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    "# Foundations of Computational Economics #6\n",
    "\n",
    "by Fedor Iskhakov, ANU\n",
    "\n",
    "<img src=\"_static/img/dag3logo.png\" style=\"width:256px;\">"
   ]
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   "source": [
    "## Two simple examples\n",
    "\n",
    "<img src=\"_static/img/lab.png\" style=\"width:64px;\">"
   ]
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    "<img src=\"_static/img/youtube.png\" style=\"width:65px;\">\n",
    "\n",
    "[https://youtu.be/UGExPIDwDMs](https://youtu.be/UGExPIDwDMs)\n",
    "\n",
    "Description: Indexing problem and its inverse, base-N number conversion"
   ]
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   "source": [
    "### Example 1\n",
    "\n",
    "Code up a function to convert $ (i,j) $ index in a two-dimensional array\n",
    "into a single index $ k $ which swipes the matrix by column.\n",
    "Also code up the inverse of this function."
   ]
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   "source": [
    "# code here"
   ]
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     "text": [
      "(0,0) --> 0 --> (0,0)\n",
      "(0,1) --> 5 --> (0,1)\n",
      "(0,2) --> 10 --> (0,2)\n",
      "(0,3) --> 15 --> (0,3)\n",
      "(0,4) --> 20 --> (0,4)\n",
      "(0,5) --> 25 --> (0,5)\n",
      "(0,6) --> 30 --> (0,6)\n",
      "(0,7) --> 35 --> (0,7)\n",
      "(0,8) --> 40 --> (0,8)\n",
      "(0,9) --> 45 --> (0,9)\n",
      "(1,0) --> 1 --> (1,0)\n",
      "(1,1) --> 6 --> (1,1)\n",
      "(1,2) --> 11 --> (1,2)\n",
      "(1,3) --> 16 --> (1,3)\n",
      "(1,4) --> 21 --> (1,4)\n",
      "(1,5) --> 26 --> (1,5)\n",
      "(1,6) --> 31 --> (1,6)\n",
      "(1,7) --> 36 --> (1,7)\n",
      "(1,8) --> 41 --> (1,8)\n",
      "(1,9) --> 46 --> (1,9)\n",
      "(2,0) --> 2 --> (2,0)\n",
      "(2,1) --> 7 --> (2,1)\n",
      "(2,2) --> 12 --> (2,2)\n",
      "(2,3) --> 17 --> (2,3)\n",
      "(2,4) --> 22 --> (2,4)\n",
      "(2,5) --> 27 --> (2,5)\n",
      "(2,6) --> 32 --> (2,6)\n",
      "(2,7) --> 37 --> (2,7)\n",
      "(2,8) --> 42 --> (2,8)\n",
      "(2,9) --> 47 --> (2,9)\n",
      "(3,0) --> 3 --> (3,0)\n",
      "(3,1) --> 8 --> (3,1)\n",
      "(3,2) --> 13 --> (3,2)\n",
      "(3,3) --> 18 --> (3,3)\n",
      "(3,4) --> 23 --> (3,4)\n",
      "(3,5) --> 28 --> (3,5)\n",
      "(3,6) --> 33 --> (3,6)\n",
      "(3,7) --> 38 --> (3,7)\n",
      "(3,8) --> 43 --> (3,8)\n",
      "(3,9) --> 48 --> (3,9)\n",
      "(4,0) --> 4 --> (4,0)\n",
      "(4,1) --> 9 --> (4,1)\n",
      "(4,2) --> 14 --> (4,2)\n",
      "(4,3) --> 19 --> (4,3)\n",
      "(4,4) --> 24 --> (4,4)\n",
      "(4,5) --> 29 --> (4,5)\n",
      "(4,6) --> 34 --> (4,6)\n",
      "(4,7) --> 39 --> (4,7)\n",
      "(4,8) --> 44 --> (4,8)\n",
      "(4,9) --> 49 --> (4,9)\n"
     ]
    }
   ],
   "source": [
    "def k(i,j,m,base0=True):\n",
    "    '''Convert (i,j) indexes in a two-dimensional array\n",
    "    with m rows into a single index computed column-wise\n",
    "    '''\n",
    "    if base0:\n",
    "        return j*m + i\n",
    "    else:\n",
    "        return (j-1)*m + i\n",
    "\n",
    "def ik(k,m,base0=True):\n",
    "    '''Convert k index in a two-dimensional array\n",
    "    with m rows into a pair of (i,j) indexes\n",
    "    '''\n",
    "    if base0:\n",
    "        j = k//m\n",
    "        i = k%m\n",
    "    else:\n",
    "        j = k//m + 1\n",
    "        i = k%m\n",
    "    return i,j\n",
    "\n",
    "m=5\n",
    "for i in range(5):\n",
    "    for j in range(10):\n",
    "        k0 = k(i,j,m)\n",
    "        i1,j1 = ik(k0,m)\n",
    "        print('(%d,%d) --> %d --> (%d,%d)'%(i,j,k0,i1,j1))"
   ]
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     "text": [
      "(1,1) --> 1 --> (1,1)\n",
      "(1,2) --> 6 --> (1,2)\n",
      "(1,3) --> 11 --> (1,3)\n",
      "(1,4) --> 16 --> (1,4)\n",
      "(1,5) --> 21 --> (1,5)\n",
      "(1,6) --> 26 --> (1,6)\n",
      "(1,7) --> 31 --> (1,7)\n",
      "(1,8) --> 36 --> (1,8)\n",
      "(1,9) --> 41 --> (1,9)\n",
      "(1,10) --> 46 --> (1,10)\n",
      "(2,1) --> 2 --> (2,1)\n",
      "(2,2) --> 7 --> (2,2)\n",
      "(2,3) --> 12 --> (2,3)\n",
      "(2,4) --> 17 --> (2,4)\n",
