--- /dev/null
+"""Bisection algorithms."""\r
+\r
+def insort_right(a, x, lo=0, hi=None):\r
+ """Insert item x in list a, and keep it sorted assuming a is sorted.\r
+\r
+ If x is already in a, insert it to the right of the rightmost x.\r
+\r
+ Optional args lo (default 0) and hi (default len(a)) bound the\r
+ slice of a to be searched.\r
+ """\r
+\r
+ if lo < 0:\r
+ raise ValueError('lo must be non-negative')\r
+ if hi is None:\r
+ hi = len(a)\r
+ while lo < hi:\r
+ mid = (lo+hi)//2\r
+ if x < a[mid]: hi = mid\r
+ else: lo = mid+1\r
+ a.insert(lo, x)\r
+\r
+insort = insort_right # backward compatibility\r
+\r
+def bisect_right(a, x, lo=0, hi=None):\r
+ """Return the index where to insert item x in list a, assuming a is sorted.\r
+\r
+ The return value i is such that all e in a[:i] have e <= x, and all e in\r
+ a[i:] have e > x. So if x already appears in the list, a.insert(x) will\r
+ insert just after the rightmost x already there.\r
+\r
+ Optional args lo (default 0) and hi (default len(a)) bound the\r
+ slice of a to be searched.\r
+ """\r
+\r
+ if lo < 0:\r
+ raise ValueError('lo must be non-negative')\r
+ if hi is None:\r
+ hi = len(a)\r
+ while lo < hi:\r
+ mid = (lo+hi)//2\r
+ if x < a[mid]: hi = mid\r
+ else: lo = mid+1\r
+ return lo\r
+\r
+bisect = bisect_right # backward compatibility\r
+\r
+def insort_left(a, x, lo=0, hi=None):\r
+ """Insert item x in list a, and keep it sorted assuming a is sorted.\r
+\r
+ If x is already in a, insert it to the left of the leftmost x.\r
+\r
+ Optional args lo (default 0) and hi (default len(a)) bound the\r
+ slice of a to be searched.\r
+ """\r
+\r
+ if lo < 0:\r
+ raise ValueError('lo must be non-negative')\r
+ if hi is None:\r
+ hi = len(a)\r
+ while lo < hi:\r
+ mid = (lo+hi)//2\r
+ if a[mid] < x: lo = mid+1\r
+ else: hi = mid\r
+ a.insert(lo, x)\r
+\r
+\r
+def bisect_left(a, x, lo=0, hi=None):\r
+ """Return the index where to insert item x in list a, assuming a is sorted.\r
+\r
+ The return value i is such that all e in a[:i] have e < x, and all e in\r
+ a[i:] have e >= x. So if x already appears in the list, a.insert(x) will\r
+ insert just before the leftmost x already there.\r
+\r
+ Optional args lo (default 0) and hi (default len(a)) bound the\r
+ slice of a to be searched.\r
+ """\r
+\r
+ if lo < 0:\r
+ raise ValueError('lo must be non-negative')\r
+ if hi is None:\r
+ hi = len(a)\r
+ while lo < hi:\r
+ mid = (lo+hi)//2\r
+ if a[mid] < x: lo = mid+1\r
+ else: hi = mid\r
+ return lo\r
+\r
+# Overwrite above definitions with a fast C implementation\r
+try:\r
+ from _bisect import *\r
+except ImportError:\r
+ pass\r