banyan supports deleting intervals from the tree. For example, to remove a minimal number of intervals from a list of intervals such that the intervals that are left do not overlap in O(n log n), banyan.SortedSet (augmented red-black tree) could be used:
from banyan import SortedSet, OverlappingIntervalsUpdator # pip install banyan
def maximize_nonoverlapping_count(intervals):
# build "interval" tree sorted by the end-point O(n log n)
tree = SortedSet(intervals, key=lambda (start, end): (end, (end - start)),
updator=OverlappingIntervalsUpdator)
result = []
while tree: # until there are intervals left to consider
# pop the interval with the smallest end-point, keep it in the result
result.append(tree.pop()) # O(log n)
# remove intervals that overlap with the popped interval
overlapping_intervals = tree.overlap(result[-1]) # O(m log n)
tree -= overlapping_intervals # O(m log n)
return result
Example:
print maximize_nonoverlapping_count([[3, 4], [5, 8], [0, 6], [1, 2]])
# -> [[1, 2], [3, 4], [5, 8]]
See Python - Removing overlapping lists.
