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|
discard """
output: '''1 [2, 3, 4, 7]
[0, 0]'''
"""
# Nim RTree and R*Tree implementation
# S. Salewski, 06-JAN-2018
# http://www-db.deis.unibo.it/courses/SI-LS/papers/Gut84.pdf
# http://dbs.mathematik.uni-marburg.de/publications/myPapers/1990/BKSS90.pdf
# RT: range type like float, int
# D: Dimension
# M: Max entries in one node
# LT: leaf type
type
Dim* = static[int]
Ext[RT] = tuple[a, b: RT] # extend (range)
Box*[D: Dim; RT] = array[D, Ext[RT]] # Rectangle for 2D
BoxCenter*[D: Dim; RT] = array[D, RT]
L*[D: Dim; RT, LT] = tuple[b: Box[D, RT]; l: LT] # called Index Entry or index record in the Guttman paper
H[M, D: Dim; RT, LT] = ref object of RootRef
parent: H[M, D, RT, LT]
numEntries: int
level: int
N[M, D: Dim; RT, LT] = tuple[b: Box[D, RT]; n: H[M, D, RT, LT]]
LA[M, D: Dim; RT, LT] = array[M, L[D, RT, LT]]
NA[M, D: Dim; RT, LT] = array[M, N[M, D, RT, LT]]
Leaf[M, D: Dim; RT, LT] = ref object of H[M, D, RT, LT]
a: LA[M, D, RT, LT]
Node[M, D: Dim; RT, LT] = ref object of H[M, D, RT, LT]
a: NA[M, D, RT, LT]
RTree*[M, D: Dim; RT, LT] = ref object of RootRef
root: H[M, D, RT, LT]
bigM: int
m: int
RStarTree*[M, D: Dim; RT, LT] = ref object of RTree[M, D, RT, LT]
firstOverflow: array[32, bool]
p: int
proc newLeaf[M, D: Dim; RT, LT](): Leaf[M, D, RT, LT] =
new result
proc newNode[M, D: Dim; RT, LT](): Node[M, D, RT, LT] =
new result
proc newRTree*[M, D: Dim; RT, LT](minFill: range[30 .. 50] = 40): RTree[M, D, RT, LT] =
assert(M > 1 and M < 101)
new result
result.bigM = M
result.m = M * minFill div 100
result.root = newLeaf[M, D, RT, LT]()
proc newRStarTree*[M, D: Dim; RT, LT](minFill: range[30 .. 50] = 40): RStarTree[M, D, RT, LT] =
assert(M > 1 and M < 101)
new result
result.bigM = M
result.m = M * minFill div 100
result.p = M * 30 div 100
result.root = newLeaf[M, D, RT, LT]()
proc center(r: Box): auto =#BoxCenter[r.len, type(r[0].a)] =
var result: BoxCenter[r.len, type(r[0].a)]
for i in 0 .. r.high:
when r[0].a is SomeInteger:
result[i] = (r[i].a + r[i].b) div 2
elif r[0].a is SomeFloat:
result[i] = (r[i].a + r[i].b) / 2
else: assert false
return result
proc distance(c1, c2: BoxCenter): auto =
var result: type(c1[0])
for i in 0 .. c1.high:
result += (c1[i] - c2[i]) * (c1[i] - c2[i])
return result
proc overlap(r1, r2: Box): auto =
result = type(r1[0].a)(1)
for i in 0 .. r1.high:
result *= (min(r1[i]. b, r2[i]. b) - max(r1[i]. a, r2[i]. a))
if result <= 0: return 0
proc union(r1, r2: Box): Box =
for i in 0 .. r1.high:
result[i]. a = min(r1[i]. a, r2[i]. a)
result[i]. b = max(r1[i]. b, r2[i]. b)
proc intersect(r1, r2: Box): bool =
for i in 0 .. r1.high:
if r1[i].b < r2[i].a or r1[i].a > r2[i].b:
return false
return true
proc area(r: Box): auto = #type(r[0].a) =
result = type(r[0].a)(1)
for i in 0 .. r.high:
result *= r[i]. b - r[i]. a
proc margin(r: Box): auto = #type(r[0].a) =
result = type(r[0].a)(0)
for i in 0 .. r.high:
result += r[i]. b - r[i]. a
