Euler.31.ipynb

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    "#Project Euler\n",
    "###Problem 31: Coin sums\n",
    "In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:\n",
    "\n",
    "1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).\n",
    "It is possible to make £2 in the following way:\n",
    "\n",
    "1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p\n",
    "How many different ways can £2 be made using any number of coins?\n",
    "___"
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    "To make it easier we will consider cents, not pounds."
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       "<pre class='cython line score-0' onclick='toggleDiv(this)'>+09: <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">nr_coins</span> <span class=\"o\">=</span> <span class=\"mf\">8</span></pre>\n",
       "<pre class='cython code score-0'>  __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_nr_coins = 8;\n",
       "</pre><pre class='cython line score-0'>&#xA0;10: </pre>\n",
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       "<pre class='cython line score-2' onclick='toggleDiv(this)'>+12: <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">cdivide</span><span class=\"p\">(</span><span class=\"nb\">int</span> <span class=\"n\">n</span><span class=\"p\">,</span><span class=\"nb\">int</span> <span class=\"n\">m</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-2'>static int __pyx_f_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_cdivide(int __pyx_v_n, int __pyx_v_m) {\n",
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       "<pre class='cython line score-0' onclick='toggleDiv(this)'>+14:         <span class=\"nb\">int</span> <span class=\"n\">count</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0'>  __pyx_v_count = 0;\n",
       "</pre><pre class='cython line score-0' onclick='toggleDiv(this)'>+15:         <span class=\"nb\">int</span> <span class=\"n\">i</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0'>  __pyx_v_i = 0;\n",
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       "<pre class='cython line score-4' onclick='toggleDiv(this)'>+17:     <span class=\"k\">while</span> <span class=\"n\">i</span> <span class=\"o\">&lt;</span> <span class=\"n\">nr_coins</span> <span class=\"ow\">and</span> <span class=\"n\">divisors</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">&lt;</span> <span class=\"n\">n</span> <span class=\"ow\">and</span> <span class=\"n\">divisors</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">&lt;=</span> <span class=\"n\">m</span><span class=\"p\">:</span></pre>\n",
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       "    __pyx_t_3 = __pyx_v_i;\n",
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       "    __pyx_t_2 = (((*((int *) ( /* dim=0 */ (__pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.data + __pyx_t_3 * __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.strides[0]) ))) &lt; __pyx_v_n) != 0);\n",
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       "    if (__pyx_t_4 &lt; 0) __pyx_t_4 += __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.shape[0];\n",
       "    __pyx_t_2 = (((*((int *) ( /* dim=0 */ (__pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.data + __pyx_t_4 * __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.strides[0]) ))) &lt;= __pyx_v_m) != 0);\n",
       "    __pyx_t_1 = __pyx_t_2;\n",
       "    __pyx_L5_bool_binop_done:;\n",
       "    if (!__pyx_t_1) break;\n",
       "</pre><pre class='cython line score-4' onclick='toggleDiv(this)'>+18:         <span class=\"n\">count</span> <span class=\"o\">+=</span> <span class=\"n\">cdivide</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"o\">-</span><span class=\"n\">divisors</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">],</span><span class=\"n\">divisors</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">])</span></pre>\n",
       "<pre class='cython code score-4'>    if (unlikely(!__pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.memview)) { <span class='pyx_c_api'>__Pyx_RaiseUnboundLocalError</span>(\"divisors\"); <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 18; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span> }\n",
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       "    if (unlikely(!__pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.memview)) { <span class='pyx_c_api'>__Pyx_RaiseUnboundLocalError</span>(\"divisors\"); <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 18; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span> }\n",
       "    __pyx_t_6 = __pyx_v_i;\n",
       "    if (__pyx_t_6 &lt; 0) __pyx_t_6 += __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.shape[0];\n",
