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简单的Floyd-Warshall算法Java实现似乎不起作用?

发布时间:2020-12-15 02:11:19 所属栏目:Java 来源:网络整理
导读:我一直在尝试用 Java实现Floyd-Warshall算法而不使用“三循环嵌套”方式,但我似乎无法弄清楚我在代码中出错的地方. 这是显示我的顶点如何连接的地图.白色数字是顶点,黑色数字是连接顶点之间的距离. 顶点地图:http://i.imgur.com/htcaA4y.png 运行迭代后,我
我一直在尝试用 Java实现Floyd-Warshall算法而不使用“三循环嵌套”方式,但我似乎无法弄清楚我在代码中出错的地方.

这是显示我的顶点如何连接的地图.白色数字是顶点,黑色数字是连接顶点之间的距离.

顶点地图:http://i.imgur.com/htcaA4y.png

运行迭代后,我得到以下最终距离和序列矩阵.说“出错了”的是最终序列矩阵的第8列(右边的那个).为了从任何其他顶点到达顶点8,路径必须首先从顶点8变为9,然后变为10(根据矩阵不是这种情况 – 它从顶点8直接变为10).

输出矩阵:http://i.imgur.com/o6fQweH.png

这是代码.这似乎是什么问题?

import java.util.ArrayList;

public class Main_Simple {

    public static void main(String[] args) {

        // 1. Setup the distance matrix
        //  -inf for vertices that are not connected
        //  -### for edge weights of vertices that are connected
        //  -0 across the diagonal

        int inf = 1000000; // Temporary 'infinity' variable

        // Initial distance matrix must be n x n
        int[][] initialDistanceMatrix = {
                {0,1,inf,inf},{1,{inf,2,2},1},0}
        };

        // 2. Setup the sequence matrix
        //  -All of column-1 are ones
        //  -All of column-2 are twos
        //  -etc
        //  -0 across the diagonal

        // Initial sequence matrix must be the same size as the initial distance matrix
        int[][] initialSequenceMatrix = new int[initialDistanceMatrix.length][initialDistanceMatrix.length];
        for (int row = 0; row < initialSequenceMatrix.length; row++) {
            for (int column = 0; column < initialSequenceMatrix.length; column++) {
                if (row == column) {
                    initialSequenceMatrix[row][column] = 0;
                } else {
                    initialSequenceMatrix[row][column] = column + 1; // +1 to account 0-based array
                }
            }
        }

        // 3. Iterate through the matrices (n-1) times
        //  -On the kth iteration,copy the kth column and kth row down to the next distance and sequence matrix
        //  -On the kth iteration,check matrix (k-1) and take the minimum of the following two:
        //      -d(ij)
        //      -d(ik)+d(kj)
        //      where i = row number,j = column number,and k = iteration number
        //  -After the distance matrix has been calculated,compare the current distance matrix to the previous.
        //  If the numbers are the same,keep the sequence matrix the same.  Otherwise,change the sequence
        //  matrix to the current iteration's number.

        ArrayList<int[][]> distanceMatrices = new ArrayList<int[][]>();
        distanceMatrices.add(initialDistanceMatrix);

        ArrayList<int[][]> sequenceMatrices = new ArrayList<int[][]>();
        sequenceMatrices.add(initialSequenceMatrix);

        // Print the matrices to make sure they are made correctly
        printMatrix(initialDistanceMatrix,"Initial distance matrix");
        printMatrix(initialSequenceMatrix,"Initial sequence matrix");

        // Matrix Iteration Loops
        for (int iteration = 1; iteration < initialDistanceMatrix.length; iteration++) {

            // Initialize new distance matrix
            int[][] currentDistanceMatrix = new int[initialDistanceMatrix.length][initialDistanceMatrix.length];
            for (int row = 0; row < currentDistanceMatrix.length; row++) {
                for (int column = 0; column < currentDistanceMatrix.length; column++) {
                    currentDistanceMatrix[row][column] = 0;
                } // ends 'column' loop
            } // ends 'row' loop

