 8), ('B', 9)], 'pcol': [('A', 3), ('C', 3), ('D', 3), ('E', 3), ('F', 3), ('G', 3), ('H', 3), ('I', 3)], 'psquares': [('A', 1), ('A', 2), ('A', 3), ('B', 1), ('B', 2), ('C', 1), ('C', 2), ('C', 3)]}), ('B', 4): defaultdict(<class 'list'>, {'prow': [('B', 1), ('B', 2), ('B', 3), ('B', 5), ('B', 6), ('B', 7), ('B', 8), ('B', 9)], 'pcol': [('A', 4), ('C', 4), ('D', 4), ('E', 4), ('F', 4), ('G', 4), ('H', 4), ('I', 4)], 'psquares': [('A', 4), ('A', 5), ('A', 6), ('B', 5), ('B', 6), ('C', 4), ('C', 5), ('C', 6)]}), ('B', 5): defaultdict(<class 'list'>, {'prow': [('B', 1), ('B', 2), ('B', 3), ('B', 4), ('B', 6), ('B', 7), ('B', 8), ('B', 9)], 'pcol': [('A', 5), ('C', 5), ('D', 5), ('E', 5), ('F', 5), ('G', 5), ('H', 5), ('I', 5)], 'psquares': [('A', 4), ('A', 5), ('A', 6), ('B', 4), ('B', 6), ('C', 4), ('C', 5), ('C', 6)]}), ('B', 6): defaultdict(<class 'list'>, {'prow': [('B', 1), ('B', 2), ('B', 3), ('B', 4), ('B', 5), ('B', 7), ('B', 8), ('B', 9)], 'pcol': [('A', 6), ('C', 6), ('D', 6), ('E', 6), ('F', 6), ('G', 6), ('H', 6), ('I', 6)], 'psquares': [('A', 4), ('A', 5), ('A', 6), ('B', 4), ('B', 5), ('C', 4), ('C', 5), ('C', 6)]}), ('B', 7): defaultdict(<class 'list'>, {'prow': [('B', 1), ('B', 2), ('B', 3), ('B', 4), ('B', 5), ('B', 6), ('B', 8), ('B', 9)], 'pcol': [('A', 7), ('C', 7), ('D', 7), ('E', 7), ('F', 7), ('G', 7), ('H', 7), ('I', 7)], 'psquares': [('A', 7), ('A', 8), ('A', 9), ('B', 8), ('B', 9), ('C', 7), ('C', 8), ('C', 9)]}), ('B', 8): defaultdict(<class 'list'>, {'prow': [('B', 1), ('B', 2), ('B', 3), ('B', 4), ('B', 5), ('B', 6), ('B', 7), ('B', 9)], 'pcol': [('A', 8), ('C', 8), ('D', 8), ('E', 8), ('F', 8), ('G', 8), ('H', 8), ('I', 8)], 'psquares': [('A', 7), ('A', 8), ('A', 9), ('B', 7), ('B', 9), ('C', 7), ('C', 8), ('C', 9)]}), ('B', 9): defaultdict(<class 'list'>, {'prow': [('B', 1), ('B', 2), ('B', 3), ('B', 4), ('B', 5), ('B', 6), ('B', 7), ('B', 8)], 'pcol': [('A', 9), ('C', 9), ('D', 9), ('E', 9), ('F', 9), ('G', 9), ('H', 9), ('I', 9)], 'psquares': [('A', 7), ('A', 8), ('A', 9), ('B', 7), ('B', 8), ('C', 7), ('C', 8), ('C', 9)]}), ('C', 1): defaultdict(<class 'list'>, {'prow': [('C', 2), ('C', 3), ('C', 4), ('C', 5), ('C', 6), ('C', 7), ('C', 8), ('C', 9)], 'pcol': [('A', 1), ('B', 1), ('D', 1), ('E', 1), ('F', 1), ('G', 1), ('H', 1), ('I', 1)], 'psquares': [('A', 1), ('A', 2), ('A', 3), ('B', 1), ('B', 2), ('B', 3), ('C', 2), ('C', 3)]}), ('C', 2): defaultdict(<class 'list'>, {'prow': [('C', 1), ('C', 3), ('C', 4), ('C', 5), ('C', 6), ('C', 7), ('C', 8), ('C', 9)], 'pcol': [('A', 2), ('B', 2), ('D', 2), ('E', 2), ('F', 2), ('G', 2), ('H', 2), ('I', 2)], 'psquares': [('A', 1), ('A', 2), ('A', 3), ('B', 1), ('B', 2), ('B', 3), ('C', 1), ('C', 3)]}), ('C', 3): defaultdict(<class 'list'>, {'prow': [('C', 1), ('C', 2), ('C', 4), ('C', 5), ('C', 6), ('C', 7), ('C', 8), ('C', 9)], 'pcol': [('A', 3), ('B', 3), ('D', 3), ('E', 3), ('F', 3), ('G', 3), ('H', 3), ('I', 3)], 'psquares': [('A', 1), ('A', 2), ('A', 3), ('B', 1), ('B', 2), ('B', 3), ('C', 1), ('C', 2)]}), ('C', 4): defaultdict(<class 'list'>, {'prow': [('C', 1), ('C', 2), ('C', 3), ('C', 5), ('C', 6), ('C', 7), ('C', 8), ('C', 9)], 'pcol': [('A', 4), ('B', 4), ('D', 4), ('E', 4), ('F', 4), ('G', 