integer-square-root.ipynb

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    "# Efficient Computation of the Integer Square Root"
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    "## Assignment\n",
    "\n",
    "Given $n \\in \\mathbb{N}$, the **integer square root** of $n$ is the largest number $r \\in \\mathbb{N}$ such that $r^2$ is less or equal than $n$, i.e. we have $isqrt(n) := max({r \\in \\mathbb{N} | r^2 \\leq n})$.\n",
    "\n",
    "Develop a recursive algorithm that computes $isqrt(n)$ in terms of $isqrt(n // 4)$."
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    "def isqrt(n):\n",
    "    if n == 0:\n",
    "        return 0\n",
    "\n",
    "    r = isqrt(n // 4)\n",
    "\n",
    "    if (2 * r + 1) ** 2 <= n:\n",
    "        return 2 * r + 1\n",
    "\n",
    "    return 2 * r"
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     "text": [
      "1\n",
      "2\n"
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    "print(isqrt(3)) # 1\n",
    "print(isqrt(4)) # 2"
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