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kotlin.reflect.jvm.internal.pcollections.IntTree Maven / Gradle / Ivy
/*
* Copyright 2010-2015 JetBrains s.r.o.
*
* Licensed 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 kotlin.reflect.jvm.internal.pcollections;
/**
* A non-public utility class for persistent balanced tree maps with integer keys.
*
* To allow for efficiently increasing all keys above a certain value or decreasing
* all keys below a certain value, the keys values are stored relative to their parent.
* This makes this map a good backing for fast insertion and removal of indices in a
* vector.
*
* This implementation is thread-safe except for its iterators.
*
* Other than that, this tree is based on the Glasgow Haskell Compiler's Data.Map implementation,
* which in turn is based on "size balanced binary trees" as described by:
*
* Stephen Adams, "Efficient sets: a balancing act",
* Journal of Functional Programming 3(4):553-562, October 1993,
* http://www.swiss.ai.mit.edu/~adams/BB/.
*
* J. Nievergelt and E.M. Reingold, "Binary search trees of bounded balance",
* SIAM journal of computing 2(1), March 1973.
*
* @author harold
*/
final class IntTree {
// marker value:
static final IntTree EMPTYNODE = new IntTree();
// we use longs so relative keys can express all ints
// (e.g. if this has key -10 and right has 'absolute' key MAXINT,
// then its relative key is MAXINT+10 which overflows)
// there might be some way to deal with this based on left-verse-right logic,
// but that sounds like a mess.
private final long key;
private final V value; // null value means this is empty node
private final IntTree left, right;
private final int size;
private IntTree() {
size = 0;
key = 0;
value = null;
left = null;
right = null;
}
private IntTree(long key, V value, IntTree left, IntTree right) {
this.key = key;
this.value = value;
this.left = left;
this.right = right;
size = 1 + left.size + right.size;
}
private IntTree withKey(long newKey) {
if (size == 0 || newKey == key) return this;
return new IntTree(newKey, value, left, right);
}
boolean containsKey(long key) {
if (size == 0)
return false;
if (key < this.key)
return left.containsKey(key - this.key);
if (key > this.key)
return right.containsKey(key - this.key);
// otherwise key==this.key:
return true;
}
V get(long key) {
if (size == 0)
return null;
if (key < this.key)
return left.get(key - this.key);
if (key > this.key)
return right.get(key - this.key);
// otherwise key==this.key:
return value;
}
IntTree plus(long key, V value) {
if (size == 0)
return new IntTree(key, value, this, this);
if (key < this.key)
return rebalanced(left.plus(key - this.key, value), right);
if (key > this.key)
return rebalanced(left, right.plus(key - this.key, value));
// otherwise key==this.key, so we simply replace this, with no effect on balance:
if (value == this.value)
return this;
return new IntTree(key, value, left, right);
}
IntTree minus(long key) {
if (size == 0)
return this;
if (key < this.key)
return rebalanced(left.minus(key - this.key), right);
if (key > this.key)
return rebalanced(left, right.minus(key - this.key));
// otherwise key==this.key, so we are killing this node:
if (left.size == 0) // we can just become right node
// make key 'absolute':
return right.withKey(right.key + this.key);
if (right.size == 0) // we can just become left node
return left.withKey(left.key + this.key);
// otherwise replace this with the next key (i.e. the smallest key to the right):
// TODO have minNode() instead of minKey to avoid having to call get()
// TODO get node from larger subtree, i.e. if left.size>right.size use left.maxNode()
// TODO have faster minusMin() instead of just using minus()
long newKey = right.minKey() + this.key;
//(right.minKey() is relative to this; adding this.key makes it 'absolute'
// where 'absolute' really means relative to the parent of this)
V newValue = right.get(newKey - this.key);
// now that we've got the new stuff, take it out of the right subtree:
IntTree newRight = right.minus(newKey - this.key);
// lastly, make the subtree keys relative to newKey (currently they are relative to this.key):
newRight = newRight.withKey((newRight.key + this.key) - newKey);
// left is definitely not empty:
IntTree newLeft = left.withKey((left.key + this.key) - newKey);
return rebalanced(newKey, newValue, newLeft, newRight);
}
/**
* Changes every key k>=key to k+delta.