4), ('H', 4), ('I', 4)], 'psquares': [('A', 4), ('A', 5), ('A', 6), ('B', 4), ('B', 5), ('B', 6), ('C', 5), ('C', 6)]}), ('C', 5): defaultdict(<class 'list'>, {'prow': [('C', 1), ('C', 2), ('C', 3), ('C', 4), ('C', 6), ('C', 7), ('C', 8), ('C', 9)], 'pcol': [('A', 5), ('B', 5), ('D', 5), ('E', 5), ('F', 5), ('G', 5), ('H', 5), ('I', 5)], 'psquares': [('A', 4), ('A', 5), ('A', 6), ('B', 4), ('B', 5), ('B', 6), ('C', 4), ('C', 6)]}), ('C', 6): defaultdict(<class 'list'>, {'prow': [('C', 1), ('C', 2), ('C', 3), ('C', 4), ('C', 5), ('C', 7), ('C', 8), ('C', 9)], 'pcol': [('A', 6), ('B', 6), ('D', 6), ('E', 6), ('F', 6), ('G', 6), ('H', 6), ('I', 6)], 'psquares': [('A', 4), ('A', 5), ('A', 6), ('B', 4), ('B', 5), ('B', 6), ('C', 4), ('C', 5)]}), ('C', 7): defaultdict(<class 'list'>, {'prow': [('C', 1), ('C', 2), ('C', 3), ('C', 4), ('C', 5), ('C', 6), ('C', 8), ('C', 9)], 'pcol': [('A', 7), ('B', 7), ('D', 7), ('E', 7), ('F', 7), ('G', 7), ('H', 7), ('I', 7)], 'psquares': [('A', 7), ('A', 8), ('A', 9), ('B', 7), ('B', 8), ('B', 9), ('C', 8), ('C', 9)]}), ('C', 8): defaultdict(<class 'list'>, {'prow': [('C', 1), ('C', 2), ('C', 3), ('C', 4), ('C', 5), ('C', 6), ('C', 7), ('C', 9)], 'pcol': [('A', 8), ('B', 8), ('D', 8), ('E', 8), ('F', 8), ('G', 8), ('H', 8), ('I', 8)], 'psquares': [('A', 7), ('A', 8), ('A', 9), ('B', 7), ('B', 8), ('B', 9), ('C', 7), ('C', 9)]}), ('C', 9): defaultdict(<class 'list'>, {'prow': [('C', 1), ('C', 2), ('C', 3), ('C', 4), ('C', 5), ('C', 6), ('C', 7), ('C', 8)], 'pcol': [('A', 9), ('B', 9), ('D', 9), ('E', 9), ('F', 9), ('G', 9), ('H', 9), ('I', 9)], 'psquares': [('A', 7), ('A', 8), ('A', 9), ('B', 7), ('B', 8), ('B', 9), ('C', 7), ('C', 8)]}), ('D', 1): defaultdict(<class 'list'>, {'prow': [('D', 2), ('D', 3), ('D', 4), ('D', 5), ('D', 6), ('D', 7), ('D', 8), ('D', 9)], 'pcol': [('A', 1), ('B', 1), ('C', 1), ('E', 1), ('F', 1), ('G', 1), ('H', 1), ('I', 1)], 'psquares': [('D', 2), ('D', 3), ('E', 1), ('E', 2), ('E', 3), ('F', 1), ('F', 2), ('F', 3)]}), ('D', 2): defaultdict(<class 'list'>, {'prow': [('D', 1), ('D', 3), ('D', 4), ('D', 5), ('D', 6), ('D', 7), ('D', 8), ('D', 9)], 'pcol': [('A', 2), ('B', 2), ('C', 2), ('E', 2), ('F', 2), ('G', 2), ('H', 2), ('I', 2)], 'psquares': [('D', 1), ('D', 3), ('E', 1), ('E', 2), ('E', 3), ('F', 1), ('F', 2), ('F', 3)]}), ('D', 3): defaultdict(<class 'list'>, {'prow': [('D', 1), ('D', 2), ('D', 4), ('D', 5), ('D', 6), ('D', 7), ('D', 8), ('D', 9)], 'pcol': [('A', 3), ('B', 3), ('C', 3), ('E', 3), ('F', 3), ('G', 3), ('H', 3), ('I', 3)], 'psquares': [('D', 1), ('D', 2), ('E', 1), ('E', 2), ('E', 3), ('F', 1), ('F', 2), ('F', 3)]}), ('D', 4): defaultdict(<class 'list'>, {'prow': [('D', 1), ('D', 2), ('D', 3), ('D', 5), ('D', 6), ('D', 7), ('D', 8), ('D', 9)], 'pcol': [('A', 4), ('B', 4), ('C', 4), ('E', 4), ('F', 4), ('G', 4), ('H', 4), ('I', 4)], 'psquares': [('D', 5), ('D', 6), ('E', 4), ('E', 5), ('E', 6), ('F', 4), ('F', 5), ('F', 6)]}), ('D', 5): defaultdict(<class 'list'>, {'prow': [('D', 1), ('D', 2), ('D', 3), ('D', 4), ('D', 6), ('D', 7), ('D', 8), ('D', 9)], 'pcol': [('A', 5), ('B', 5), ('C', 5), ('E', 5), ('F', 5), ('G', 5), ('H', 5), ('I', 5)], 'psquares': [('D', 4), ('D', 6), ('E', 4), ('E', 5), ('E', 