# how much enlargement does r1 need to include r2
proc enlargement(r1, r2: Box): auto =
area(union(r1, r2)) - area(r1)
proc search*[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; b: Box[D, RT]): seq[LT] =
proc s[M, D: Dim; RT, LT](n: H[M, D, RT, LT]; b: Box[D, RT]; res: var seq[LT]) =
if n of Node[M, D, RT, LT]:
let h = Node[M, D, RT, LT](n)
for i in 0 ..< n.numEntries:
if intersect(h.a[i].b, b):
s(h.a[i].n, b, res)
elif n of Leaf[M, D, RT, LT]:
let h = Leaf[M, D, RT, LT](n)
for i in 0 ..< n.numEntries:
if intersect(h.a[i].b, b):
res.add(h.a[i].l)
else: assert false
result = newSeq[LT]()
s(t.root, b, result)
# Insertion
# a R*TREE proc
proc chooseSubtree[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; b: Box[D, RT]; level: int): H[M, D, RT, LT] =
assert level >= 0
var n = t.root
while n.level > level:
let nn = Node[M, D, RT, LT](n)
var i0 = 0 # selected index
var minLoss = type(b[0].a).high
if n.level == 1: # childreen are leaves -- determine the minimum overlap costs
for i in 0 ..< n.numEntries:
let nx = union(nn.a[i].b, b)
var loss = 0
for j in 0 ..< n.numEntries:
if i == j: continue
loss += (overlap(nx, nn.a[j].b) - overlap(nn.a[i].b, nn.a[j].b)) # overlap (i, j) == (j, i), so maybe cache that?
var rep = loss < minLoss
if loss == minLoss:
let l2 = enlargement(nn.a[i].b, b) - enlargement(nn.a[i0].b, b)
rep = l2 < 0
if l2 == 0:
let l3 = area(nn.a[i].b) - area(nn.a[i0].b)
rep = l3 < 0
if l3 == 0:
rep = nn.a[i].n.numEntries < nn.a[i0].n.numEntries
if rep:
i0 = i
minLoss = loss
else:
for i in 0 ..< n.numEntries:
let loss = enlargement(nn.a[i].b, b)
var rep = loss < minLoss
if loss == minLoss:
let l3 = area(nn.a[i].b) - area(nn.a[i0].b)
rep = l3 < 0
if l3 == 0:
rep = nn.a[i].n.numEntries < nn.a[i0].n.numEntries
if rep:
i0 = i
minLoss = loss
n = nn.a[i0].n
return n
proc chooseLeaf[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; b: Box[D, RT]; level: int): H[M, D, RT, LT] =
assert level >= 0
var n = t.root
while n.level > level:
var j = -1 # selected index
var x: type(b[0].a)
let nn = Node[M, D, RT, LT](n)
for i in 0 ..< n.numEntries:
let h = enlargement(nn.a[i].b, b)
if j < 0 or h < x or (x == h and area(nn.a[i].b) < area(nn.a[j].b)):
x = h
j = i
n = nn.a[j].n
return n
proc pickSeeds[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; n: Node[M, D, RT, LT] | Leaf[M, D, RT, LT]; bx: Box[D, RT]): (int, int) =
var i0, j0: int
var bi, bj: type(bx)
var largestWaste = type(bx[0].a).low
for i in -1 .. n.a.high:
for j in 0 .. n.a.high:
if unlikely(i == j): continue
if unlikely(i < 0):
bi = bx
else:
bi = n.a[i].b
bj = n.a[j].b
let b = union(bi, bj)
let h = area(b) - area(bi) - area(bj)
if h > largestWaste:
largestWaste = h
i0 = i
j0 = j
return (i0, j0)
proc pickNext[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; n0, n1, n2: Node[M, D, RT, LT] | Leaf[M, D, RT, LT]; b1, b2: Box[D, RT]): int =
let a1 = area(b1)
let a2 = area(b2)
var d = type(a1).low
for i in 0 ..< n0.numEntries:
let d1 = area(union(b1, n0.a[i].b)) - a1