*
* This method will create an _invalid_ tree if delta<0
* and the distance between the smallest k>=key in this
* and the largest j changeKeysAbove(long key, int delta) {
if (size == 0 || delta == 0)
return this;
if (this.key >= key)
// adding delta to this.key changes the keys of _all_ children of this,
// so we now need to un-change the children of this smaller than key,
// all of which are to the left. note that we still use the 'old' relative key...:
return new IntTree(this.key + delta, value, left.changeKeysBelow(key - this.key, -delta), right);
// otherwise, doesn't apply yet, look to the right:
IntTree newRight = right.changeKeysAbove(key - this.key, delta);
if (newRight == right) return this;
return new IntTree(this.key, value, left, newRight);
}
/**
* Changes every key k=key in this is delta or less.
*
* In other words, this method must not result in any overlap or change
* in the order of the keys in this, since the tree _structure_ is
* not being changed at all.
*/
IntTree changeKeysBelow(long key, int delta) {
if (size == 0 || delta == 0)
return this;
if (this.key < key)
// adding delta to this.key changes the keys of _all_ children of this,
// so we now need to un-change the children of this larger than key,
// all of which are to the right. note that we still use the 'old' relative key...:
return new IntTree(this.key + delta, value, left, right.changeKeysAbove(key - this.key, -delta));
// otherwise, doesn't apply yet, look to the left:
IntTree newLeft = left.changeKeysBelow(key - this.key, delta);
if (newLeft == left) return this;
return new IntTree(this.key, value, newLeft, right);
}
// min key in this:
private long minKey() {
if (left.size == 0)
return key;
// make key 'absolute' (i.e. relative to the parent of this):
return left.minKey() + this.key;
}
private IntTree rebalanced(IntTree newLeft, IntTree newRight) {
if (newLeft == left && newRight == right)
return this; // already balanced
return rebalanced(key, value, newLeft, newRight);
}
private static final int OMEGA = 5;
private static final int ALPHA = 2;
// rebalance a tree that is off-balance by at most 1:
private static IntTree rebalanced(long key, V value, IntTree left, IntTree right) {
if (left.size + right.size > 1) {
if (left.size >= OMEGA * right.size) { // rotate to the right
IntTree ll = left.left, lr = left.right;
if (lr.size < ALPHA * ll.size) // single rotation
return new IntTree(left.key + key, left.value,
ll,
new IntTree(-left.key, value,
lr.withKey(lr.key + left.key),
right));
else { // double rotation:
IntTree lrl = lr.left, lrr = lr.right;
return new IntTree(lr.key + left.key + key, lr.value,
new IntTree(-lr.key, left.value,
ll,
lrl.withKey(lrl.key + lr.key)),
new IntTree(-left.key - lr.key, value,
lrr.withKey(lrr.key + lr.key + left.key),
right));
}
} else if (right.size >= OMEGA * left.size) { // rotate to the left
IntTree rl = right.left, rr = right.right;
if (rl.size < ALPHA * rr.size) // single rotation
return new IntTree(right.key + key, right.value,
new IntTree(-right.key, value,
left,
rl.withKey(rl.key + right.key)),
rr);
else { // double rotation:
IntTree rll = rl.left, rlr = rl.right;
return new IntTree(rl.key + right.key + key, rl.value,
new IntTree(-right.key - rl.key, value,
left,
rll.withKey(rll.key + rl.key + right.key)),
new IntTree(-rl.key, right.value,
rlr.withKey(rlr.key + rl.key),
rr));
}
}
}
// otherwise already balanced enough:
return new IntTree(key, value, left, right);
}
}
