*
     * We start out with a double-precision approximation, which may be higher or lower than the
     * true value. Therefore, we perform at least one Newton iteration to get a guess that's
     * definitely >= floor(sqrt(x)), and then continue the iteration until we reach a fixed point.
     */
    BigInteger sqrt0;
    int log2 = log2(x, FLOOR);

        AvlNode<E> newTop = pred();
        // newTop is the maximum node in my left subtree
        newTop.left = left.removeMax(newTop);
        newTop.right = right;
        newTop.distinctElements = distinctElements - 1;
        newTop.totalCount = totalCount - oldElemCount;
        return newTop.rebalance();
      } else {
        AvlNode<E> newTop = succ();

 */

package com.google.common.graph;

import com.google.common.base.Optional;

/**
 * A base class for builders that construct graphs with user-defined properties.
 *
 * @author James Sexton
 */
abstract class AbstractGraphBuilder<N> {
  final boolean directed;
  boolean allowsSelfLoops = false;
  ElementOrder<N> nodeOrder = ElementOrder.insertion();

import java.util.Collections;
import java.util.Map;
import java.util.Set;
import org.jspecify.annotations.Nullable;

/**
 * A base implementation of {@link NetworkConnections} for undirected networks.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 */
abstract class AbstractUndirectedNetworkConnections<N, E> implements NetworkConnections<N, E> {

        AvlNode<E> newTop = pred();
        // newTop is the maximum node in my left subtree
        newTop.left = left.removeMax(newTop);
        newTop.right = right;
        newTop.distinctElements = distinctElements - 1;
        newTop.totalCount = totalCount - oldElemCount;
        return newTop.rebalance();
      } else {
        AvlNode<E> newTop = succ();

import java.util.Collections;
import java.util.Map;
import java.util.Set;

/**
 * An implementation of {@link NetworkConnections} for undirected networks.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 */
final class UndirectedNetworkConnections<N, E> extends AbstractUndirectedNetworkConnections<N, E> {

 *
 * <p>The {@link #nodeToOutEdge} map means this class only works on networks without parallel edges.
 * See {@link MultiEdgesConnecting} for a class that works with parallel edges.
 *
 * @author James Sexton
 * @param <E> Edge parameter type
 */
final class EdgesConnecting<E> extends AbstractSet<E> {

  private final Map<?, E> nodeToOutEdge;
  private final Object targetNode;

/**
 * A class to allow {@link ValueGraph} implementations to be backed by a provided delegate. This is
 * not currently planned to be released as a general-purpose forwarding class.
 *
 * @author James Sexton
 * @author Joshua O'Madadhain
 */
abstract class ForwardingValueGraph<N, V> extends AbstractValueGraph<N, V> {

  abstract ValueGraph<N, V> delegate();

  @Override
  public Set<N> nodes() {

import java.util.Set;
import org.jspecify.annotations.Nullable;

/**
 * An interface for representing and manipulating an origin node's adjacent nodes and edge values in
 * a {@link Graph}.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 */
interface GraphConnections<N, V> {

  Set<N> adjacentNodes();

  Set<N> predecessors();

  Set<N> successors();

  /**

/**
 * A {@link MapIteratorCache} that adds additional caching. In addition to the caching provided by
 * {@link MapIteratorCache}, this structure caches values for the two most recently retrieved keys.
 *
 * @author James Sexton
 */
final class MapRetrievalCache<K, V> extends MapIteratorCache<K, V> {
  // See the note about volatile in the superclass.
  private transient volatile @Nullable CacheEntry<K, V> cacheEntry1;