Project Euler Q31 - LO Man Hei

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   "source": [
    "### Q31\n",
    "How many different ways can £2 be made using any number of coins?"
   ]
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    "def vector_add(x_vector,i,v):\n",
    "    x_vector[i] = v\n",
    "    return x_vector\n",
    "\n",
    "def count_coin_comb(need,coin_i=0,coin_counts=[0,0,0,0,0,0,0,0],coin_faces=[1,2,5,10,20,50,100,200]):\n",
    "    return ( sum( 1 for p in range(0,need//coin_faces[coin_i]+1) \n",
    "                 if need-coin_faces[coin_i]*p==0\n",
    "                )  if coin_i >= len(coin_faces)-1 else \n",
    "             sum( count_coin_comb(need-coin_faces[coin_i]*p,\n",
    "                           coin_i+1,\n",
    "                           vector_add(coin_counts,coin_i,p))  \n",
    "                for p in range(0,need//coin_faces[coin_i]+1)\n",
    "                )\n",
    "            ) "
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      "CPU times: user 4.4 s, sys: 0 ns, total: 4.4 s\n",
      "Wall time: 4.4 s\n"
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   "source": [
    "%%time\n",
    "count_coin_comb(200)"
   ]
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    "def count_coin_comb_1(need,coin_faces=[0,1,2,5,10,20,50,100,200]):\n",
    "    num_coin_type = len(coin_faces)\n",
    "    result_matrix = [[0 for j in range(need+1)] for i in range(num_coin_type)]\n",
    "    for i in range(1,need+1):\n",
    "        result_matrix[1][i] = 1\n",
    "    for i in range(1,num_coin_type):\n",
    "        result_matrix[i][0] = 1\n",
    "    for i in range(1,num_coin_type):\n",
    "        for j in range(1,need+1):\n",
    "            for k in range(j//coin_faces[i]+1):\n",
    "                result_matrix[i][j]+=result_matrix[i-1][j-k*coin_faces[i]];\n",
    "    return result_matrix[-1][-1]\n",
    "            "
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     "text": [
      "CPU times: user 4.93 ms, sys: 0 ns, total: 4.93 ms\n",
      "Wall time: 4.72 ms\n"
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       "73682"
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     "execution_count": 4,
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   "source": [
    "%%time\n",
    "count_coin_comb_1(200)"
   ]
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