estimate.ipynb

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   "source": [
    "from math import ceil\n",
    "\n",
    "\n",
    "def level(n, w, d):\n",
    "    '''\n",
    "    n: number of validators\n",
    "    w: number of workers\n",
    "    d: duration per task\n",
    "    '''\n",
    "    return ceil(n/w) * d\n",
    "\n",
    "\n",
    "def predict(n, w):\n",
    "    '''\n",
    "    n: number of validators\n",
    "    w: number of workers\n",
    "    '''\n",
    "    ans = level(n, w, 30)\n",
    "    for i in range(1, 31+1):\n",
    "        v = ceil(n / 2**i)\n",
    "        x = level(v, w, 1.5)\n",
    "        ans += x\n",
    "    return ans\n",
    "\n",
    "\n",
    "def estimate(n, t=3000):\n",
    "    '''\n",
    "    n: number of validators\n",
    "    t: time limit in seconds\n",
    "    '''\n",
    "    low = 1\n",
    "    high = 2**10\n",
    "    while low <= high:\n",
    "        w = (low + high) // 2\n",
    "        x = predict(n, w)\n",
    "        if x < t:\n",
    "            high = w-1\n",
    "        elif x > t:\n",
    "            low = w+1\n",
    "        else:\n",
    "            return w\n",
    "    return low"
   ]
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       "2"
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     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimate(100)"
   ]
  },
  {
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   "execution_count": 3,
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       "11"
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "estimate(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "13d492f7-69b7-49b9-8976-4d6bec292bf0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "107"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimate(10000)"
   ]
  }
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