Project Euler Q48 - LO Man Hei

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   "source": [
    "### Q48\n",
    "Find the last ten digits of the series, \\(1^1 + 2^2 + 3^3 + ... + 1000^{1000}\\)."
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    "def dec_to_bin(dec):\n",
    "    return bin(dec).replace(\"0b\", \"\")\n",
    "\n",
    "def tranc_num_multiply(num_a,num_b,tranc):\n",
    "    return (num_a * num_b) % (10 ** tranc)\n",
    "\n",
    "def tranc_num_pow2n(num,n,tranc):\n",
    "    return tranc_num_pow2n(tranc_num_multiply(num,num,tranc),n-1,tranc) if n>=1 else num\n",
    "\n",
    "def tranc_num_pow(num,p,tranc):\n",
    "    exponent = dec_to_bin(p)[::-1]\n",
    "    result = 1\n",
    "    for num in [tranc_num_pow2n(num,i,tranc) for i in range(len(exponent)) if exponent[i]==\"1\"]:\n",
    "        result = tranc_num_multiply(result,num,tranc)\n",
    "    return result\n",
    "\n",
    "def tranc_sum(x_vector,tranc):\n",
    "    result = 0\n",
    "    for i in x_vector:\n",
    "        result = (result + i) % (10 ** tranc)\n",
    "    return result\n",
    "\n",
    "def last_n_digit_of_self_powers_m(m,n):\n",
    "    return tranc_sum((tranc_num_pow(i,i,n) for i in range(1,m+1)),n)"
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      "CPU times: user 8.22 ms, sys: 1.33 ms, total: 9.55 ms\n",
      "Wall time: 9.34 ms\n"
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     "execution_count": 2,
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   "source": [
    "%%time\n",
    "last_n_digit_of_self_powers_m(1000,10)"
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   "id": "66144a20-fad4-4ed4-aa76-4ce0dfc7e84a",
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   "source": [
    "def last_n_digit_of_self_powers_m_2(m,n):\n",
    "    return sum(i**i for i in range(1,m+1))%(10**n)"
   ]
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     "text": [
      "CPU times: user 2.87 ms, sys: 713 µs, total: 3.58 ms\n",
      "Wall time: 3.58 ms\n"
     ]
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       "9110846700"
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     "execution_count": 4,
     "metadata": {},
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   ],
   "source": [
    "%%time\n",
    "last_n_digit_of_self_powers_m_2(1000,10)"
   ]
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   "execution_count": null,
   "id": "86396837-af8c-4f05-9ccb-8ba7e0db24a2",
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