Chapter_17_Amortized_Analysis/exercises_17.1.ipynb

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   "source": [
    "## 17.1 Aggregate analysis"
   ]
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   "source": [
    "### 17.1-1\n",
    "\n",
    "> If the set of stack operations included a MULTIPUSH operation, which pushses $k$ items onto the stack, would the $O(1)$ bound on the amortized cost of stack operations continue to hold?"
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   "source": [
    "No."
   ]
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   "source": [
    "### 17.1-2\n",
    "\n",
    "> Show that if a DECREMENT operatoin were included in the $k$-bit counter example, $n$ operations could cost as much as $\\Theta(nk)$ time."
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   "source": [
    "Increment and decrement repeatly on $011\\cdots11$."
   ]
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   "source": [
    "### 17.1-3\n",
    "\n",
    "> Suppose we perform a sequence of $n$ operations on a data structure in which the $i$th operation costs $i$ if $i$ is an exact power of $2$, and $1$ otherwise. Use aggregate analysis to determine the amortized cost per operation."
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   "source": [
    "$1 + 2 + 2^2 + \\cdots + 2^{\\lfloor \\lg n \\rfloor} \\le 2n$"
   ]
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