6), ('F', 4), ('F', 5), ('F', 6)]}), ('D', 6): defaultdict(<class 'list'>, {'prow': [('D', 1), ('D', 2), ('D', 3), ('D', 4), ('D', 5), ('D', 7), ('D', 8), ('D', 9)], 'pcol': [('A', 6), ('B', 6), ('C', 6), ('E', 6), ('F', 6), ('G', 6), ('H', 6), ('I', 6)], 'psquares': [('D', 4), ('D', 5), ('E', 4), ('E', 5), ('E', 6), ('F', 4), ('F', 5), ('F', 6)]}), ('D', 7): defaultdict(<class 'list'>, {'prow': [('D', 1), ('D', 2), ('D', 3), ('D', 4), ('D', 5), ('D', 6), ('D', 8), ('D', 9)], 'pcol': [('A', 7), ('B', 7), ('C', 7), ('E', 7), ('F', 7), ('G', 7), ('H', 7), ('I', 7)], 'psquares': [('D', 8), ('D', 9), ('E', 7), ('E', 8), ('E', 9), ('F', 7), ('F', 8), ('F', 9)]}), ('D', 8): defaultdict(<class 'list'>, {'prow': [('D', 1), ('D', 2), ('D', 3), ('D', 4), ('D', 5), ('D', 6), ('D', 7), ('D', 9)], 'pcol': [('A', 8), ('B', 8), ('C', 8), ('E', 8), ('F', 8), ('G', 8), ('H', 8), ('I', 8)], 'psquares': [('D', 7), ('D', 9), ('E', 7), ('E', 8), ('E', 9), ('F', 7), ('F', 8), ('F', 9)]}), ('D', 9): defaultdict(<class 'list'>, {'prow': [('D', 1), ('D', 2), ('D', 3), ('D', 4), ('D', 5), ('D', 6), ('D', 7), ('D', 8)], 'pcol': [('A', 9), ('B', 9), ('C', 9), ('E', 9), ('F', 9), ('G', 9), ('H', 9), ('I', 9)], 'psquares': [('D', 7), ('D', 8), ('E', 7), ('E', 8), ('E', 9), ('F', 7), ('F', 8), ('F', 9)]}), ('E', 1): defaultdict(<class 'list'>, {'prow': [('E', 2), ('E', 3), ('E', 4), ('E', 5), ('E', 6), ('E', 7), ('E', 8), ('E', 9)], 'pcol': [('A', 1), ('B', 1), ('C', 1), ('D', 1), ('F', 1), ('G', 1), ('H', 1), ('I', 1)], 'psquares': [('D', 1), ('D', 2), ('D', 3), ('E', 2), ('E', 3), ('F', 1), ('F', 2), ('F', 3)]}), ('E', 2): defaultdict(<class 'list'>, {'prow': [('E', 1), ('E', 3), ('E', 4), ('E', 5), ('E', 6), ('E', 7), ('E', 8), ('E', 9)], 'pcol': [('A', 2), ('B', 2), ('C', 2), ('D', 2), ('F', 2), ('G', 2), ('H', 2), ('I', 2)], 'psquares': [('D', 1), ('D', 2), ('D', 3), ('E', 1), ('E', 3), ('F', 1), ('F', 2), ('F', 3)]}), ('E', 3): defaultdict(<class 'list'>, {'prow': [('E', 1), ('E', 2), ('E', 4), ('E', 5), ('E', 6), ('E', 7), ('E', 8), ('E', 9)], 'pcol': [('A', 3), ('B', 3), ('C', 3), ('D', 3), ('F', 3), ('G', 3), ('H', 3), ('I', 3)], 'psquares': [('D', 1), ('D', 2), ('D', 3), ('E', 1), ('E', 2), ('F', 1), ('F', 2), ('F', 3)]}), ('E', 4): defaultdict(<class 'list'>, {'prow': [('E', 1), ('E', 2), ('E', 3), ('E', 5), ('E', 6), ('E', 7), ('E', 8), ('E', 9)], 'pcol': [('A', 4), ('B', 4), ('C', 4), ('D', 4), ('F', 4), ('G', 4), ('H', 4), ('I', 4)], 'psquares': [('D', 4), ('D', 5), ('D', 6), ('E', 5), ('E', 6), ('F', 4), ('F', 5), ('F', 6)]}), ('E', 5): defaultdict(<class 'list'>, {'prow': [('E', 1), ('E', 2), ('E', 3), ('E', 4), ('E', 6), ('E', 7), ('E', 8), ('E', 9)], 'pcol': [('A', 5), ('B', 5), ('C', 5), ('D', 5), ('F', 5), ('G', 5), ('H', 5), ('I', 5)], 'psquares': [('D', 4), ('D', 5), ('D', 6), ('E', 4), ('E', 6), ('F', 4), ('F', 5), ('F', 6)]}), ('E', 6): defaultdict(<class 'list'>, {'prow': [('E', 1), ('E', 2), ('E', 3), ('E', 4), ('E', 5), ('E', 7), ('E', 8), ('E', 9)], 'pcol': [('A', 6), ('B', 6), ('C', 6), ('D', 6), ('F', 6), ('G', 6), ('H', 6), ('I', 6)], 'psquares': [('D', 4), ('D', 5), ('D', 6), ('E', 4), ('E', 5), ('F', 4), ('F', 5), ('F', 6)]}), ('E', 7): defaultdict(<class 