/* 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.
 */

package gumtreediff.utils;

import java.util.Arrays;

/**
 * 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.
 * 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.

 * 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 double[][] costMatrix;
    private final int rows;
    private final int cols;
    private final int dim;
    private final double[] labelByWorker;
    private final double[] labelByJob;
    private final int[] minSlackWorkerByJob;
    private final double[] minSlackValueByJob;
    private final int[] matchJobByWorker;
    private final int[] 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.
     */
    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 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");
                }
                this.costMatrix[w] = Arrays.copyOf(costMatrix[w], this.dim);
            } else {
                this.costMatrix[w] = new double[this.dim];
            }
        }
        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[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).
     * 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) {
                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 {
                int worker = matchWorkerByJob[minSlackJob];
                committedWorkers[worker] = true;
                for (int j = 0; j < dim; j++) {
                    if (parentWorkerByCommittedJob[j] == -1) {
                        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[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[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[w][j] < min) {
                    min = costMatrix[w][j];
                }
            }
            for (int j = 0; j < dim; j++) {
                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[w][j] < min[j]) {
                    min[j] = costMatrix[w][j];
                }
            }
        }
        for (int w = 0; w < dim; w++) {
            for (int j = 0; j < dim; 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;
            }
        }
    }
}
