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The Apache Cassandra Project develops a highly scalable second-generation distributed database, bringing together Dynamo's fully distributed design and Bigtable's ColumnFamily-based data model.
/*
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.cassandra.db.tries;
import java.util.ArrayList;
import java.util.Collection;
import java.util.List;
import com.google.common.collect.Iterables;
/**
* A merged view of multiple tries.
*
* This is accomplished by walking the cursors in parallel; the merged cursor takes the position and features of the
* smallest and advances with it; when multiple cursors are equal, all of them are advanced. The ordered view of the
* cursors is maintained using a custom binary min-heap, built for efficiently reforming the heap when the top elements
* are advanced (see {@link CollectionMergeCursor}).
*
* Crucial for the efficiency of this is the fact that when they are advanced like this, we can compare cursors'
* positions by their depth descending and then incomingTransition ascending.
*
* See Trie.md for further details.
*/
class CollectionMergeTrie extends Trie
{
private final CollectionMergeResolver resolver; // only called on more than one input
protected final Collection> inputs;
CollectionMergeTrie(Collection> inputs, CollectionMergeResolver resolver)
{
this.resolver = resolver;
this.inputs = inputs;
}
@Override
protected Cursor cursor()
{
return new CollectionMergeCursor<>(resolver, inputs);
}
/**
* Compare the positions of two cursors. One is before the other when
* - its depth is greater, or
* - its depth is equal, and the incoming transition is smaller.
*/
static boolean greaterCursor(Cursor c1, Cursor c2)
{
int c1depth = c1.depth();
int c2depth = c2.depth();
if (c1depth != c2depth)
return c1depth < c2depth;
return c1.incomingTransition() > c2.incomingTransition();
}
static boolean equalCursor(Cursor c1, Cursor c2)
{
return c1.depth() == c2.depth() && c1.incomingTransition() == c2.incomingTransition();
}
/*
* The merge cursor is a variation of the idea of a merge iterator with one key observation: because we advance
* the source iterators together, we can compare them just by depth and incoming transition.
*
* The most straightforward way to implement merging of iterators is to use a {@code PriorityQueue},
* {@code poll} it to find the next item to consume, then {@code add} the iterator back after advancing.
* This is not very efficient as {@code poll} and {@code add} in all cases require at least
* {@code log(size)} comparisons and swaps (usually more than {@code 2*log(size)}) per consumed item, even
* if the input is suitable for fast iteration.
*
* The implementation below makes use of the fact that replacing the top element in a binary heap can be
* done much more efficiently than separately removing it and placing it back, especially in the cases where
* the top iterator is to be used again very soon (e.g. when there are large sections of the output where
* only a limited number of input iterators overlap, which is normally the case in many practically useful
* situations, e.g. levelled compaction).
*
* The implementation builds and maintains a binary heap of sources (stored in an array), where we do not
* add items after the initial construction. Instead we advance the smallest element (which is at the top
* of the heap) and push it down to find its place for its new position. Should this source be exhausted,
* we swap it with the last source in the heap and proceed by pushing that down in the heap.
*
* In the case where we have multiple sources with matching positions, the merging algorithm
* must be able to merge all equal values. To achieve this {@code content} walks the heap to
* find all equal cursors without advancing them, and separately {@code advance} advances
* all equal sources and restores the heap structure.
*
* The latter is done equivalently to the process of initial construction of a min-heap using back-to-front
* heapification as done in the classic heapsort algorithm. It only needs to heapify subheaps whose top item
* is advanced (i.e. one whose position matches the current), and we can do that recursively from
* bottom to top. Should a source be exhausted when advancing, it can be thrown away by swapping in the last
* source in the heap (note: we must be careful to advance that source too if required).
*
* To make it easier to advance efficienty in single-sourced branches of tries, we extract the current smallest
* cursor (the head) separately, and start any advance with comparing that to the heap's first. When the smallest
* cursor remains the same (e.g. in branches coming from a single source) this makes it possible to advance with
* just one comparison instead of two at the expense of increasing the number by one in the general case.
*
* Note: This is a simplification of the MergeIterator code from CASSANDRA-8915, without the leading ordered
* section and equalParent flag since comparisons of cursor positions are cheap.
*/
static class CollectionMergeCursor implements Cursor
{
private final CollectionMergeResolver resolver;
/**
* The smallest cursor, tracked separately to improve performance in single-source sections of the trie.
*/
private Cursor head;
/**
* Binary heap of the remaining cursors. The smallest element is at position 0.
* Every element i is smaller than or equal to its two children, i.e.
* heap[i] <= heap[i*2 + 1] && heap[i] <= heap[i*2 + 2]
*/
private final Cursor[] heap;
/**
* A list used to collect contents during content() calls.
*/
private final List contents;
public CollectionMergeCursor(CollectionMergeResolver resolver, Collection> inputs)
{
this.resolver = resolver;
int count = inputs.size();
// Get cursors for all inputs. Put one of them in head and the rest in the heap.
heap = new Cursor[count - 1];
contents = new ArrayList<>(count);
int i = -1;
for (Trie trie : inputs)
{
Cursor cursor = trie.cursor();
assert cursor.depth() == 0;
if (i >= 0)
heap[i] = cursor;
else
head = cursor;
++i;
}
// The cursors are all currently positioned on the root and thus in valid heap order.
}
/**
* Interface for internal operations that can be applied to the equal top elements of the heap.