'list'>, {'prow': [('E', 1), ('E', 2), ('E', 3), ('E', 4), ('E', 5), ('E', 6), ('E', 8), ('E', 9)], 'pcol': [('A', 7), ('B', 7), ('C', 7), ('D', 7), ('F', 7), ('G', 7), ('H', 7), ('I', 7)], 'psquares': [('D', 7), ('D', 8), ('D', 9), ('E', 8), ('E', 9), ('F', 7), ('F', 8), ('F', 9)]}), ('E', 8): defaultdict(<class 'list'>, {'prow': [('E', 1), ('E', 2), ('E', 3), ('E', 4), ('E', 5), ('E', 6), ('E', 7), ('E', 9)], 'pcol': [('A', 8), ('B', 8), ('C', 8), ('D', 8), ('F', 8), ('G', 8), ('H', 8), ('I', 8)], 'psquares': [('D', 7), ('D', 8), ('D', 9), ('E', 7), ('E', 9), ('F', 7), ('F', 8), ('F', 9)]}), ('E', 9): defaultdict(<class 'list'>, {'prow': [('E', 1), ('E', 2), ('E', 3), ('E', 4), ('E', 5), ('E', 6), ('E', 7), ('E', 8)], 'pcol': [('A', 9), ('B', 9), ('C', 9), ('D', 9), ('F', 9), ('G', 9), ('H', 9), ('I', 9)], 'psquares': [('D', 7), ('D', 8), ('D', 9), ('E', 7), ('E', 8), ('F', 7), ('F', 8), ('F', 9)]}), ('F', 1): defaultdict(<class 'list'>, {'prow': [('F', 2), ('F', 3), ('F', 4), ('F', 5), ('F', 6), ('F', 7), ('F', 8), ('F', 9)], 'pcol': [('A', 1), ('B', 1), ('C', 1), ('D', 1), ('E', 1), ('G', 1), ('H', 1), ('I', 1)], 'psquares': [('D', 1), ('D', 2), ('D', 3), ('E', 1), ('E', 2), ('E', 3), ('F', 2), ('F', 3)]}), ('F', 2): defaultdict(<class 'list'>, {'prow': [('F', 1), ('F', 3), ('F', 4), ('F', 5), ('F', 6), ('F', 7), ('F', 8), ('F', 9)], 'pcol': [('A', 2), ('B', 2), ('C', 2), ('D', 2), ('E', 2), ('G', 2), ('H', 2), ('I', 2)], 'psquares': [('D', 1), ('D', 2), ('D', 3), ('E', 1), ('E', 2), ('E', 3), ('F', 1), ('F', 3)]}), ('F', 3): defaultdict(<class 'list'>, {'prow': [('F', 1), ('F', 2), ('F', 4), ('F', 5), ('F', 6), ('F', 7), ('F', 8), ('F', 9)], 'pcol': [('A', 3), ('B', 3), ('C', 3), ('D', 3), ('E', 3), ('G', 3), ('H', 3), ('I', 3)], 'psquares': [('D', 1), ('D', 2), ('D', 3), ('E', 1), ('E', 2), ('E', 3), ('F', 1), ('F', 2)]}), ('F', 4): defaultdict(<class 'list'>, {'prow': [('F', 1), ('F', 2), ('F', 3), ('F', 5), ('F', 6), ('F', 7), ('F', 8), ('F', 9)], 'pcol': [('A', 4), ('B', 4), ('C', 4), ('D', 4), ('E', 4), ('G', 4), ('H', 4), ('I', 4)], 'psquares': [('D', 4), ('D', 5), ('D', 6), ('E', 4), ('E', 5), ('E', 6), ('F', 5), ('F', 6)]}), ('F', 5): defaultdict(<class 'list'>, {'prow': [('F', 1), ('F', 2), ('F', 3), ('F', 4), ('F', 6), ('F', 7), ('F', 8), ('F', 9)], 'pcol': [('A', 5), ('B', 5), ('C', 5), ('D', 5), ('E', 5), ('G', 5), ('H', 5), ('I', 5)], 'psquares': [('D', 4), ('D', 5), ('D', 6), ('E', 4), ('E', 5), ('E', 6), ('F', 4), ('F', 6)]}), ('F', 6): defaultdict(<class 'list'>, {'prow': [('F', 1), ('F', 2), ('F', 3), ('F', 4), ('F', 5), ('F', 7), ('F', 8), ('F', 9)], 'pcol': [('A', 6), ('B', 6), ('C', 6), ('D', 6), ('E', 6), ('G', 6), ('H', 6), ('I', 6)], 'psquares': [('D', 4), ('D', 5), ('D', 6), ('E', 4), ('E', 5), ('E', 6), ('F', 4), ('F', 5)]}), ('F', 7): defaultdict(<class 'list'>, {'prow': [('F', 1), ('F', 2), ('F', 3), ('F', 4), ('F', 5), ('F', 6), ('F', 8), ('F', 9)], 'pcol': [('A', 7), ('B', 7), ('C', 7), ('D', 7), ('E', 7), ('G', 7), ('H', 7), ('I', 7)], 'psquares': [('D', 7), ('D', 8), ('D', 9), ('E', 7), ('E', 8), ('E', 9), ('F', 8), ('F', 9)]}), ('F', 8): defaultdict(<class 'list'>, {'prow': [('F', 1), ('F', 2), ('F', 3), ('F', 4), ('F', 5), ('F', 6), ('F', 7), ('F', 