let d2 = area(union(b2, n0.a[i].b)) - a2
if (d1 - d2) * (d1 - d2) > d:
result = i
d = (d1 - d2) * (d1 - d2)
from algorithm import SortOrder, sort
proc sortPlus[T](a: var openArray[T], ax: var T, cmp: proc (x, y: T): int {.closure.}, order = algorithm.SortOrder.Ascending) =
var j = 0
let sign = if order == algorithm.SortOrder.Ascending: 1 else: -1
for i in 1 .. a.high:
if cmp(a[i], a[j]) * sign < 0:
j = i
if cmp(a[j], ax) * sign < 0:
swap(ax, a[j])
a.sort(cmp, order)
# R*TREE procs
proc rstarSplit[M, D: Dim; RT, LT](t: RStarTree[M, D, RT, LT]; n: var Node[M, D, RT, LT] | var Leaf[M, D, RT, LT]; lx: L[D, RT, LT] | N[M, D, RT, LT]): type(n) =
type NL = type(lx)
var nBest: type(n)
new nBest
var lx = lx
when n is Node[M, D, RT, LT]:
lx.n.parent = n
var lxbest: type(lx)
var m0 = lx.b[0].a.high
for d2 in 0 ..< 2 * D:
let d = d2 div 2
if d2 mod 2 == 0:
sortPlus(n.a, lx, proc (x, y: NL): int = cmp(x.b[d].a, y.b[d].a))
else:
sortPlus(n.a, lx, proc (x, y: NL): int = cmp(x.b[d].b, y.b[d].b))
for i in t.m - 1 .. n.a.high - t.m + 1:
var b = lx.b
for j in 0 ..< i: # we can precalculate union() for range 0 .. t.m - 1, but that seems to give no real benefit. Maybe for very large M?
#echo "x",j
b = union(n.a[j].b, b)
var m = margin(b)
b = n.a[^1].b
for j in i ..< n.a.high: # again, precalculation of tail would be possible
#echo "y",j
b = union(n.a[j].b, b)
m += margin(b)
if m < m0:
nbest[] = n[]
lxbest = lx
m0 = m
var i0 = -1
var o0 = lx.b[0].a.high
for i in t.m - 1 .. n.a.high - t.m + 1:
var b1 = lxbest.b
for j in 0 ..< i:
b1 = union(nbest.a[j].b, b1)
var b2 = nbest.a[^1].b
for j in i ..< n.a.high:
b2 = union(nbest.a[j].b, b2)
let o = overlap(b1, b2)
if o < o0:
i0 = i
o0 = o
n.a[0] = lxbest
for i in 0 ..< i0:
n.a[i + 1] = nbest.a[i]
new result
result.level = n.level
result.parent = n.parent
for i in i0 .. n.a.high:
result.a[i - i0] = nbest.a[i]
n.numEntries = i0 + 1
result.numEntries = M - i0
when n is Node[M, D, RT, LT]:
for i in 0 ..< result.numEntries:
result.a[i].n.parent = result
proc quadraticSplit[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; n: var Node[M, D, RT, LT] | var Leaf[M, D, RT, LT]; lx: L[D, RT, LT] | N[M, D, RT, LT]): type(n) =
var n1, n2: type(n)
var s1, s2: int
new n1
new n2
n1.parent = n.parent
n2.parent = n.parent
n1.level = n.level
n2.level = n.level
var lx = lx
when n is Node[M, D, RT, LT]:
lx.n.parent = n
(s1, s2) = pickSeeds(t, n, lx.b)
assert s1 >= -1 and s2 >= 0
if unlikely(s1 < 0):
n1.a[0] = lx
else:
n1.a[0] = n.a[s1]
dec(n.numEntries)
if s2 == n.numEntries: # important fix
s2 = s1
n.a[s1] = n.a[n.numEntries]
inc(n1.numEntries)
var b1 = n1.a[0].b
n2.a[0] = n.a[s2]
dec(n.numEntries)
n.a[s2] = n.a[n.numEntries]
inc(n2.numEntries)
var b2 = n2.a[0].b
if s1 >= 0:
n.a[n.numEntries] = lx
inc(n.numEntries)
while n.numEntries > 0 and n1.numEntries < (t.bigM + 1 - t.m) and n2.numEntries < (t.bigM + 1 - t.m):
let next = pickNext(t, n, n1, n2, b1, b2)
let d1 = area(union(b1, n.a[next].b)) - area(b1)
let d2 = area(union(b2, n.a[next].b)) - area(b2)
