// Copyright (c) 2015-2023 MinIO, Inc.
//
// This file is part of MinIO Object Storage stack
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful

## Additional servers { #additional-servers }

/// warning

This is a more advanced use case. Feel free to skip it.

///

By default, **FastAPI** will create a `server` in the OpenAPI schema with the URL for the `root_path`.

     * linear-time operation, and it can even have side effects. Thus, we limit the special case to
     * List, which is _even more likely_ to have size() implemented to be fast and side-effect-free.
     *
     * We could consider recognizing specific other collections as safe (like ImmutableCollection,
     * except ContiguousSet!) or as not worth this optimization (CopyOnWriteArrayList?).
     */

// Copyright (c) 2015-2024 MinIO, Inc.
//
// This file is part of MinIO Object Storage stack
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful

    return x > 0 & (x & (x - 1)) == 0;
  }

  /**
   * Returns 1 if {@code x < y} as unsigned longs, and 0 otherwise. Assumes that x - y fits into a
   * signed long. The implementation is branch-free, and benchmarks suggest it is measurably faster
   * than the straightforward ternary expression.
   */
  @VisibleForTesting
  static int lessThanBranchFree(long x, long y) {
    // Returns the sign bit of x - y.

// Copyright (c) 2015-2021 MinIO, Inc.
//
// This file is part of MinIO Object Storage stack
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful

// Copyright (c) 2015-2025 MinIO, Inc.
//
// This file is part of MinIO Object Storage stack
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful

// Copyright (c) 2015-2021 MinIO, Inc.
//
// This file is part of MinIO Object Storage stack
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful

		return
	}
	z.Total, err = dc.ReadUint64()
	if err != nil {
		err = msgp.WrapError(err, "Total")
		return
	}
	z.Free, err = dc.ReadUint64()
	if err != nil {
		err = msgp.WrapError(err, "Free")
		return
	}
	z.Used, err = dc.ReadUint64()
	if err != nil {
		err = msgp.WrapError(err, "Used")
		return
	}
	z.UsedInodes, err = dc.ReadUint64()

   */
  public static <N> boolean hasCycle(Graph<N> graph) {
    int numEdges = graph.edges().size();
    if (numEdges == 0) {
      return false; // An edge-free graph is acyclic by definition.
    }
    if (!graph.isDirected() && numEdges >= graph.nodes().size()) {
      return true; // Optimization for the undirected case: at least one cycle must exist.
    }