Chess Problem.ipynb

{
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    {
     "ename": "TypeError",
     "evalue": "can only concatenate str (not \"list\") to str",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-29-5d82f2be2720>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     38\u001b[0m     \u001b[0mlisty\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 40\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"listy\"\u001b[0m \u001b[0;34m+\u001b[0m\u001b[0mlisty\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     41\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     42\u001b[0m \u001b[0mcomb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcombinations\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlisty\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: can only concatenate str (not \"list\") to str"
     ]
    }
   ],
   "source": [
    "'''Here I have set up the code for n = 5. I am using duality so I check all the combinations of 3 positions on the 5x5\n",
    "by placing queens in those 3 places and checking the number of pawns that can be placed safely. Below it shows that if \n",
    "I place 3 queens, max 5 pawns can be placed and so we can say that if 5 queens are there, 3 pawns can be placed safely.\n",
    "The code can be tweaked for n = 6 but is pretty slow as I have not made use of symmetries yet. '''\n",
    "\n",
    "from itertools import combinations\n",
    "n = 5\n",
    "board = [[] for x in range(n)]\n",
    "\n",
    "def initialise_board(n):\n",
    "    for x in range(n):\n",
    "        for y in range(n):\n",
    "            board[x].append(' ')\n",
    "            \n",
    "def reset_board(n):\n",
    "    for x in range(n):\n",
    "        for y in range(n):\n",
    "            board[x][y] = ' '\n",
    "            \n",
    "def print_board():\n",
    "    printy = \"\"\n",
    "    for x in range(n):\n",
    "        for y in range(n):\n",
    "            if y < (n-1):\n",
    "                printy = printy + board[x][y] + \"|\"\n",
    "            else:\n",
    "                printy = printy + board[x][y] + '\\n'\n",
    "                 \n",
    "        if x < (n - 1):\n",
    "            printy = printy + '-'*(n*2-1) + '\\n' \n",
    "    return print(printy)\n",
    "\n",
    "\n",
    "help_listy = list(range(0,n-2))\n",
    "\n",
    "listy = list(combinations(help_listy,2))\n",
    "for x in help_listy:\n",
    "    listy.append((x,x))\n",
    "\n",
    "print(\"listy\" + listy)\n",
    "    \n",
    "comb = list(combinations(listy,3))\n",
    "\n",
    "print(comb)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def f1fill_diagonal(pos):\n",
    "    i1 = int(pos[0])\n",
    "    i2 = int(pos[1])\n",
    "    if i1 == 4 or i2 == 4:\n",
    "        no = 1\n",
    "    elif i1 == 3 or i2 == 3:\n",
    "        no = 2\n",
    "    elif i1 == 2 or i2 == 2:\n",
    "        no = 3\n",
    "    elif i1 == 1 or i2 == 1:\n",
    "        no = 4\n",
    "    else: \n",
    "        no = 5\n",
    "    for x in range(no):\n",
    "        board[i1][i2] = 'D'\n",
    "        i1 += 1\n",
    "        i2 += 1\n",
    "        \n",
    "def f2fill_diagonal(pos):\n",
    "    i1 = int(pos[0])\n",
    "    i2 = int(pos[1])\n",
    "    if i1 == 0 or i2 == 0:\n",
    "        no = 1\n",
    "    elif i1 == 1 or i2 == 1:\n",
    "        no = 2\n",
    "    elif i1 == 2 or i2 == 2:\n",
    "        no = 3\n",
    "    elif i1 == 3 or i2 == 3:\n",
    "        no = 4\n",
    "    else: \n",
    "        no = 5\n",
    "    for x in range(no):\n",
    "        board[i1][i2] = 'D'\n",
    "        i1 -= 1\n",
    "        i2 -= 1\n",
    "    \n",
    "def b1fill_diagonal(pos):\n",
    "    i1 = int(pos[0])\n",
    "    i2 = int(pos[1])\n",
    "    if i1 == 4 or i2 == 0:\n",
    "        no = 1\n",
    "    elif i1 == 3 or i2 == 1 :\n",
    "        no = 2\n",
    "    elif i1 == 2 or i2 == 2:\n",
    "        no = 3\n",
    "    elif i1 == 1 or i2 == 3:\n",
    "        no = 4\n",
    "    else: \n",
    "        no = 5\n",
    "    for x in range(no):\n",
    "        board[i1][i2] = 'D'\n",
    "        i1 += 1\n",
    "        i2 -= 1\n",
    "        \n",
    "        \n",
    "def b2fill_diagonal(pos):\n",
    "    i1 = int(pos[0])\n",
    "    i2 = int(pos[1])\n",
    "    if i1 == 0 or i2 == 4:\n",
    "        no = 1\n",
    "    elif i1 == 1 or i2 == 3:\n",
    "        no = 2\n",
    "    elif i1 == 2 or i2 == 2:\n",
    "        no = 3\n",
    "    elif i1 == 3 or i2 == 1:\n",
    "        no = 4\n",
    "    else: \n",
    "        no = 5\n",
    "    for x in range(no):\n",
    "        board[i1][i2] = 'D'\n",
    "        i1 -= 1\n",
    "        i2 += 1\n",
    "        \n",
    "def check(pos):\n",
    "    'vertical'\n",
    "    for x in range(n):\n",
    "        idx2 = int(pos[1])\n",
    "        board[x][idx2] = 'D'\n",
    "    'horizontal'\n",
    "    for x in range(n):\n",
    "        idx1 = int(pos[0])\n",
    "        board[idx1][x] = 'D'\n",
    "    'diagonal1'\n",
    "    f1fill_diagonal(pos)\n",
    "    'diagonal2'\n",
    "    f2fill_diagonal(pos)\n",
    "    b1fill_diagonal(pos)\n",
    "    b2fill_diagonal(pos)\n",
    "    \n",
    "def pawns():\n",
    "    count = 0\n",
    "    for x in range(n):\n",
    "        for y in range(n):\n",
    "            if board[x][y] != 'D':\n",
    "                count += 1\n",
    "    return count\n",
    "            \n",
    "        \n",
    "\n",
    "list3 =[]\n",
    "initialise_board(5)\n",
    "for y in comb:\n",
    "    reset_board(n)\n",
    "    for x in y:\n",
    "        check(x)\n",
    "        print_board()\n",
    "    print(pawns())    \n",
    "    list3.append(pawns())\n",
    "\n",
    "max(list3)\n",
    "    "
   ]
  },
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   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2]\n",
      "[(0, 1), (0, 2), (1, 2), (0, 0), (1, 1), (2, 2)]\n"
     ]
    }
   ],
   "source": [
    "help_listy = list(range(0,n-2))\n",
    "\n",
    "listy = list(combinations(help_listy,2))\n",
    "for x in help_listy:\n",
    "    listy.append((x,x))\n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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