if (d1 < d2) or (d1 == d2 and ((area(b1) < area(b2)) or (area(b1) == area(b2) and n1.numEntries < n2.numEntries))):
n1.a[n1.numEntries] = n.a[next]
b1 = union(b1, n.a[next].b)
inc(n1.numEntries)
else:
n2.a[n2.numEntries] = n.a[next]
b2 = union(b2, n.a[next].b)
inc(n2.numEntries)
dec(n.numEntries)
n.a[next] = n.a[n.numEntries]
if n.numEntries == 0:
discard
elif n1.numEntries == (t.bigM + 1 - t.m):
while n.numEntries > 0:
dec(n.numEntries)
n2.a[n2.numEntries] = n.a[n.numEntries]
inc(n2.numEntries)
elif n2.numEntries == (t.bigM + 1 - t.m):
while n.numEntries > 0:
dec(n.numEntries)
n1.a[n1.numEntries] = n.a[n.numEntries]
inc(n1.numEntries)
when n is Node[M, D, RT, LT]:
for i in 0 ..< n2.numEntries:
n2.a[i].n.parent = n2
n[] = n1[]
return n2
proc overflowTreatment[M, D: Dim; RT, LT](t: RStarTree[M, D, RT, LT]; n: var Node[M, D, RT, LT] | var Leaf[M, D, RT, LT]; lx: L[D, RT, LT] | N[M, D, RT, LT]): type(n)
proc adjustTree[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; l, ll: H[M, D, RT, LT]; hb: Box[D, RT]) =
var n = l
var nn = ll
assert n != nil
while true:
if n == t.root:
if nn == nil:
break
t.root = newNode[M, D, RT, LT]()
t.root.level = n.level + 1
Node[M, D, RT, LT](t.root).a[0].n = n
n.parent = t.root
nn.parent = t.root
t.root.numEntries = 1
let p = Node[M, D, RT, LT](n.parent)
var i = 0
while p.a[i].n != n:
inc(i)
var b: type(p.a[0].b)
if n of Leaf[M, D, RT, LT]:
when false:#if likely(nn.isNil): # no performance gain
b = union(p.a[i].b, Leaf[M, D, RT, LT](n).a[n.numEntries - 1].b)
else:
b = Leaf[M, D, RT, LT](n).a[0].b
for j in 1 ..< n.numEntries:
b = trtree.union(b, Leaf[M, D, RT, LT](n).a[j].b)
elif n of Node[M, D, RT, LT]:
b = Node[M, D, RT, LT](n).a[0].b
for j in 1 ..< n.numEntries:
b = union(b, Node[M, D, RT, LT](n).a[j].b)
else:
assert false
#if nn.isNil and p.a[i].b == b: break # no performance gain
p.a[i].b = b
n = H[M, D, RT, LT](p)
if unlikely(nn != nil):
if nn of Leaf[M, D, RT, LT]:
b = Leaf[M, D, RT, LT](nn).a[0].b
for j in 1 ..< nn.numEntries:
b = union(b, Leaf[M, D, RT, LT](nn).a[j].b)
elif nn of Node[M, D, RT, LT]:
b = Node[M, D, RT, LT](nn).a[0].b
for j in 1 ..< nn.numEntries:
b = union(b, Node[M, D, RT, LT](nn).a[j].b)
else:
assert false
if p.numEntries < p.a.len:
p.a[p.numEntries].b = b
p.a[p.numEntries].n = nn
inc(p.numEntries)
assert n != nil
nn = nil
else:
let h: N[M, D, RT, LT] = (b, nn)
if t of RStarTree[M, D, RT, LT]:
nn = overflowTreatment(RStarTree[M, D, RT, LT](t), p, h)
elif t of RTree[M, D, RT, LT]:
nn = quadraticSplit(RTree[M, D, RT, LT](t), p, h)
else:
assert false
assert n == H[M, D, RT, LT](p)
assert n != nil
assert t.root != nil
proc insert*[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; leaf: N[M, D, RT, LT] | L[D, RT, LT]; level: int = 0) =
when leaf is N[M, D, RT, LT]:
assert level > 0
type NodeLeaf = Node[M, D, RT, LT]
else:
assert level == 0
type NodeLeaf = Leaf[M, D, RT, LT]
for d in leaf.b:
assert d.a <= d.b
let l = NodeLeaf(chooseSubtree(t, leaf.b, level))
