Hot-keys on this page

r m x p   toggle line displays

j k   next/prev highlighted chunk

0   (zero) top of page

1   (one) first highlighted chunk

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

"""Bisection algorithms.""" 

 

def insort_right(a, x, lo=0, hi=None): 

    """Insert item x in list a, and keep it sorted assuming a is sorted. 

 

    If x is already in a, insert it to the right of the rightmost x. 

 

    Optional args lo (default 0) and hi (default len(a)) bound the 

    slice of a to be searched. 

    """ 

 

    if lo < 0: 

        raise ValueError('lo must be non-negative') 

    if hi is None: 

        hi = len(a) 

    while lo < hi: 

        mid = (lo+hi)//2 

        if x < a[mid]: hi = mid 

        else: lo = mid+1 

    a.insert(lo, x) 

 

insort = insort_right   # backward compatibility 

 

def bisect_right(a, x, lo=0, hi=None): 

    """Return the index where to insert item x in list a, assuming a is sorted. 

 

    The return value i is such that all e in a[:i] have e <= x, and all e in 

    a[i:] have e > x.  So if x already appears in the list, a.insert(x) will 

    insert just after the rightmost x already there. 

 

    Optional args lo (default 0) and hi (default len(a)) bound the 

    slice of a to be searched. 

    """ 

 

    if lo < 0: 

        raise ValueError('lo must be non-negative') 

    if hi is None: 

        hi = len(a) 

    while lo < hi: 

        mid = (lo+hi)//2 

        if x < a[mid]: hi = mid 

        else: lo = mid+1 

    return lo 

 

bisect = bisect_right   # backward compatibility 

 

def insort_left(a, x, lo=0, hi=None): 

    """Insert item x in list a, and keep it sorted assuming a is sorted. 

 

    If x is already in a, insert it to the left of the leftmost x. 

 

    Optional args lo (default 0) and hi (default len(a)) bound the 

    slice of a to be searched. 

    """ 

 

    if lo < 0: 

        raise ValueError('lo must be non-negative') 

    if hi is None: 

        hi = len(a) 

    while lo < hi: 

        mid = (lo+hi)//2 

        if a[mid] < x: lo = mid+1 

        else: hi = mid 

    a.insert(lo, x) 

 

 

def bisect_left(a, x, lo=0, hi=None): 

    """Return the index where to insert item x in list a, assuming a is sorted. 

 

    The return value i is such that all e in a[:i] have e < x, and all e in 

    a[i:] have e >= x.  So if x already appears in the list, a.insert(x) will 

    insert just before the leftmost x already there. 

 

    Optional args lo (default 0) and hi (default len(a)) bound the 

    slice of a to be searched. 

    """ 

 

    if lo < 0: 

        raise ValueError('lo must be non-negative') 

    if hi is None: 

        hi = len(a) 

    while lo < hi: 

        mid = (lo+hi)//2 

        if a[mid] < x: lo = mid+1 

        else: hi = mid 

    return lo 

 

# Overwrite above definitions with a fast C implementation 

try: 

    from _bisect import * 

except ImportError: 

    pass