9)], 'pcol': [('A', 8), ('B', 8), ('C', 8), ('D', 8), ('E', 8), ('G', 8), ('H', 8), ('I', 8)], 'psquares': [('D', 7), ('D', 8), ('D', 9), ('E', 7), ('E', 8), ('E', 9), ('F', 7), ('F', 9)]}), ('F', 9): defaultdict(<class 'list'>, {'prow': [('F', 1), ('F', 2), ('F', 3), ('F', 4), ('F', 5), ('F', 6), ('F', 7), ('F', 8)], 'pcol': [('A', 9), ('B', 9), ('C', 9), ('D', 9), ('E', 9), ('G', 9), ('H', 9), ('I', 9)], 'psquares': [('D', 7), ('D', 8), ('D', 9), ('E', 7), ('E', 8), ('E', 9), ('F', 7), ('F', 8)]}), ('G', 1): defaultdict(<class 'list'>, {'prow': [('G', 2), ('G', 3), ('G', 4), ('G', 5), ('G', 6), ('G', 7), ('G', 8), ('G', 9)], 'pcol': [('A', 1), ('B', 1), ('C', 1), ('D', 1), ('E', 1), ('F', 1), ('H', 1), ('I', 1)], 'psquares': [('G', 2), ('G', 3), ('H', 1), ('H', 2), ('H', 3), ('I', 1), ('I', 2), ('I', 3)]}), ('G', 2): defaultdict(<class 'list'>, {'prow': [('G', 1), ('G', 3), ('G', 4), ('G', 5), ('G', 6), ('G', 7), ('G', 8), ('G', 9)], 'pcol': [('A', 2), ('B', 2), ('C', 2), ('D', 2), ('E', 2), ('F', 2), ('H', 2), ('I', 2)], 'psquares': [('G', 1), ('G', 3), ('H', 1), ('H', 2), ('H', 3), ('I', 1), ('I', 2), ('I', 3)]}), ('G', 3): defaultdict(<class 'list'>, {'prow': [('G', 1), ('G', 2), ('G', 4), ('G', 5), ('G', 6), ('G', 7), ('G', 8), ('G', 9)], 'pcol': [('A', 3), ('B', 3), ('C', 3), ('D', 3), ('E', 3), ('F', 3), ('H', 3), ('I', 3)], 'psquares': [('G', 1), ('G', 2), ('H', 1), ('H', 2), ('H', 3), ('I', 1), ('I', 2), ('I', 3)]}), ('G', 4): defaultdict(<class 'list'>, {'prow': [('G', 1), ('G', 2), ('G', 3), ('G', 5), ('G', 6), ('G', 7), ('G', 8), ('G', 9)], 'pcol': [('A', 4), ('B', 4), ('C', 4), ('D', 4), ('E', 4), ('F', 4), ('H', 4), ('I', 4)], 'psquares': [('G', 5), ('G', 6), ('H', 4), ('H', 5), ('H', 6), ('I', 4), ('I', 5), ('I', 6)]}), ('G', 5): defaultdict(<class 'list'>, {'prow': [('G', 1), ('G', 2), ('G', 3), ('G', 4), ('G', 6), ('G', 7), ('G', 8), ('G', 9)], 'pcol': [('A', 5), ('B', 5), ('C', 5), ('D', 5), ('E', 5), ('F', 5), ('H', 5), ('I', 5)], 'psquares': [('G', 4), ('G', 6), ('H', 4), ('H', 5), ('H', 6), ('I', 4), ('I', 5), ('I', 6)]}), ('G', 6): defaultdict(<class 'list'>, {'prow': [('G', 1), ('G', 2), ('G', 3), ('G', 4), ('G', 5), ('G', 7), ('G', 8), ('G', 9)], 'pcol': [('A', 6), ('B', 6), ('C', 6), ('D', 6), ('E', 6), ('F', 6), ('H', 6), ('I', 6)], 'psquares': [('G', 4), ('G', 5), ('H', 4), ('H', 5), ('H', 6), ('I', 4), ('I', 5), ('I', 6)]}), ('G', 7): defaultdict(<class 'list'>, {'prow': [('G', 1), ('G', 2), ('G', 3), ('G', 4), ('G', 5), ('G', 6), ('G', 8), ('G', 9)], 'pcol': [('A', 7), ('B', 7), ('C', 7), ('D', 7), ('E', 7), ('F', 7), ('H', 7), ('I', 7)], 'psquares': [('G', 8), ('G', 9), ('H', 7), ('H', 8), ('H', 9), ('I', 7), ('I', 8), ('I', 9)]}), ('G', 8): defaultdict(<class 'list'>, {'prow': [('G', 1), ('G', 2), ('G', 3), ('G', 4), ('G', 5), ('G', 6), ('G', 7), ('G', 9)], 'pcol': [('A', 8), ('B', 8), ('C', 8), ('D', 8), ('E', 8), ('F', 8), ('H', 8), ('I', 8)], 'psquares': [('G', 7), ('G', 9), ('H', 7), ('H', 8), ('H', 9), ('I', 7), ('I', 8), ('I', 9)]}), ('G', 9): defaultdict(<class 'list'>, {'prow': [('G', 1), ('G', 2), ('G', 3), ('G', 4), ('G', 5), ('G', 6), ('G', 7), ('G', 8)], 'pcol': [('A', 9), ('B', 9), ('C', 9), ('D', 9), ('E', 9), ('F', 9), ('H', 