* comparator utilities, see either {@code Comparator} itself (for Java 8+), or {@code
 * com.google.common.collect.Ordering} (otherwise).
 *
 * <h3>Relationship to {@code Ordering}</h3>
 *
 * <p>In light of the significant enhancements to {@code Comparator} in Java 8, the overwhelming
 * majority of usages of {@code Ordering} can be written using only built-in JDK APIs. This class is

 *
 * <p>As this interface extends {@code java.util.function.Predicate}, an instance of this type may
 * be used as a {@code Predicate} directly. To use a {@code java.util.function.Predicate} where a
 * {@code com.google.common.base.Predicate} is expected, use the method reference {@code
 * predicate::test}.
 *
 * <p>This interface is now a legacy type. Use {@code java.util.function.Predicate} (or the

   * String.class}, then {@code new TypeResolver().where(formal, actual)} will {@linkplain
   * #resolveType resolve} {@code ParameterizedType List<T>} to {@code List<String>}, and resolve
   * {@code Map<T, Something>} to {@code Map<String, Something>} etc. Similarly, {@code formal} and
   * {@code actual} can be {@code Map<K, V>} and {@code Map<String, Integer>} respectively, or they

 * .compare(a.foo, b.bar)}. {@code ComparisonChain} also has a potential performance problem that
 * {@code Comparator} doesn't: it evaluates all the parameters of all the {@code .compare} calls,
 * even when the result of the comparison is already known from previous {@code .compare} calls.
 * That can be expensive.
 *
 * @author Mark Davis
 * @author Kevin Bourrillion
 * @since 2.0
 */
@GwtCompatible

  /**
   * Computes or retrieves the value corresponding to {@code key}.
   *
   * @param key the non-null key whose value should be loaded
   * @return the value associated with {@code key}; <b>must not be null</b>
   * @throws Exception if unable to load the result
   * @throws InterruptedException if this method is interrupted. {@code InterruptedException} is
   *     treated like any other {@code Exception} in all respects except that, when it is caught,

   * execute/submit/schedule}, as in {@link CallerRunsPolicy}. This applies both to individually
   * submitted tasks and to collections of tasks submitted via {@code invokeAll}, {@code invokeAny},
   * {@code schedule}, {@code scheduleAtFixedRate}, and {@code scheduleWithFixedDelay}. In the case
   * of tasks submitted by {@code invokeAll} or {@code invokeAny}, tasks will run serially on the

  };

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, or {@link Long#MAX_VALUE} if the result does not fit in a {@code long}.
   *
   * @throws IllegalArgumentException if {@code n < 0}, {@code k < 0}, or {@code k > n}
   */
  public static long binomial(int n, int k) {
    checkNonNegative("n", n);

   * such index exists. Equivalent to {@code asList().lastIndexOf(target)}.
   */
  public int lastIndexOf(int target) {
    for (int i = end - 1; i >= start; i--) {
      if (array[i] == target) {
        return i - start;
      }
    }
    return -1;
  }

  /**

   * {@code allRequired} is sorted and that {@code allRequired[i]} are in the range [{@code from},
   * {@code to}] for all {@code i} in the range [{@code requiredFrom}, {@code requiredTo}]. The
   * value returned by this method is the {@code i} in that range such that {@code allRequired[i]}
   * is as close as possible to the center of the range [{@code from}, {@code to}]. Choosing the

  }

  /**
   * Returns {@code throwable}'s cause, cast to {@code expectedCauseType}.
   *
   * <p>Prefer this method instead of manually casting an exception's cause. For example, {@code
   * (IOException) e.getCause()} throws a {@link ClassCastException} that discards the original
   * exception {@code e} if the cause is not an {@link IOException}, but {@code