Python Bisect Usage.md

Tasks involving search in a sorted list are pretty common. Sometimes using list literal would be very convenient and fast enough for small list, e.g., [v for v >= x for v in a].

However, when the list is too large, this kind of linear search can cost much time than it is actually needed. Using binary search is preffered in this situation.

Python has a built in library bisect for this kind of job. Sometimes it could be quite confusing how to use, though.

Here I tried to summary the basic usage and some useful application of bisect.

python_bisect_usage.ipynb

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      "a=[1, 2, 3, 3, 4, 5]\n",
      "x=4\n",
      "lo=1\n",
      "hi=5\n",
      "\n",
      "###Basic Usage###\n",
      "\n",
      "Find right most insert index, use bisect_right\n",
      "all(v <= x for v in a[lo:i]) for the left side and all(v > x for v in a[i:hi])\n",
      "bisect.bisect_right(a, x)=5\n",
      "Find left most insert index, use bisect_left\n",
      "all(v < x for v in a[lo:i]) for the left side and all(v >= x for v in a[i:hi])\n",
      "bisect.bisect_left(a, x)=4\n",
      "\n",
      "###Application###\n",
      "\n",
      "[v for v < x for v in a]\n",
      "a[:bisect.bisect_left(a, x)]=[1, 2, 3, 3]\n",
      "[v for v <= x for v in a]\n",
      "a[:bisect.bisect_right(a, x)]=[1, 2, 3, 3, 4]\n",
      "[v for v > x for v in a]\n",
      "a[bisect.bisect_right(a, x):]=[5]\n",
      "[v for v >= x for v in a]\n",
      "a[bisect.bisect_left(a, x):]=[4, 5]\n",
      "\n",
      "[v for v < x for v in a[lo:hi]]\n",
      "a[lo:bisect.bisect_left(a, x, lo, hi)]=[2, 3, 3]\n",
      "[v for v <= x for v in a[lo:hi]]\n",
      "a[lo:bisect.bisect_right(a, x, lo, hi)]=[2, 3, 3, 4]\n",
      "[v for v > x for v in a[lo:hi]]\n",
      "a[bisect.bisect_right(a, x, lo, hi):hi]=[]\n",
      "[v for v >= x for v in a[lo:hi]]\n",
      "a[bisect.bisect_left(a, x, lo, hi):hi]=[4]\n"
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    "import bisect\n",
    "a = [1,2,3,3,4,5]\n",
    "x = 4\n",
    "lo=1\n",
    "hi=5\n",
    "print(f'a={a}')\n",
    "print(f'x={x}')\n",
    "print(f'lo={lo}')\n",
    "print(f'hi={hi}')\n",
    "print()\n",
    "print('###Basic Usage###')\n",
    "print()\n",
    "print('Find right most insert index, use bisect_right')\n",
    "print('all(v <= x for v in a[lo:i]) for the left side and all(v > x for v in a[i:hi])')\n",
    "print(f'bisect.bisect_right(a, x)={bisect.bisect_right(a, x)}')\n",
    "print('Find left most insert index, use bisect_left')\n",
    "print('all(v < x for v in a[lo:i]) for the left side and all(v >= x for v in a[i:hi])')\n",
    "print(f'bisect.bisect_left(a, x)={bisect.bisect_left(a, x)}')\n",
    "print()\n",
    "print(f'###Application###')\n",
    "print()\n",
    "print('[v for v < x for v in a]')\n",
    "print(f'a[:bisect.bisect_left(a, x)]={a[:bisect.bisect_left(a, x)]}')\n",
    "print('[v for v <= x for v in a]')\n",
    "print(f'a[:bisect.bisect_right(a, x)]={a[:bisect.bisect_right(a, x)]}')\n",
    "print('[v for v > x for v in a]')\n",
    "print(f'a[bisect.bisect_right(a, x):]={a[bisect.bisect_right(a, x):]}')\n",
    "print('[v for v >= x for v in a]')\n",
    "print(f'a[bisect.bisect_left(a, x):]={a[bisect.bisect_left(a, x):]}')\n",
    "print()\n",
    "print('[v for v < x for v in a[lo:hi]]')\n",
    "print(f'a[lo:bisect.bisect_left(a, x, lo, hi)]={a[lo:bisect.bisect_left(a, x, lo, hi)]}')\n",
    "print('[v for v <= x for v in a[lo:hi]]')\n",
    "print(f'a[lo:bisect.bisect_right(a, x, lo, hi)]={a[lo:bisect.bisect_right(a, x, lo, hi)]}')\n",
    "print('[v for v > x for v in a[lo:hi]]')\n",
    "print(f'a[bisect.bisect_right(a, x, lo, hi):hi]={a[bisect.bisect_right(a, x, lo, hi):hi]}')\n",
    "print('[v for v >= x for v in a[lo:hi]]')\n",
    "print(f'a[bisect.bisect_left(a, x, lo, hi):hi]={a[bisect.bisect_left(a, x, lo, hi):hi]}')\n"
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