9), ('I', 9)], 'psquares': [('G', 7), ('G', 8), ('H', 7), ('H', 8), ('H', 9), ('I', 7), ('I', 8), ('I', 9)]}), ('H', 1): defaultdict(<class 'list'>, {'prow': [('H', 2), ('H', 3), ('H', 4), ('H', 5), ('H', 6), ('H', 7), ('H', 8), ('H', 9)], 'pcol': [('A', 1), ('B', 1), ('C', 1), ('D', 1), ('E', 1), ('F', 1), ('G', 1), ('I', 1)], 'psquares': [('G', 1), ('G', 2), ('G', 3), ('H', 2), ('H', 3), ('I', 1), ('I', 2), ('I', 3)]}), ('H', 2): defaultdict(<class 'list'>, {'prow': [('H', 1), ('H', 3), ('H', 4), ('H', 5), ('H', 6), ('H', 7), ('H', 8), ('H', 9)], 'pcol': [('A', 2), ('B', 2), ('C', 2), ('D', 2), ('E', 2), ('F', 2), ('G', 2), ('I', 2)], 'psquares': [('G', 1), ('G', 2), ('G', 3), ('H', 1), ('H', 3), ('I', 1), ('I', 2), ('I', 3)]}), ('H', 3): defaultdict(<class 'list'>, {'prow': [('H', 1), ('H', 2), ('H', 4), ('H', 5), ('H', 6), ('H', 7), ('H', 8), ('H', 9)], 'pcol': [('A', 3), ('B', 3), ('C', 3), ('D', 3), ('E', 3), ('F', 3), ('G', 3), ('I', 3)], 'psquares': [('G', 1), ('G', 2), ('G', 3), ('H', 1), ('H', 2), ('I', 1), ('I', 2), ('I', 3)]}), ('H', 4): defaultdict(<class 'list'>, {'prow': [('H', 1), ('H', 2), ('H', 3), ('H', 5), ('H', 6), ('H', 7), ('H', 8), ('H', 9)], 'pcol': [('A', 4), ('B', 4), ('C', 4), ('D', 4), ('E', 4), ('F', 4), ('G', 4), ('I', 4)], 'psquares': [('G', 4), ('G', 5), ('G', 6), ('H', 5), ('H', 6), ('I', 4), ('I', 5), ('I', 6)]}), ('H', 5): defaultdict(<class 'list'>, {'prow': [('H', 1), ('H', 2), ('H', 3), ('H', 4), ('H', 6), ('H', 7), ('H', 8), ('H', 9)], 'pcol': [('A', 5), ('B', 5), ('C', 5), ('D', 5), ('E', 5), ('F', 5), ('G', 5), ('I', 5)], 'psquares': [('G', 4), ('G', 5), ('G', 6), ('H', 4), ('H', 6), ('I', 4), ('I', 5), ('I', 6)]}), ('H', 6): defaultdict(<class 'list'>, {'prow': [('H', 1), ('H', 2), ('H', 3), ('H', 4), ('H', 5), ('H', 7), ('H', 8), ('H', 9)], 'pcol': [('A', 6), ('B', 6), ('C', 6), ('D', 6), ('E', 6), ('F', 6), ('G', 6), ('I', 6)], 'psquares': [('G', 4), ('G', 5), ('G', 6), ('H', 4), ('H', 5), ('I', 4), ('I', 5), ('I', 6)]}), ('H', 7): defaultdict(<class 'list'>, {'prow': [('H', 1), ('H', 2), ('H', 3), ('H', 4), ('H', 5), ('H', 6), ('H', 8), ('H', 9)], 'pcol': [('A', 7), ('B', 7), ('C', 7), ('D', 7), ('E', 7), ('F', 7), ('G', 7), ('I', 7)], 'psquares': [('G', 7), ('G', 8), ('G', 9), ('H', 8), ('H', 9), ('I', 7), ('I', 8), ('I', 9)]}), ('H', 8): defaultdict(<class 'list'>, {'prow': [('H', 1), ('H', 2), ('H', 3), ('H', 4), ('H', 5), ('H', 6), ('H', 7), ('H', 9)], 'pcol': [('A', 8), ('B', 8), ('C', 8), ('D', 8), ('E', 8), ('F', 8), ('G', 8), ('I', 8)], 'psquares': [('G', 7), ('G', 8), ('G', 9), ('H', 7), ('H', 9), ('I', 7), ('I', 8), ('I', 9)]}), ('H', 9): defaultdict(<class 'list'>, {'prow': [('H', 1), ('H', 2), ('H', 3), ('H', 4), ('H', 5), ('H', 6), ('H', 7), ('H', 8)], 'pcol': [('A', 9), ('B', 9), ('C', 9), ('D', 9), ('E', 9), ('F', 9), ('G', 9), ('I', 9)], 'psquares': [('G', 7), ('G', 8), ('G', 9), ('H', 7), ('H', 8), ('I', 7), ('I', 8), ('I', 9)]}), ('I', 1): defaultdict(<class 'list'>, {'prow': [('I', 2), ('I', 3), ('I', 4), ('I', 5), ('I', 6), ('I', 7), ('I', 8), ('I', 9)], 'pcol': [('A', 1), ('B', 1), ('C', 1), ('D', 1), ('E', 1), ('F', 1), ('G', 1), ('H', 1)], 'psquares': [('G', 1), ('G', 2), ('G', 3), ('H', 1), ('H', 