if l.numEntries < l.a.len:
l.a[l.numEntries] = leaf
inc(l.numEntries)
when leaf is N[M, D, RT, LT]:
leaf.n.parent = l
adjustTree(t, l, nil, leaf.b)
else:
let l2 = quadraticSplit(t, l, leaf)
assert l2.level == l.level
adjustTree(t, l, l2, leaf.b)
# R*Tree insert procs
proc rsinsert[M, D: Dim; RT, LT](t: RStarTree[M, D, RT, LT]; leaf: N[M, D, RT, LT] | L[D, RT, LT]; level: int)
proc reInsert[M, D: Dim; RT, LT](t: RStarTree[M, D, RT, LT]; n: var Node[M, D, RT, LT] | var Leaf[M, D, RT, LT]; lx: L[D, RT, LT] | N[M, D, RT, LT]) =
type NL = type(lx)
var lx = lx
var buf: type(n.a)
let p = Node[M, D, RT, LT](n.parent)
var i = 0
while p.a[i].n != n:
inc(i)
let c = center(p.a[i].b)
sortPlus(n.a, lx, proc (x, y: NL): int = cmp(distance(center(x.b), c), distance(center(y.b), c)))
n.numEntries = M - t.p
swap(n.a[n.numEntries], lx)
inc n.numEntries
var b = n.a[0].b
for i in 1 ..< n.numEntries:
b = union(b, n.a[i].b)
p.a[i].b = b
for i in M - t.p + 1 .. n.a.high:
buf[i] = n.a[i]
rsinsert(t, lx, n.level)
for i in M - t.p + 1 .. n.a.high:
rsinsert(t, buf[i], n.level)
proc overflowTreatment[M, D: Dim; RT, LT](t: RStarTree[M, D, RT, LT]; n: var Node[M, D, RT, LT] | var Leaf[M, D, RT, LT]; lx: L[D, RT, LT] | N[M, D, RT, LT]): type(n) =
if n.level != t.root.level and t.firstOverflow[n.level]:
t.firstOverflow[n.level] = false
reInsert(t, n, lx)
return nil
else:
let l2 = rstarSplit(t, n, lx)
assert l2.level == n.level
return l2
proc rsinsert[M, D: Dim; RT, LT](t: RStarTree[M, D, RT, LT]; leaf: N[M, D, RT, LT] | L[D, RT, LT]; level: int) =
when leaf is N[M, D, RT, LT]:
assert level > 0
type NodeLeaf = Node[M, D, RT, LT]
else:
assert level == 0
type NodeLeaf = Leaf[M, D, RT, LT]
let l = NodeLeaf(chooseSubtree(t, leaf.b, level))
if l.numEntries < l.a.len:
l.a[l.numEntries] = leaf
inc(l.numEntries)
when leaf is N[M, D, RT, LT]:
leaf.n.parent = l
adjustTree(t, l, nil, leaf.b)
else:
when leaf is N[M, D, RT, LT]: # TODO do we need this?
leaf.n.parent = l
let l2 = overflowTreatment(t, l, leaf)
if l2 != nil:
assert l2.level == l.level
adjustTree(t, l, l2, leaf.b)
proc insert*[M, D: Dim; RT, LT](t: RStarTree[M, D, RT, LT]; leaf: L[D, RT, LT]) =
for d in leaf.b:
assert d.a <= d.b
for i in mitems(t.firstOverflow):
i = true
rsinsert(t, leaf, 0)
# delete
proc findLeaf[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; leaf: L[D, RT, LT]): Leaf[M, D, RT, LT] =
proc fl[M, D: Dim; RT, LT](h: H[M, D, RT, LT]; leaf: L[D, RT, LT]): Leaf[M, D, RT, LT] =
var n = h
if n of Node[M, D, RT, LT]:
for i in 0 ..< n.numEntries:
if intersect(Node[M, D, RT, LT](n).a[i].b, leaf.b):
let l = fl(Node[M, D, RT, LT](n).a[i].n, leaf)
if l != nil:
return l
elif n of Leaf[M, D, RT, LT]:
for i in 0 ..< n.numEntries:
if Leaf[M, D, RT, LT](n).a[i] == leaf:
return Leaf[M, D, RT, LT](n)
else:
assert false
return nil
fl(t.root, leaf)
proc condenseTree[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; leaf: Leaf[M, D, RT, LT]) =
var n: H[M, D, RT, LT] = leaf
var q = newSeq[H[M, D, RT, LT]]()
