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1 """Bisection algorithms."""
2
3 def insort_right(a, x, lo=0, hi=None):
4 """Insert item x in list a, and keep it sorted assuming a is sorted.
5
6 If x is already in a, insert it to the right of the rightmost x.
7
8 Optional args lo (default 0) and hi (default len(a)) bound the
9 slice of a to be searched.
10 """
11
12 if lo < 0:
13 raise ValueError('lo must be non-negative')
14 if hi is None:
15 hi = len(a)
16 while lo < hi:
17 mid = (lo+hi)//2
18 if x < a[mid]: hi = mid
19 else: lo = mid+1
20 a.insert(lo, x)
21
22 insort = insort_right # backward compatibility
23
24 def bisect_right(a, x, lo=0, hi=None):
25 """Return the index where to insert item x in list a, assuming a is sorted.
26
27 The return value i is such that all e in a[:i] have e <= x, and all e in
28 a[i:] have e > x. So if x already appears in the list, a.insert(x) will
29 insert just after the rightmost x already there.
30
31 Optional args lo (default 0) and hi (default len(a)) bound the
32 slice of a to be searched.
33 """
34
35 if lo < 0:
36 raise ValueError('lo must be non-negative')
37 if hi is None:
38 hi = len(a)
39 while lo < hi:
40 mid = (lo+hi)//2
41 if x < a[mid]: hi = mid
42 else: lo = mid+1
43 return lo
44
45 bisect = bisect_right # backward compatibility
46
47 def insort_left(a, x, lo=0, hi=None):
48 """Insert item x in list a, and keep it sorted assuming a is sorted.
49
50 If x is already in a, insert it to the left of the leftmost x.
51
52 Optional args lo (default 0) and hi (default len(a)) bound the
53 slice of a to be searched.
54 """
55
56 if lo < 0:
57 raise ValueError('lo must be non-negative')
58 if hi is None:
59 hi = len(a)
60 while lo < hi:
61 mid = (lo+hi)//2
62 if a[mid] < x: lo = mid+1
63 else: hi = mid
64 a.insert(lo, x)
65
66
67 def bisect_left(a, x, lo=0, hi=None):
68 """Return the index where to insert item x in list a, assuming a is sorted.
69
70 The return value i is such that all e in a[:i] have e < x, and all e in
71 a[i:] have e >= x. So if x already appears in the list, a.insert(x) will
72 insert just before the leftmost x already there.
73
74 Optional args lo (default 0) and hi (default len(a)) bound the
75 slice of a to be searched.
76 """
77
78 if lo < 0:
79 raise ValueError('lo must be non-negative')
80 if hi is None:
81 hi = len(a)
82 while lo < hi:
83 mid = (lo+hi)//2
84 if a[mid] < x: lo = mid+1
85 else: hi = mid
86 return lo
87
88 # Overwrite above definitions with a fast C implementation
89 try:
90 from _bisect import *
91 except ImportError:
92 pass