day 74 - google interview question.ipynb

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    "import numpy as np"
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    "## algorithm"
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    "def solve_question(trials):\n",
    "    # range to search in\n",
    "    probability_range = np.array([0., 1.])\n",
    "\n",
    "    while True:\n",
    "        # prob. to see car in 10 minutes\n",
    "        probability_10min = probability_range.mean()\n",
    "        \n",
    "        # simulate three 10-minute intervals\n",
    "        events = np.random.rand(trials, 3) < probability_10min\n",
    "        events = np.sum(events, axis=1) > 0\n",
    "\n",
    "        # prob. to see car in 30 minutes\n",
    "        probability_30min = np.mean(events)\n",
    "        if abs(probability_30min - .95) < 1e-4:\n",
    "            return probability_10min\n",
    "\n",
    "        # bisection\n",
    "        i = 0 if probability_30min < .95 else 1\n",
    "        probability_range[i] = probability_10min"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## run"
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    "solve_question(10**6)"
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       "0.6328125"
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    "solve_question(10**6)"
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    "solve_question(10**6)"
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   "source": [
    "expected result"
   ]
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    {
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       "0.6315968501359612"
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     "execution_count": 6,
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   "source": [
    "1 - pow(0.05, 1/3)"
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