Project Euler Q1 - LO Man Hei

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   "source": [
    "### Q1\n",
    "Find the sum of all the multiples of 3 or 5 below 1000."
   ]
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    "# Loops, O(m*n), n is range, m in number of selected multipliers\n",
    "def sum_multiple_n_in_range_brutal(multipliers, start, end, exclude_end = True):\n",
    "    if exclude_end:\n",
    "        end -= 1\n",
    "    result = 0\n",
    "    for n in range(start,end+1):\n",
    "        if any([n%i==0 for i in multipliers]):\n",
    "            result += n\n",
    "    return result"
   ]
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     "text": [
      "CPU times: user 268 µs, sys: 65 µs, total: 333 µs\n",
      "Wall time: 337 µs\n"
     ]
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       "233168"
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   "source": [
    "%%time\n",
    "sum_multiple_n_in_range_brutal([3,5],1,1000)"
   ]
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   "source": [
    "# Semi-analytical, O(2^m)\n",
    "def sum_n_in_range(multiplier, start, end, exclude_end = True):\n",
    "    if exclude_end:\n",
    "        end -= 1\n",
    "    first_term = start + ((multiplier - start)%multiplier)\n",
    "    last_term = end - (end%multiplier)\n",
    "    n_terms = (last_term - first_term) // multiplier + 1\n",
    "    return (first_term + last_term) * n_terms // 2\n",
    "\n",
    "def gcd(x, y):\n",
    "    while(y):\n",
    "        x, y = y, x % y\n",
    "    return x\n",
    "\n",
    "def lcm(x, y):\n",
    "    return (x*y)//gcd(x,y)  \n",
    "\n",
    "def lcm_list(x_vector):\n",
    "    temp_vector = x_vector.copy()\n",
    "    temp_lcm = temp_vector.pop()\n",
    "    while temp_vector:\n",
    "        temp_lcm = lcm(temp_lcm,temp_vector.pop())\n",
    "    return temp_lcm\n",
    "\n",
    "def combinations(elements):\n",
    "    if len(elements) == 0: \n",
    "        return [[]]\n",
    "    comb = []\n",
    "    for i in combinations(elements[1:]):\n",
    "        comb += [i, i+[elements[0]]]\n",
    "    return comb\n",
    "\n",
    "def sum_multiple_n_in_range(multipliers, start, end, exclude_end = True):\n",
    "    result = 0\n",
    "    for comb in combinations(multipliers)[1:]:\n",
    "        result += sum_n_in_range(lcm_list(comb),start,end,exclude_end)*((-1)**(len(comb)-1))\n",
    "    return result\n"
   ]
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     "text": [
      "CPU times: user 13 µs, sys: 3 µs, total: 16 µs\n",
      "Wall time: 18.8 µs\n"
     ]
    },
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     "data": {
      "text/plain": [
       "233168"
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     },
     "execution_count": 4,
     "metadata": {},
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   ],
   "source": [
    "%%time\n",
    "sum_multiple_n_in_range([3,5],1,1000)"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "9445d691-6501-4d83-8e9f-e5b7d5b15431",
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