import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import scala.Tuple2;

/* Copyright (c) 2012 Kevin L. Stern
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 */

/**
 * An implementation of the Hungarian algorithm for solving the assignment problem. An instance of
 * the assignment problem consists of a number of workers along with a number of jobs and a cost
 * matrix which gives the cost of assigning the i'th worker to the j'th job at position (i, j). The
 * goal is to find an assignment of workers to jobs so that no job is assigned more than one worker
 * and so that no worker is assigned to more than one job in such a manner so as to minimize the
 * total cost of completing the jobs. <p>
 *
 * An assignment for a cost matrix that has more workers than jobs will necessarily include
 * unassigned workers, indicated by an assignment value of -1; in no other circumstance will there
 * be unassigned workers. Similarly, an assignment for a cost matrix that has more jobs than workers
 * will necessarily include unassigned jobs; in no other circumstance will there be unassigned jobs.
 * For completeness, an assignment for a square cost matrix will give exactly one unique worker to
 * each job. <p>
 *
 * This version of the Hungarian algorithm runs in time O(n^3), where n is the maximum among the
 * number of workers and the number of jobs.
 *
 * @author Kevin L. Stern
 */
public class HungarianAlgorithm {

  private final Map<Tuple2<Integer, Integer>, Double> costMatrix;
  private final int rows, cols, dim;
  private final double[] labelByWorker, labelByJob;
  private final int[] minSlackWorkerByJob;
  private final double[] minSlackValueByJob;
  private final int[] matchJobByWorker, matchWorkerByJob;
  private final int[] parentWorkerByCommittedJob;
  private final boolean[] committedWorkers;

  /**
   * Construct an instance of the algorithm.
   *
   * @param costMatrix the cost matrix, where matrix[i][j] holds the cost of assigning worker i to
   * job j, for all i, j. The cost matrix must not be irregular in the sense that all rows must be
   * the same length; in addition, all entries must be non-infinite numbers.
   */
  public HungarianAlgorithm(double[][] costMatrix) {
    this.dim = Math.max(costMatrix.length, costMatrix[0].length);
    this.rows = costMatrix.length;
    this.cols = costMatrix[0].length;
    this.costMatrix = new HashMap<>();
//    this.costMatrix = new double[this.dim][this.dim];
    for (int w = 0; w < this.dim; w++) {
      if (w < costMatrix.length) {
        if (costMatrix[w].length != this.cols) {
          throw new IllegalArgumentException("Irregular cost matrix");
        }
        for (int j = 0; j < this.cols; j++) {
          if (Double.isInfinite(costMatrix[w][j])) {
            throw new IllegalArgumentException("Infinite cost");
          }
          if (Double.isNaN(costMatrix[w][j])) {
            throw new IllegalArgumentException("NaN cost");
          }
          if(costMatrix[w][j] != 0.) {
            this.costMatrix.put(new Tuple2<>(w, j), costMatrix[w][j]);
          }
        }
      } else {
        System.err.println("ERROR HERE");
        System.exit(1);
      }
    }
    labelByWorker = new double[this.dim];
    labelByJob = new double[this.dim];
    minSlackWorkerByJob = new int[this.dim];
    minSlackValueByJob = new double[this.dim];
    committedWorkers = new boolean[this.dim];
    parentWorkerByCommittedJob = new int[this.dim];
    matchJobByWorker = new int[this.dim];
    Arrays.fill(matchJobByWorker, -1);
    matchWorkerByJob = new int[this.dim];
    Arrays.fill(matchWorkerByJob, -1);
  }

  public HungarianAlgorithm(Map<Tuple2<Integer, Integer>, Double> sim, int rows, int cols) {
    this.dim = Math.max(rows, cols);
    this.rows = rows;
    this.cols = cols;
    this.costMatrix = new HashMap<>(sim);
    labelByWorker = new double[this.dim];
    labelByJob = new double[this.dim];
    minSlackWorkerByJob = new int[this.dim];
    minSlackValueByJob = new double[this.dim];
    committedWorkers = new boolean[this.dim];
    parentWorkerByCommittedJob = new int[this.dim];
    matchJobByWorker = new int[this.dim];
    Arrays.fill(matchJobByWorker, -1);
    matchWorkerByJob = new int[this.dim];
    Arrays.fill(matchWorkerByJob, -1);
  }