      "(2,5) --> 22 --> (2,5)\n",
      "(2,6) --> 27 --> (2,6)\n",
      "(2,7) --> 32 --> (2,7)\n",
      "(2,8) --> 37 --> (2,8)\n",
      "(2,9) --> 42 --> (2,9)\n",
      "(2,10) --> 47 --> (2,10)\n",
      "(3,1) --> 3 --> (3,1)\n",
      "(3,2) --> 8 --> (3,2)\n",
      "(3,3) --> 13 --> (3,3)\n",
      "(3,4) --> 18 --> (3,4)\n",
      "(3,5) --> 23 --> (3,5)\n",
      "(3,6) --> 28 --> (3,6)\n",
      "(3,7) --> 33 --> (3,7)\n",
      "(3,8) --> 38 --> (3,8)\n",
      "(3,9) --> 43 --> (3,9)\n",
      "(3,10) --> 48 --> (3,10)\n",
      "(4,1) --> 4 --> (4,1)\n",
      "(4,2) --> 9 --> (4,2)\n",
      "(4,3) --> 14 --> (4,3)\n",
      "(4,4) --> 19 --> (4,4)\n",
      "(4,5) --> 24 --> (4,5)\n",
      "(4,6) --> 29 --> (4,6)\n",
      "(4,7) --> 34 --> (4,7)\n",
      "(4,8) --> 39 --> (4,8)\n",
      "(4,9) --> 44 --> (4,9)\n",
      "(4,10) --> 49 --> (4,10)\n",
      "(5,1) --> 5 --> (0,2)\n",
      "(5,2) --> 10 --> (0,3)\n",
      "(5,3) --> 15 --> (0,4)\n",
      "(5,4) --> 20 --> (0,5)\n",
      "(5,5) --> 25 --> (0,6)\n",
      "(5,6) --> 30 --> (0,7)\n",
      "(5,7) --> 35 --> (0,8)\n",
      "(5,8) --> 40 --> (0,9)\n",
      "(5,9) --> 45 --> (0,10)\n",
      "(5,10) --> 50 --> (0,11)\n"
     ]
    }
   ],
   "source": [
    "# Running the check for base1 reveals the bug when i=5!\n",
    "\n",
    "m=5\n",
    "for i in range(1,m+1):\n",
    "    for j in range(1,11):\n",
    "        k0 = k(i,j,m,base0=False)\n",
    "        i1,j1 = ik(k0,m,base0=False)\n",
    "        print('(%d,%d) --> %d --> (%d,%d)'%(i,j,k0,i1,j1))\n",
    "\n",
    "# So, the correct inverse conversion in base1 should be:\n",
    "\n",
    "def ik(k,m,base0=True):\n",
    "    '''Convert k index in a two-dimensional array\n",
    "    with m rows into a pair of (i,j) indexes\n",
    "    '''\n",
    "    if base0:\n",
    "        j = k//m\n",
    "        i = k%m\n",
    "    else:\n",
    "        j = (k-1)//m + 1\n",
    "        i = (k-1)%m + 1\n",
    "    return i,j"
   ]
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   "execution_count": 29,
   "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1,1) --> 1 --> (1,1)\n",
      "(1,2) --> 6 --> (1,2)\n",
      "(1,3) --> 11 --> (1,3)\n",
      "(1,4) --> 16 --> (1,4)\n",
      "(2,1) --> 2 --> (2,1)\n",
      "(2,2) --> 7 --> (2,2)\n",
      "(2,3) --> 12 --> (2,3)\n",
      "(2,4) --> 17 --> (2,4)\n",
      "(3,1) --> 3 --> (3,1)\n",
      "(3,2) --> 8 --> (3,2)\n",
      "(3,3) --> 13 --> (3,3)\n",
      "(3,4) --> 18 --> (3,4)\n",
      "(4,1) --> 4 --> (4,1)\n",
      "(4,2) --> 9 --> (4,2)\n",
      "(4,3) --> 14 --> (4,3)\n",
      "(4,4) --> 19 --> (4,4)\n",
      "(5,1) --> 5 --> (5,1)\n",
      "(5,2) --> 10 --> (5,2)\n",
      "(5,3) --> 15 --> (5,3)\n",
      "(5,4) --> 20 --> (5,4)\n"
     ]
    }
   ],
   "source": [
    "m=5\n",
    "for i in range(1,m+1):\n",
    "    for j in range(1,5):\n",
    "        k0 = k(i,j,m,base0=False)\n",
    "        i1,j1 = ik(k0,m,base0=False)\n",
    "        print('(%d,%d) --> %d --> (%d,%d)'%(i,j,k0,i1,j1)) "
   ]
  },
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   "source": [
    "### Example 2\n",
    "\n",
    "Write a function to converter a decimal number into a given base. Return the result as string."
   ]
  },
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   "outputs": [],
   "source": [
    "# code here"
   ]
  },
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   "metadata": {
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   "source": [
    "def baseN(x,base=2):\n",
    "    '''Converts given number to given base'''\n",
    "    digits = [str(i) for i in range(10)] + [chr(i) for i in range(97,123)]\n",
    "    assert 2 <= base <= len(digits),'Number base must be between 2 and %d'%(len(digits))\n",
    "    if x == 0:\n",
    "        return '0'\n",
    "    out = []\n",
    "    while x>0:\n",
    "        i = x%base\n",
    "        out.append(digits[i])\n",
    "        x = x//base\n",
    "    return ''.join(out[::-1])\n",
    "\n",
    "for n in [3,8,35,574,1023523,9999]:\n",
    "    for b in range(36,1,-4):\n",
    "        print('%d in base %d is %s' % (n,b,baseN(n,b)))\n",
    "    print()"
   ]
  }
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