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Optimize find_intersections for closed intervals #203

Merged
merged 15 commits into from
Jun 14, 2023
52 changes: 52 additions & 0 deletions src/interval_sets.jl
Original file line number Diff line number Diff line change
Expand Up @@ -521,3 +521,55 @@ function find_intersections_helper!(result, x, y, lt)

return unique!.(result)
end

function find_intersections(
x::AbstractVector{<:AbstractInterval{T1,Closed,Closed}},
y::AbstractVector{<:AbstractInterval{T2,Closed,Closed}},
) where {T1,T2}
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# Strategy:
# two binary searches per interval `I` in `x`
# * identify the set of intervals in `y` that start during-or-after `I`
# * identify the set of intervals in `y` that stop before-or-during `I`
# * intersect them
starts = first.(y)
starts_perm = sortperm(starts)
starts_sorted = starts[starts_perm]

# Sneaky performance optimization (makes a huge difference!)
# Rather than sorting `stops` relative to `y`, we sort it relative to `starts`.
# This allows us to work in the "starts" frame of reference until the very end.
# In particular, when we intersect the sets of intervals obtained from starts and from stops,
# the "starts" set can be kept as a `UnitRange`, making the intersection *much* faster.
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stops = last.(y[starts_perm])
stops_perm = sortperm(stops)
stops_sorted = stops[stops_perm]

results = Vector{Vector{Int}}(undef, length(x))
for (i, I) in enumerate(x)
# find all the starts which occur before the end of `I`
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idx_first = searchsortedlast(starts_sorted, last(I))
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if idx_first < 1
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results[i] = Int[]
continue
end

# find all the stops which occur after the start of `I`
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idx_last = searchsortedfirst(stops_sorted, first(I))
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if idx_last > length(stops_sorted)
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results[i] = Int[]
continue
end

# Working in "starts" frame of reference
starts_before_or_during = 1:idx_first
stops_during_or_after = stops_perm[idx_last:end]

# Intersect them
r = intersect(starts_before_or_during, stops_during_or_after)

# *Now* go back to y's sorting order, post-intersection.
results[i] = starts_perm[r]
end
return results
end