  /**
   * Compute an initial feasible solution by assigning zero labels to the workers and by assigning
   * to each job a label equal to the minimum cost among its incident edges.
   */
  protected void computeInitialFeasibleSolution() {
    for (int j = 0; j < dim; j++) {
      labelByJob[j] = Double.POSITIVE_INFINITY;
    }
    for (int w = 0; w < dim; w++) {
      for (int j = 0; j < dim; j++) {
        if (costMatrix.getOrDefault(new Tuple2<>(w, j), Double.MAX_VALUE) < labelByJob[j]) {
          labelByJob[j] = costMatrix.getOrDefault(new Tuple2<>(w, j), Double.MAX_VALUE);
        }
//        if (costMatrix[w][j] < labelByJob[j]) {
//          labelByJob[j] = costMatrix[w][j];
//        }
      }
    }
  }

  /**
   * Execute the algorithm.
   *
   * @return the minimum cost matching of workers to jobs based upon the provided cost matrix. A
   * matching value of -1 indicates that the corresponding worker is unassigned.
   */
  public int[] execute() {
    /*
     * Heuristics to improve performance: Reduce rows and columns by their
     * smallest element, compute an initial non-zero dual feasible solution and
     * create a greedy matching from workers to jobs of the cost matrix.
     */
    reduce();
    computeInitialFeasibleSolution();
    greedyMatch();

    int w = fetchUnmatchedWorker();
    while (w < dim) {
      initializePhase(w);
      executePhase();
      w = fetchUnmatchedWorker();
    }
    int[] result = Arrays.copyOf(matchJobByWorker, rows);
    for (w = 0; w < result.length; w++) {
      if (result[w] >= cols) {
        result[w] = -1;
      }
    }
    return result;
  }

  /**
   * Execute a single phase of the algorithm. A phase of the Hungarian algorithm consists of
   * building a set of committed workers and a set of committed jobs from a root unmatched worker by
   * following alternating unmatched/matched zero-slack edges. If an unmatched job is encountered,
   * then an augmenting path has been found and the matching is grown. If the connected zero-slack
   * edges have been exhausted, the labels of committed workers are increased by the minimum slack
   * among committed workers and non-committed jobs to create more zero-slack edges (the labels of
   * committed jobs are simultaneously decreased by the same amount in order to maintain a feasible
   * labeling). <p>
   *
   * The runtime of a single phase of the algorithm is O(n^2), where n is the dimension of the
   * internal square cost matrix, since each edge is visited at most once and since increasing the
   * labeling is accomplished in time O(n) by maintaining the minimum slack values among
   * non-committed jobs. When a phase completes, the matching will have increased in size.
   */
  protected void executePhase() {
    while (true) {
      int minSlackWorker = -1, minSlackJob = -1;
      double minSlackValue = Double.POSITIVE_INFINITY;
      for (int j = 0; j < dim; j++) {
        if (parentWorkerByCommittedJob[j] == -1) {
          if (minSlackValueByJob[j] < minSlackValue) {
            minSlackValue = minSlackValueByJob[j];
            minSlackWorker = minSlackWorkerByJob[j];
            minSlackJob = j;
          }
        }
      }
      if (minSlackValue > 0) {
        updateLabeling(minSlackValue);
      }
      parentWorkerByCommittedJob[minSlackJob] = minSlackWorker;
      if (matchWorkerByJob[minSlackJob] == -1) {
        /*
         * An augmenting path has been found.
         */
        int committedJob = minSlackJob;
        int parentWorker = parentWorkerByCommittedJob[committedJob];
        while (true) {
          int temp = matchJobByWorker[parentWorker];
          match(parentWorker, committedJob);
          committedJob = temp;
          if (committedJob == -1) {
            break;
          }
          parentWorker = parentWorkerByCommittedJob[committedJob];
        }
        return;
      } else {
        /*
         * Update slack values since we increased the size of the committed
         * workers set.
         */
        int worker = matchWorkerByJob[minSlackJob];
        committedWorkers[worker] = true;
        for (int j = 0; j < dim; j++) {
          if (parentWorkerByCommittedJob[j] == -1) {
            double slack = costMatrix.getOrDefault(new Tuple2<>(worker, j), Double.MAX_VALUE)
                - labelByWorker[worker]
                - labelByJob[j];
//            double slack = costMatrix[worker][j] - labelByWorker[worker]
//                - labelByJob[j];
            if (minSlackValueByJob[j] > slack) {
              minSlackValueByJob[j] = slack;
              minSlackWorkerByJob[j] = worker;
            }
          }
        }
      }
    }
  }

