REVERT ME: revert the re-introduction of PartialQuickSort

There are some pretty compelling reasons to use PartialQuickSort instead of ScratchQuickSort as a base case for BracketedSort.
However, PartialQuickSort can segfault for invalid but seemingly innocuous lt functions.
I don't want to talk about introducing segfaults to the default sorting algorithms or introducing a regression to PartialQuickSort in this PR
Revert this commit it you want `partialsort!(::Vector{Int}, ::Int)` not to allocate.

base/sort.jl

@@ -1151,10 +1151,8 @@ be much less than `next`'s. If the maximum additional space usage of `next` scal
 then for small k the average* maximum additional space usage of BracketedSort will be
 `O(n^(2.3/3))`.
 
-By default, BracketedSort uses the in place `PartialQuickSort` algorithm recursively for
-integer `target`s and the faster but not in place `ScratchQuickSort` for unit range
-`target`s. This is because the runtime of recursive calls is negligible for large inputs
-unless `k` is similar in size to `n`.
+By default, BracketedSort uses the `O(n)` space and `O(n + k log k)` runtime
+`ScratchQuickSort` algorithm recursively.
 
 *Sorting is unable to depend on Random.jl because Random.jl depends on sorting.
  Consequently, we use `hash` as a source of randomness. The average runtime guarantees
@@ -1178,8 +1176,7 @@ struct BracketedSort{T, F} <: Algorithm
 end
 
 # TODO: this composition between BracketedSort and ScratchQuickSort does not bring me joy
-BracketedSort(k::Integer) = BracketedSort(k, k -> InitialOptimizations(PartialQuickSort(k)))
-BracketedSort(k::OrdinalRange) = BracketedSort(k, k -> InitialOptimizations(ScratchQuickSort(k)))
+BracketedSort(k) = BracketedSort(k, k -> InitialOptimizations(ScratchQuickSort(k)))
 
 function bracket_kernel!(v::AbstractVector, lo, hi, lo_signpost, hi_signpost, o)
     i = 0

test/sorting.jl

@@ -742,8 +742,7 @@ end
     for alg in safe_algs
         @test sort(v, alg=alg, lt = <=) == s
     end
-    # Broken by the introduction of BracketedSort in #52006 which...
-    @test_broken partialsort(v, 172, lt = <=) == s[172] # ...uses PartialQuickSort which can segfault on invalid lt
+    @test partialsort(v, 172, lt = <=) == s[172]
     @test partialsort(v, 315:415, lt = <=) == s[315:415]
 
     # ...and it is consistently reverse stable. All these algorithms swap v[i] and v[j]
@@ -753,16 +752,15 @@ end
     for alg in safe_algs
         @test sort(1:n, alg=alg, lt = (i,j) -> v[i]<=v[j]) == perm
     end
-    # Broken by the introduction of BracketedSort in #52006 which...
-    @test_broken partialsort(1:n, 172, lt = (i,j) -> v[i]<=v[j]) == perm[172] # ...uses PartialQuickSort which can segfault on invalid lt
-    @test_broken partialsort(1:n, 315:415, lt = (i,j) -> v[i]<=v[j]) == perm[315:415] # ...and is unstable
+    # Broken by the introduction of BracketedSort in #52006 which is unstable
+    @test_broken partialsort(1:n, 172, lt = (i,j) -> v[i]<=v[j]) == perm[172]
+    @test_broken partialsort(1:n, 315:415, lt = (i,j) -> v[i]<=v[j]) == perm[315:415]
 
     # lt can be very poorly behaved and sort will still permute its input in some way.
     for alg in safe_algs
         @test sort!(sort(v, alg=alg, lt = (x,y) -> rand([false, true]))) == s
     end
-    # Sometimes throws a bounds error, sometimes segfaults, works. Broken by #52006 & PartialQuickSort.
-    # @test partialsort(v, 172, lt = (x,y) -> rand([false, true])) ∈ 1:5
+    @test partialsort(v, 172, lt = (x,y) -> rand([false, true])) ∈ 1:5
     @test all(partialsort(v, 315:415, lt = (x,y) -> rand([false, true])) .∈ (1:5,))
 
     # issue #32675
@@ -1097,6 +1095,10 @@ end
         x = rand(1:5, 1000)
         @test partialsort(x, i, lt=(<=)) == sort(x)[i]
     end
+    for i in [1, 7, 8, 490, 495, 852, 993, 996, 1000]
+        x = rand(1:5, 1000)
+        @test partialsort(x, i, lt=(<=)) == sort(x)[i]
+    end
 end
 
 # This testset is at the end of the file because it is slow.