*
     * 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();

import java.util.Set;

/**
 * A class to allow {@link Graph} implementations to be backed by a {@link BaseGraph}. This is not
 * currently planned to be released as a general-purpose forwarding class.
 *
 * @author James Sexton
 */
abstract class ForwardingGraph<N> extends AbstractGraph<N> {

  abstract BaseGraph<N> delegate();

  @Override
  public Set<N> nodes() {
    return delegate().nodes();
  }

  /**

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

/**
 * An implementation of {@link GraphConnections} for undirected graphs.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 */
final class UndirectedGraphConnections<N, V> implements GraphConnections<N, V> {
  private final Map<N, V> adjacentNodeValues;

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

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

 * this class rather than implement {@link ValueGraph} directly.
 *
 * <p>The methods implemented in this class should not be overridden unless the subclass admits a
 * more efficient implementation.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 * @since 20.0
 */
@Beta
public abstract class AbstractValueGraph<N, V> extends AbstractBaseGraph<N>
    implements ValueGraph<N, V> {

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;

 *
 * <p>Time complexities for mutation methods are all O(1) except for {@code removeNode(N node)},
 * which is in O(d_node) where d_node is the degree of {@code node}.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 */
final class StandardMutableGraph<N> extends ForwardingGraph<N> implements MutableGraph<N> {
  private final MutableValueGraph<N, Presence> backingValueGraph;

/**
 * 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() {