2), ('H', 3), ('I', 2), ('I', 3)]}), ('I', 2): defaultdict(<class 'list'>, {'prow': [('I', 1), ('I', 3), ('I', 4), ('I', 5), ('I', 6), ('I', 7), ('I', 8), ('I', 9)], 'pcol': [('A', 2), ('B', 2), ('C', 2), ('D', 2), ('E', 2), ('F', 2), ('G', 2), ('H', 2)], 'psquares': [('G', 1), ('G', 2), ('G', 3), ('H', 1), ('H', 2), ('H', 3), ('I', 1), ('I', 3)]}), ('I', 3): defaultdict(<class 'list'>, {'prow': [('I', 1), ('I', 2), ('I', 4), ('I', 5), ('I', 6), ('I', 7), ('I', 8), ('I', 9)], 'pcol': [('A', 3), ('B', 3), ('C', 3), ('D', 3), ('E', 3), ('F', 3), ('G', 3), ('H', 3)], 'psquares': [('G', 1), ('G', 2), ('G', 3), ('H', 1), ('H', 2), ('H', 3), ('I', 1), ('I', 2)]}), ('I', 4): defaultdict(<class 'list'>, {'prow': [('I', 1), ('I', 2), ('I', 3), ('I', 5), ('I', 6), ('I', 7), ('I', 8), ('I', 9)], 'pcol': [('A', 4), ('B', 4), ('C', 4), ('D', 4), ('E', 4), ('F', 4), ('G', 4), ('H', 4)], 'psquares': [('G', 4), ('G', 5), ('G', 6), ('H', 4), ('H', 5), ('H', 6), ('I', 5), ('I', 6)]}), ('I', 5): defaultdict(<class 'list'>, {'prow': [('I', 1), ('I', 2), ('I', 3), ('I', 4), ('I', 6), ('I', 7), ('I', 8), ('I', 9)], 'pcol': [('A', 5), ('B', 5), ('C', 5), ('D', 5), ('E', 5), ('F', 5), ('G', 5), ('H', 5)], 'psquares': [('G', 4), ('G', 5), ('G', 6), ('H', 4), ('H', 5), ('H', 6), ('I', 4), ('I', 6)]}), ('I', 6): defaultdict(<class 'list'>, {'prow': [('I', 1), ('I', 2), ('I', 3), ('I', 4), ('I', 5), ('I', 7), ('I', 8), ('I', 9)], 'pcol': [('A', 6), ('B', 6), ('C', 6), ('D', 6), ('E', 6), ('F', 6), ('G', 6), ('H', 6)], 'psquares': [('G', 4), ('G', 5), ('G', 6), ('H', 4), ('H', 5), ('H', 6), ('I', 4), ('I', 5)]}), ('I', 7): defaultdict(<class 'list'>, {'prow': [('I', 1), ('I', 2), ('I', 3), ('I', 4), ('I', 5), ('I', 6), ('I', 8), ('I', 9)], 'pcol': [('A', 7), ('B', 7), ('C', 7), ('D', 7), ('E', 7), ('F', 7), ('G', 7), ('H', 7)], 'psquares': [('G', 7), ('G', 8), ('G', 9), ('H', 7), ('H', 8), ('H', 9), ('I', 8), ('I', 9)]}), ('I', 8): defaultdict(<class 'list'>, {'prow': [('I', 1), ('I', 2), ('I', 3), ('I', 4), ('I', 5), ('I', 6), ('I', 7), ('I', 9)], 'pcol': [('A', 8), ('B', 8), ('C', 8), ('D', 8), ('E', 8), ('F', 8), ('G', 8), ('H', 8)], 'psquares': [('G', 7), ('G', 8), ('G', 9), ('H', 7), ('H', 8), ('H', 9), ('I', 7), ('I', 9)]}), ('I', 9): defaultdict(<class 'list'>, {'prow': [('I', 1), ('I', 2), ('I', 3), ('I', 4), ('I', 5), ('I', 6), ('I', 7), ('I', 8)], 'pcol': [('A', 9), ('B', 9), ('C', 9), ('D', 9), ('E', 9), ('F', 9), ('G', 9), ('H', 9)], 'psquares': [('G', 7), ('G', 8), ('G', 9), ('H', 7), ('H', 8), ('H', 9), ('I', 7), ('I', 8)]})})\n"
     ]
    }
   ],
   "source": [
    "print(d2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  -----------------------------------\n",
      " | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 2 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 9 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 3 | [1, 2, 3, 4, 5, 6, 7, 8, 9] |\n",
      "  -----------------------------------\n",
      " | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 3 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] |\n",
      "  -----------------------------------\n",
      " | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] |\n",