       "    __pyx_v_count = (__pyx_v_count + __pyx_f_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_cdivide((__pyx_v_n - (*((int *) ( /* dim=0 */ (__pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.data + __pyx_t_5 * __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.strides[0]) )))), (*((int *) ( /* dim=0 */ (__pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.data + __pyx_t_6 * __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.strides[0]) )))));\n",
       "</pre><pre class='cython line score-0' onclick='toggleDiv(this)'>+19:         <span class=\"n\">i</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0'>    __pyx_v_i = (__pyx_v_i + 1);\n",
       "  }\n",
       "</pre><pre class='cython line score-0'>&#xA0;20: </pre>\n",
       "<pre class='cython line score-2' onclick='toggleDiv(this)'>+21:     <span class=\"k\">if</span> <span class=\"n\">i</span> <span class=\"o\">&lt;</span> <span class=\"n\">nr_coins</span> <span class=\"ow\">and</span> <span class=\"n\">divisors</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">==</span> <span class=\"n\">n</span> <span class=\"ow\">and</span> <span class=\"n\">n</span> <span class=\"o\">&lt;=</span> <span class=\"n\">m</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-2'>  __pyx_t_2 = ((__pyx_v_i &lt; __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_nr_coins) != 0);\n",
       "  if (__pyx_t_2) {\n",
       "  } else {\n",
       "    __pyx_t_1 = __pyx_t_2;\n",
       "    goto __pyx_L9_bool_binop_done;\n",
       "  }\n",
       "  if (unlikely(!__pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.memview)) { <span class='pyx_c_api'>__Pyx_RaiseUnboundLocalError</span>(\"divisors\"); <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 21; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span> }\n",
       "  __pyx_t_7 = __pyx_v_i;\n",
       "  if (__pyx_t_7 &lt; 0) __pyx_t_7 += __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.shape[0];\n",
       "  __pyx_t_2 = (((*((int *) ( /* dim=0 */ (__pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.data + __pyx_t_7 * __pyx_v_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divisors.strides[0]) ))) == __pyx_v_n) != 0);\n",
       "  if (__pyx_t_2) {\n",
       "  } else {\n",
       "    __pyx_t_1 = __pyx_t_2;\n",
       "    goto __pyx_L9_bool_binop_done;\n",
       "  }\n",
       "  __pyx_t_2 = ((__pyx_v_n &lt;= __pyx_v_m) != 0);\n",
       "  __pyx_t_1 = __pyx_t_2;\n",
       "  __pyx_L9_bool_binop_done:;\n",
       "  if (__pyx_t_1) {\n",
       "</pre><pre class='cython line score-0' onclick='toggleDiv(this)'>+22:         <span class=\"n\">count</span> <span class=\"o\">+=</span> <span class=\"mf\">1</span></pre>\n",
       "<pre class='cython code score-0'>    __pyx_v_count = (__pyx_v_count + 1);\n",
       "    goto __pyx_L8;\n",
       "  }\n",
       "  __pyx_L8:;\n",
       "</pre><pre class='cython line score-0'>&#xA0;23: </pre>\n",
       "<pre class='cython line score-0' onclick='toggleDiv(this)'>+24:     <span class=\"k\">return</span> <span class=\"n\">count</span></pre>\n",
       "<pre class='cython code score-0'>  __pyx_r = __pyx_v_count;\n",
       "  goto __pyx_L0;\n",
       "</pre><pre class='cython line score-0'>&#xA0;25: </pre>\n",
       "<pre class='cython line score-16' onclick='toggleDiv(this)'>+26: <span class=\"k\">def</span> <span class=\"nf\">divide</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-16'>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_1divide(PyObject *__pyx_self, PyObject *__pyx_v_n); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_1divide = {\"divide\", (PyCFunction)__pyx_pw_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_1divide, METH_O, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_1divide(PyObject *__pyx_self, PyObject *__pyx_v_n) {\n",
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       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"divide (wrapper)\", 0);\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divide(__pyx_self, ((PyObject *)__pyx_v_n));\n",
       "\n",
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       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
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       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_divide(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_n) {\n",
