Explanation of https://arxiv.org/abs/2110.01111

explanation-of-https-arxiv-org-abs-2110-01111.ipynb

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        "<a href=\"https://colab.research.google.com/gist/enakai00/e1c4d02c18be4ed2c82a1a2a3490aa81/explanation-of-https-arxiv-org-abs-2110-01111.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "import random\n",
        "\n",
        "a = [random.randint(0, 10) for _ in range(10)]\n",
        "n = len(a)\n",
        "\n",
        "for i in range(0, n):\n",
        "\n",
        "  # Loop invariant: a[:i] is sorted.\n",
        "  assert a[:i] == sorted(a[:i])\n",
        "\n",
        "  # The following loop inserts a[i] into a[:i] so that a[:i+1] is sorted.\n",
        "  for j in range(0, i):\n",
        "    if a[i] < a[j]:\n",
        "      a[i], a[j] = a[j], a[i]\n",
        "\n",
        "  # Loop invariant: a[:i+1] is sorted.\n",
        "  assert a[:i+1] == sorted(a[:i+1])\n",
        "\n",
        "  # The following loop swaps a[i] and the max element of a[i+1:]\n",
        "  # This is unnecessary, but no harm as it doesn't break the condition that a[:i+1] is sorted.\n",
        "  for j in range(i, n):\n",
        "    if a[i] < a[j]:\n",
        "      a[i], a[j] = a[j], a[i]\n",
        "\n",
        "  # Loop invariant: a[:i+1] is sorted.\n",
        "  assert a[:i+1] == sorted(a[:i+1])\n",
        "\n",
        "  print(i, a)"
      ],
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          "text": [
            "0 [10, 2, 5, 4, 6, 6, 6, 8, 3, 7]\n",
            "1 [2, 10, 5, 4, 6, 6, 6, 8, 3, 7]\n",
            "2 [2, 5, 10, 4, 6, 6, 6, 8, 3, 7]\n",
            "3 [2, 4, 5, 10, 6, 6, 6, 8, 3, 7]\n",
            "4 [2, 4, 5, 6, 10, 6, 6, 8, 3, 7]\n",
            "5 [2, 4, 5, 6, 6, 10, 6, 8, 3, 7]\n",
            "6 [2, 4, 5, 6, 6, 6, 10, 8, 3, 7]\n",
            "7 [2, 4, 5, 6, 6, 6, 8, 10, 3, 7]\n",
            "8 [2, 3, 4, 5, 6, 6, 6, 8, 10, 7]\n",
            "9 [2, 3, 4, 5, 6, 6, 6, 7, 8, 10]\n"
          ]
        }
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