pkg/adt: refactor + add more test cases

[gyuho]

Introduction to Algorithms by Charles E. Leiserson, Clifford Stein, Ronald Rivest, and Thomas H. Cormen:

13.1 Properties of red-black trees

5. For each node, all simple paths from the node to descendant leaves contain the
   same number of black nodes.

Current delete operation violates "black-height" property.

For example, given this red-black tree:

Let's delete the node 11.

The tree should be rebalanced as below:

After deleting 11 (requires rebalancing):

                        [510,511]
                        /      \
                --------        ----------------------------
               /                                            \
           [383,384]                                     [830,831]
           /       \                                    /          \
          /         \                                  /            \
[261,262](red)     [410,411]                  [647,648]           [899,900](red)
        /               \                           \                     /    \
       /                 \                           \                   /      \
    [82,83]           [292,293]                [815,816](red)      [888,889]    [972,973]
        \                                                           /
         \                                                         /
        [238,239](red)                                       [953,954](red)

However, current implementation returns:

After deleting 11 (requires rebalancing):

                       [510,511]
                        /      \
              ----------        --------------------------
             /                                            \
         [82,83]                                       [830,831]
               \                                      /          \
                \                                    /            \
             [383,384]                        [647,648]           [899,900]
             /       \                              \                 /    \
            /         \                              \               /      \
      [261,262]      [410,411]                      [815,816] [888,889]    [972,973]
        /   \                                                                /
       /     \                                                              /
[238,239]   [292,293]                                                [953,954]

This violates "black-height" property.

Fix #10877.

[gyuho]

@xiang90 @xkeyideal This is still in progress. Still validating @xkeyideal's fix.

Current branch includes a test case to prove that the current implementation is wrong, as described in #10877.

[xkeyideal]

@gyuho I saw your code, it seem delete function doesn't be modified, nil node should be coloring black, then delete node 11, the nil node can be coloring double black

[gyuho]

@xkeyideal Yes I am still working on this. I created this PR just to validate your test case.

[jingyih]

Is the bug about correctness or just performance?

[gyuho]

@jingyih

Can you help merge this? This doesn't change any behavior with current implementation.

I created a separate issue to track this.

I think we need more time to work on this, in 3.5.

[codecov-io]

Codecov Report

Merging #10959 into master will decrease coverage by 0.32%.
The diff coverage is 90.9%.

@@            Coverage Diff             @@
##           master   #10959      +/-   ##
==========================================
- Coverage   64.21%   63.88%   -0.33%     
==========================================
  Files         401      401              
  Lines       37473    37521      +48     
==========================================
- Hits        24062    23970      -92     
- Misses      11804    11936     +132     
- Partials     1607     1615       +8

Impacted Files	Coverage Δ
auth/range_perm_cache.go	59.49% <100%> (-1.27%)	⬇️
proxy/grpcproxy/cache/store.go	91.54% <100%> (+0.12%)	⬆️
etcdserver/api/v3rpc/key.go	80.28% <100%> (ø)	⬆️
mvcc/watcher_group.go	89.7% <100%> (+0.07%)	⬆️
pkg/adt/interval_tree.go	86.47% <90.16%> (-5.12%)	⬇️
auth/store.go	48.4% <0%> (-17.5%)	⬇️
etcdserver/api/v3rpc/lease.go	67.04% <0%> (-7.96%)	⬇️
pkg/tlsutil/tlsutil.go	86.2% <0%> (-6.9%)	⬇️
clientv3/namespace/watch.go	87.87% <0%> (-6.07%)	⬇️
... and 22 more

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[jingyih]

LGTM. Thanks! Let's work on this in v3.5.