var b: type(leaf.a[0].b)
while n != t.root:
let p = Node[M, D, RT, LT](n.parent)
var i = 0
while p.a[i].n != n:
inc(i)
if n.numEntries < t.m:
dec(p.numEntries)
p.a[i] = p.a[p.numEntries]
q.add(n)
else:
if n of Leaf[M, D, RT, LT]:
b = Leaf[M, D, RT, LT](n).a[0].b
for j in 1 ..< n.numEntries:
b = union(b, Leaf[M, D, RT, LT](n).a[j].b)
elif n of Node[M, D, RT, LT]:
b = Node[M, D, RT, LT](n).a[0].b
for j in 1 ..< n.numEntries:
b = union(b, Node[M, D, RT, LT](n).a[j].b)
else:
assert false
p.a[i].b = b
n = n.parent
if t of RStarTree[M, D, RT, LT]:
for n in q:
if n of Leaf[M, D, RT, LT]:
for i in 0 ..< n.numEntries:
for i in mitems(RStarTree[M, D, RT, LT](t).firstOverflow):
i = true
rsinsert(RStarTree[M, D, RT, LT](t), Leaf[M, D, RT, LT](n).a[i], 0)
elif n of Node[M, D, RT, LT]:
for i in 0 ..< n.numEntries:
for i in mitems(RStarTree[M, D, RT, LT](t).firstOverflow):
i = true
rsinsert(RStarTree[M, D, RT, LT](t), Node[M, D, RT, LT](n).a[i], n.level)
else:
assert false
elif t of RTree[M, D, RT, LT]:
for n in q:
if n of Leaf[M, D, RT, LT]:
for i in 0 ..< n.numEntries:
insert(RTree[M, D, RT, LT](t), Leaf[M, D, RT, LT](n).a[i])
elif n of Node[M, D, RT, LT]:
for i in 0 ..< n.numEntries:
insert(RTree[M, D, RT, LT](t), Node[M, D, RT, LT](n).a[i], n.level)
else:
assert false
else:
assert false
proc delete*[M, D: Dim; RT, LT](t: RTree[M, D, RT, LT]; leaf: L[D, RT, LT]): bool {.discardable.} =
let l = findLeaf(t, leaf)
if l.isNil:
return false
else:
var i = 0
while l.a[i] != leaf:
inc(i)
dec(l.numEntries)
l.a[i] = l.a[l.numEntries]
condenseTree(t, l)
if t.root.numEntries == 1:
if t.root of Node[M, D, RT, LT]:
t.root = Node[M, D, RT, LT](t.root).a[0].n
t.root.parent = nil
return true
when isMainModule:
var t = [4, 1, 3, 2]
var xt = 7
sortPlus(t, xt, system.cmp, SortOrder.Ascending)
echo xt, " ", t
type
RSE = L[2, int, int]
RSeq = seq[RSE]
proc rseq_search(rs: RSeq; rse: RSE): seq[int] =
result = newSeq[int]()
for i in rs:
if intersect(i.b, rse.b):
result.add(i.l)
proc rseq_delete(rs: var RSeq; rse: RSE): bool =
for i in 0 .. rs.high:
if rs[i] == rse:
#rs.delete(i)
rs[i] = rs[rs.high]
rs.setLen(rs.len - 1)
return true
import random, algorithm
proc test(n: int) =
var b: Box[2, int]
echo center(b)
var x1, x2, y1, y2: int
var t = newRStarTree[8, 2, int, int]()
#var t = newRTree[8, 2, int, int]()
var rs = newSeq[RSE]()
for i in 0 .. 5:
for i in 0 .. n - 1:
x1 = rand(1000)
y1 = rand(1000)
x2 = x1 + rand(25)
y2 = y1 + rand(25)
b = [(x1, x2), (y1, y2)]
let el: L[2, int, int] = (b, i + 7)
t.insert(el)
rs.add(el)
for i in 0 .. (n div 4):
let j = rand(rs.high)
var el = rs[j]
assert t.delete(el)
assert rs.rseq_delete(el)
for i in 0 .. n - 1:
x1 = rand(1000)
y1 = rand(1000)
x2 = x1 + rand(100)
y2 = y1 + rand(100)
b = [(x1, x2), (y1, y2)]
let el: L[2, int, int] = (b, i)
let r = search(t, b)
let r2 = rseq_search(rs, el)
assert r.len == r2.len
assert r.sorted(system.cmp) == r2.sorted(system.cmp)
test(1500)
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