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"""Bisection algorithms."""
def insort(a, x, lo=0, hi=None):
"""Insert item x in list a, and keep it sorted assuming a is sorted."""
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)
def bisect(a, x, lo=0, hi=None):
"""Find the index where to insert item x in list a, assuming a is sorted."""
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
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