*/
interface HeapOp
{
void apply(CollectionMergeCursor self, Cursor cursor, int index);
}
/**
* Apply a non-interfering operation, i.e. one that does not change the cursor state, to all inputs in the heap
* that are on equal position to the head.
* For interfering operations like advancing the cursors, use {@link #advanceEqualAndRestoreHeap(AdvancingHeapOp)}.
*/
private void applyToEqualOnHeap(HeapOp action)
{
applyToEqualElementsInHeap(action, 0);
}
/**
* Interface for internal advancing operations that can be applied to the heap cursors. This interface provides
* the code to restore the heap structure after advancing the cursors.
*/
interface AdvancingHeapOp extends HeapOp
{
void apply(Cursor cursor);
default void apply(CollectionMergeCursor self, Cursor cursor, int index)
{
// Apply the operation, which should advance the position of the element.
apply(cursor);
// This method is called on the back path of the recursion. At this point the heaps at both children are
// advanced and well-formed.
// Place current node in its proper position.
self.heapifyDown(cursor, index);
// The heap rooted at index is now advanced and well-formed.
}
}
/**
* Advance the state of all inputs in the heap that are on equal position as the head and restore the heap
* invariant.
*/
private void advanceEqualAndRestoreHeap(AdvancingHeapOp action)
{
applyToEqualElementsInHeap(action, 0);
}
/**
* Apply an operation to all elements on the heap that are equal to the head. Descends recursively in the heap
* structure to all equal children and applies the operation on the way back.
*
* This operation can be something that does not change the cursor state (see {@link #content}) or an operation
* that advances the cursor to a new state, wrapped in a {@link AdvancingHeapOp} ({@link #advance} or
* {@link #skipChildren}). The latter interface takes care of pushing elements down in the heap after advancing
* and restores the subheap state on return from each level of the recursion.
*/
private void applyToEqualElementsInHeap(HeapOp action, int index)
{
if (index >= heap.length)
return;
Cursor item = heap[index];
if (!equalCursor(item, head))
return;
// If the children are at the same position, they also need advancing and their subheap
// invariant to be restored.
applyToEqualElementsInHeap(action, index * 2 + 1);
applyToEqualElementsInHeap(action, index * 2 + 2);
// Apply the action. This is done on the reverse direction to give the action a chance to form proper
// subheaps and combine them on processing the parent.
action.apply(this, item, index);
}
/**
* Push the given state down in the heap from the given index until it finds its proper place among
* the subheap rooted at that position.
*/
private void heapifyDown(Cursor item, int index)
{
while (true)
{
int next = index * 2 + 1;
if (next >= heap.length)
break;
// Select the smaller of the two children to push down to.
if (next + 1 < heap.length && greaterCursor(heap[next], heap[next + 1]))
++next;
// If the child is greater or equal, the invariant has been restored.
if (!greaterCursor(item, heap[next]))
break;
heap[index] = heap[next];
index = next;
}
heap[index] = item;
}
/**
* Check if the head is greater than the top element in the heap, and if so, swap them and push down the new
* top until its proper place.
* @param headDepth the depth of the head cursor (as returned by e.g. advance).
* @return the new head element's depth
*/
private int maybeSwapHead(int headDepth)
{
int heap0Depth = heap[0].depth();
if (headDepth > heap0Depth ||
(headDepth == heap0Depth && head.incomingTransition() <= heap[0].incomingTransition()))
return headDepth; // head is still smallest
// otherwise we need to swap heap and heap[0]
Cursor newHeap0 = head;
head = heap[0];
heapifyDown(newHeap0, 0);
return heap0Depth;
}
@Override
public int advance()
{
advanceEqualAndRestoreHeap(Cursor::advance);
return maybeSwapHead(head.advance());
}
@Override
public int advanceMultiple(TransitionsReceiver receiver)
{
// If the current position is present in just one cursor, we can safely descend multiple levels within
// its branch as no one of the other tries has content for it.
if (equalCursor(heap[0], head))
return advance(); // More than one source at current position, do single-step advance.
// If there are no children, i.e. the cursor ascends, we have to check if it's become larger than some
// other candidate.
return maybeSwapHead(head.advanceMultiple(receiver));
}
@Override
public int skipChildren()
{
advanceEqualAndRestoreHeap(Cursor::skipChildren);
return maybeSwapHead(head.skipChildren());
}
@Override
public int depth()
{
return head.depth();
}
@Override
public int incomingTransition()
{
return head.incomingTransition();
}
@Override
public T content()
{
applyToEqualOnHeap(CollectionMergeCursor::collectContent);
collectContent(head, -1);
T toReturn;
switch (contents.size())
{
case 0:
toReturn = null;
break;
case 1:
toReturn = contents.get(0);
break;
default:
toReturn = resolver.resolve(contents);
break;
}
contents.clear();
return toReturn;
}
private void collectContent(Cursor item, int index)
{
T itemContent = item.content();
if (itemContent != null)
contents.add(itemContent);
}
}
/**
* Special instance for sources that are guaranteed distinct. The main difference is that we can form unordered
* value list by concatenating sources.
*/
static class Distinct extends CollectionMergeTrie
{
Distinct(Collection> inputs)
{
super(inputs, throwingResolver());
}
@Override
public Iterable valuesUnordered()
{
return Iterables.concat(Iterables.transform(inputs, Trie::valuesUnordered));
}
}
}
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