       "  PyObject *__pyx_r = NULL;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"divide\", 0);\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_t_3);\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_ed33d82b4d6559c962da9aa6a2db453e.divide\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple__19 = <span class='py_c_api'>PyTuple_Pack</span>(1, __pyx_n_s_n);<span class='error_goto'> if (unlikely(!__pyx_tuple__19)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 26; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple__19);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple__19);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_1divide, NULL, __pyx_n_s_cython_magic_ed33d82b4d6559c962);<span class='error_goto'> if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 26; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_divide, __pyx_t_1) &lt; 0) <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 26; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "  __pyx_codeobj__20 = (PyObject*)<span class='pyx_c_api'>__Pyx_PyCode_New</span>(1, 0, 1, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__19, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_C_Users_Laurens_ipython_cython, __pyx_n_s_divide, 26, __pyx_empty_bytes);<span class='error_goto'> if (unlikely(!__pyx_codeobj__20)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 26; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "</pre><pre class='cython line score-7' onclick='toggleDiv(this)'>+27:     <span class=\"k\">return</span> <span class=\"n\">cdivide</span><span class=\"p\">(</span><span class=\"n\">n</span><span class=\"p\">,</span><span class=\"n\">n</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-7'>  <span class='pyx_macro_api'>__Pyx_XDECREF</span>(__pyx_r);\n",
       "  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_PyInt_As_int</span>(__pyx_v_n);<span class='error_goto'> if (unlikely((__pyx_t_1 == (int)-1) &amp;&amp; PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 27; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  __pyx_t_2 = <span class='pyx_c_api'>__Pyx_PyInt_As_int</span>(__pyx_v_n);<span class='error_goto'> if (unlikely((__pyx_t_2 == (int)-1) &amp;&amp; PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 27; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  __pyx_t_3 = <span class='pyx_c_api'>__Pyx_PyInt_From_int</span>(__pyx_f_46_cython_magic_ed33d82b4d6559c962da9aa6a2db453e_cdivide(__pyx_t_1, __pyx_t_2));<span class='error_goto'> if (unlikely(!__pyx_t_3)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 27; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_3);\n",
       "  __pyx_r = __pyx_t_3;\n",
       "  __pyx_t_3 = 0;\n",
       "  goto __pyx_L0;\n",
       "</pre></div></body></html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%cython -a\n",
    "\n",
    "import numpy as np\n",
    "cimport numpy as np\n",
    "import sys\n",
    "cimport cython\n",
    "\n",
    "cdef int[:] divisors = np.int_([1,2,5,10,20,50,100,200])\n",
    "\n",
    "cdef int nr_coins = 8\n",
    "\n",
    "@cython.boundscheck(False)\n",
    "cdef int cdivide(int n,int m):\n",
    "    cdef:\n",
    "        int count = 0\n",
    "        int i = 0\n",
    "    \n",
    "    while i < nr_coins and divisors[i] < n and divisors[i] <= m:\n",
    "        count += cdivide(n-divisors[i],divisors[i])\n",
    "        i += 1\n",
    "            \n",
    "    if i < nr_coins and divisors[i] == n and n <= m:\n",
    "        count += 1\n",
    "    \n",
    "    return count\n",
    "\n",
    "def divide(n):\n",
    "    return cdivide(n,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 1.63 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1960497"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time divide(400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "divisors = np.int_([1,2,5,10,20,50,100,200])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(divisors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(divisors[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "import array\n",
    "divisors = array.array('i',[1,2,3,4])\n",
    "cdef int[:] mv = divisors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'array.array' object has no attribute 'data'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-28-689ae2d16390>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0marray\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mdivisors\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0marray\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'i'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mdivisors\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdata\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m: 'array.array' object has no attribute 'data'"
     ]
    }
   ],
   "source": [
    "import array\n",
    "divisors = array.array('i',[1,2,3,4])\n",
    "divisors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "bytes can only contain ASCII literal characters. (<ipython-input-33-585228ebd186>, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-33-585228ebd186>\"\u001b[1;36m, line \u001b[1;32m1\u001b[0m\n\u001b[1;33m    type(b'피읖')\u001b[0m\n\u001b[1;37m        ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m bytes can only contain ASCII literal characters.\n"
     ]
    }
   ],
   "source": [
    "type(b'피읖')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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