      "  -----------------------------------\n",
      " | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 4 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 6 |\n",
      "  -----------------------------------\n",
      " | 9 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] |\n",
      "  -----------------------------------\n",
      " | 2 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 9 | [1, 2, 3, 4, 5, 6, 7, 8, 9] |\n",
      "  -----------------------------------\n",
      " | 8 | 9 | 7 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] |\n",
      "  -----------------------------------\n",
      " | 3 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 9 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 8 |\n",
      "  -----------------------------------\n",
      " | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 3 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | 6 | [1, 2, 3, 4, 5, 6, 7, 8, 9] | [1, 2, 3, 4, 5, 6, 7, 8, 9] |\n",
      "  -----------------------------------\n"
     ]
    }
   ],
   "source": [
    "print_grid(d3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  -----------------------------------\n",
      " | [1, 4, 5, 6, 7] | [1, 5, 6, 7, 8] | [1, 4, 5, 6, 8] | 2 | [1, 4, 5, 6, 7, 8] | 9 | [1, 4, 5, 7, 8] | 3 | [1, 4, 5, 7] |\n",
      "  -----------------------------------\n",
      " | [1, 4, 5, 6, 7] | [1, 2, 5, 6, 7, 8] | 3 | [1, 4, 5, 6, 7, 8] | [1, 4, 5, 6, 7, 8] | [1, 4, 5, 6, 7, 8] | [1, 2, 4, 5, 7, 8, 9] | [1, 2, 4, 5, 6, 7, 8] | [1, 2, 4, 5, 7, 9] |\n",
      "  -----------------------------------\n",
      " | [1, 4, 5, 6, 7] | [1, 2, 5, 6, 7, 8] | [1, 2, 4, 5, 6, 8, 9] | [1, 3, 4, 5, 6, 7, 8] | [1, 4, 5, 6, 7, 8] | [1, 3, 4, 5, 6, 7, 8] | [1, 2, 4, 5, 7, 8, 9] | [1, 2, 4, 5, 6, 7, 8] | [1, 2, 4, 5, 7, 9] |\n",
      "  -----------------------------------\n",
      " | [1, 5, 7] | 4 | [1, 5, 8] | [1, 3, 5, 7, 8] | [1, 2, 5, 7, 8, 9] | [1, 2, 3, 5, 7, 8] | [1, 2, 3, 5, 7, 8] | [1, 2, 5, 7, 8] | 6 |\n",
      "  -----------------------------------\n",
      " | 9 | [1, 3, 5, 6, 7, 8] | [1, 5, 6, 8] | [1, 3, 4, 5, 6, 7, 8] | [1, 2, 4, 5, 6, 7, 8] | [1, 2, 3, 4, 5, 6, 7, 8] | [1, 2, 3, 4, 5, 7, 8] | [1, 2, 4, 5, 7, 8] | [1, 2, 3, 4, 5, 7] |\n",
      "  -----------------------------------\n",
      " | 2 | [1, 3, 5, 6, 7, 8] | [1, 5, 6, 8] | [1, 3, 4, 5, 6, 7, 8] | [1, 4, 5, 6, 7, 8] | [1, 3, 4, 5, 6, 7, 8] | [1, 3, 4, 5, 7, 8] | 9 | [1, 3, 4, 5, 7] |\n",
      "  -----------------------------------\n",
      " | 8 | 9 | 7 | [1, 4, 5, 6] | [1, 2, 4, 5, 6] | [1, 2, 4, 5, 6] | [1, 2, 3, 4, 5] | [1, 2, 4, 5] | [1, 2, 3, 4, 5] |\n",
      "  -----------------------------------\n",
      " | 3 | [1, 2, 5, 6] | [1, 2, 4, 5, 6] | 9 | [1, 2, 4, 5, 6, 7] | [1, 2, 4, 5, 6, 7] | [1, 2, 4, 5, 7] | [1, 2, 4, 5, 7] | 8 |\n",
      "  -----------------------------------\n",
      " | [1, 4, 5] | [1, 2, 5] | [1, 2, 4, 5] | [1, 4, 5, 7, 8] | 3 | [1, 2, 4, 5, 7, 8] | 6 | [1, 2, 4, 5, 7] | [1, 2, 4, 5, 7, 9] |\n",
      "  -----------------------------------\n"
     ]
    }
   ],
   "source": [
    "print_grid(solver2(d1, d2, d3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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