  /**
   * @return the first unmatched worker or {@link #dim} if none.
   */
  protected int fetchUnmatchedWorker() {
    int w;
    for (w = 0; w < dim; w++) {
      if (matchJobByWorker[w] == -1) {
        break;
      }
    }
    return w;
  }

  /**
   * Find a valid matching by greedily selecting among zero-cost matchings. This is a heuristic to
   * jump-start the augmentation algorithm.
   */
  protected void greedyMatch() {
    for (int w = 0; w < dim; w++) {
      for (int j = 0; j < dim; j++) {
        if (matchJobByWorker[w] == -1 && matchWorkerByJob[j] == -1
            && costMatrix.getOrDefault(new Tuple2<>(w,j), Double.MAX_VALUE) - labelByWorker[w] - labelByJob[j] == 0) {
//        if (matchJobByWorker[w] == -1 && matchWorkerByJob[j] == -1
//            && costMatrix[w][j] - labelByWorker[w] - labelByJob[j] == 0) {
          match(w, j);
        }
      }
    }
  }

  /**
   * Initialize the next phase of the algorithm by clearing the committed workers and jobs sets and
   * by initializing the slack arrays to the values corresponding to the specified root worker.
   *
   * @param w the worker at which to root the next phase.
   */
  protected void initializePhase(int w) {
    Arrays.fill(committedWorkers, false);
    Arrays.fill(parentWorkerByCommittedJob, -1);
    committedWorkers[w] = true;
    for (int j = 0; j < dim; j++) {
      minSlackValueByJob[j] = costMatrix.getOrDefault(new Tuple2<>(w, j), Double.MAX_VALUE) - labelByWorker[w]
          - labelByJob[j];
//      minSlackValueByJob[j] = costMatrix[w][j] - labelByWorker[w]
//          - labelByJob[j];
      minSlackWorkerByJob[j] = w;
    }
  }

  /**
   * Helper method to record a matching between worker w and job j.
   */
  protected void match(int w, int j) {
    matchJobByWorker[w] = j;
    matchWorkerByJob[j] = w;
  }

  /**
   * Reduce the cost matrix by subtracting the smallest element of each row from all elements of the
   * row as well as the smallest element of each column from all elements of the column. Note that
   * an optimal assignment for a reduced cost matrix is optimal for the original cost matrix.
   */
  protected void reduce() {
    for (int w = 0; w < dim; w++) {
      double min = Double.POSITIVE_INFINITY;
      for (int j = 0; j < dim; j++) {
        if (costMatrix.getOrDefault(new Tuple2<>(w,j), Double.MAX_VALUE) < min) {
          min = costMatrix.getOrDefault(new Tuple2<>(w,j), Double.MAX_VALUE);
        }
//        if (costMatrix[w][j] < min) {
//          min = costMatrix[w][j];
//        }
      }
      for (int j = 0; j < dim; j++) {
        costMatrix.put(new Tuple2<>(w, j), costMatrix.getOrDefault(new Tuple2<>(w,j), Double.MAX_VALUE) - min);
//        costMatrix[w][j] -= min;
      }
    }
    double[] min = new double[dim];
    for (int j = 0; j < dim; j++) {
      min[j] = Double.POSITIVE_INFINITY;
    }
    for (int w = 0; w < dim; w++) {
      for (int j = 0; j < dim; j++) {
        if (costMatrix.getOrDefault(new Tuple2<>(w,j), Double.MAX_VALUE) < min[j]) {
          min[j] = costMatrix.getOrDefault(new Tuple2<>(w,j), Double.MAX_VALUE);
        }
//        if (costMatrix[w][j] < min[j]) {
//          min[j] = costMatrix[w][j];
//        }
      }
    }
    for (int w = 0; w < dim; w++) {
      for (int j = 0; j < dim; j++) {
        costMatrix.put(new Tuple2<>(w, j), costMatrix.getOrDefault(new Tuple2<>(w,j), Double.MAX_VALUE) - min[j]);
//        costMatrix[w][j] -= min[j];
      }
    }
  }

  /**
   * Update labels with the specified slack by adding the slack value for committed workers and by
   * subtracting the slack value for committed jobs. In addition, update the minimum slack values
   * appropriately.
   */
  protected void updateLabeling(double slack) {
    for (int w = 0; w < dim; w++) {
      if (committedWorkers[w]) {
        labelByWorker[w] += slack;
      }
    }
    for (int j = 0; j < dim; j++) {
      if (parentWorkerByCommittedJob[j] != -1) {
        labelByJob[j] -= slack;
      } else {
        minSlackValueByJob[j] -= slack;
      }
    }
  }
}