            // Distance Matrix iteration
            for (int row = 0; row < currentDistanceMatrix.length; row++) {
                for (int column = 0; column < currentDistanceMatrix.length; column++) {

                    if (row == column) { // If you are on the diagonal,insert '0'
                        currentDistanceMatrix[row][column] = 0;
                    } else if (row == (iteration - 1) || column == (iteration - 1)) { // Brings down the row and column of the iteration (-1 to account 0-based array)
                        currentDistanceMatrix[row][column] = distanceMatrices.get(iteration - 1)[row][column];
                    } else { // If you are on any other square...
                        int Dij = distanceMatrices.get(iteration - 1)[row][column];
                        int Dik_Dkj = distanceMatrices.get(iteration - 1)[row][iteration - 1] + distanceMatrices.get(iteration - 1)[iteration - 1][column];

                        if (Dij > Dik_Dkj) currentDistanceMatrix[row][column] = Dik_Dkj;
                        else currentDistanceMatrix[row][column] = Dij;
                    }

                } // ends 'column' loop
            } // ends 'row' loop

            // Add the distance matrix to the matrix array
            distanceMatrices.add(currentDistanceMatrix);

            // Initialize new sequence matrix
            int[][] currentSequenceMatrix = new int[initialDistanceMatrix.length][initialDistanceMatrix.length];

            // Sequence Matrix iteration
            for (int row = 0; row < currentSequenceMatrix.length; row++) {
                for (int column = 0; column < currentSequenceMatrix.length; column++) {

                    if (row == column) { // If you are along the diagonal...
                        currentSequenceMatrix[row][column] = 0;
                    } else if (row == (iteration - 1) || column == (iteration - 1)) { // If you are on the same row or column as the iteration...
                        currentSequenceMatrix[row][column] = sequenceMatrices.get(iteration - 1)[row][column];
                    } else { // If you are on any other square...
                        // You need to check the current distance matrix to see if it matches the previous.
                        // If it does match,keep the same number.
                        // If it changed,changed the number in that cell to the current iteration

                        // Compare the most recent distance matrix to the one before it
                        if (distanceMatrices.get(distanceMatrices.size() - 1)[row][column] == distanceMatrices.get(distanceMatrices.size() - 2)[row][column]) {
                            currentSequenceMatrix[row][column] = sequenceMatrices.get(sequenceMatrices.size() - 1)[row][column];
                        } else {
                            currentSequenceMatrix[row][column] = iteration;
                        }
                    }

                } // ends 'column' loop
            } // ends 'row' loop

            // Add the sequence matrix to the matrix array
            sequenceMatrices.add(currentSequenceMatrix);

        } // ends matrix iteration loops

        System.out.println("-------------------------------------------------------");

        printMatrix(distanceMatrices.get(distanceMatrices.size() - 1),"Final Distance Matrix");
        printMatrix(sequenceMatrices.get(sequenceMatrices.size() - 1),"Final Sequence Matrix");

    } // ends main method

    public static void printMatrix(int[][] matrix,String message) {
        System.out.println("n" + message);
        for (int row = 0; row < matrix.length; row++) {
            for (int column = 0; column < matrix.length; column++) {
                System.out.print(matrix[row][column] + "t");
            } // ends 'column' loop
            System.out.println();
        } // ends 'row' loop
        System.out.println();
    }

} // ends class Main_Simple

解决方法

您没有在第一个循环上正确迭代所有顶点.

for (int iteration = 1; iteration < initialDistanceMatrix.length; iteration++)

应该:

for (int iteration = 1; iteration < initialDistanceMatrix.length + 1; iteration++)

或者,更好的是,不是使用迭代 – 1为所有数组索引,使用迭代,然后您可以使用:

for (int iteration = 0; iteration < initialDistanceMatrix.length; iteration++)

这样可以使所有索引保持零,而不是混合它们.只有这个代码更改(以及更小的测试用例)我得到了正确的答案.

(编辑:李大同)

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