Freud's algorithm of data structure and algorithm (36)

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Introduction to Freud Algorithm

Freud algorithm analysis

1. Taking the vertex A as the middle vertex, the distance from B-> A-> C is from N-> 9, and the same is true from C to B; the distance from C-> A-> G is from N-> 12, and the distance from G-C
2. Replace the intermediate vertices and perform operations in a loop until all vertices are updated as intermediate vertices and the calculation ends

Code

public class FloydAlgorithm {
    private static final int N = 65535;

    public static void main(String args[]) {
        char[] vertex = {'A', 'B', 'C', 'D', 'E', 'F', 'G'};
        //创建邻接矩阵
        int[][] matrix = new int[vertex.length][vertex.length];
        matrix[0] = new int[]{0, 5, 7, N, N, N, 2};
        matrix[1] = new int[]{5, 0, N, 9, N, N, 3};
        matrix[2] = new int[]{7, N, 0, N, 8, N, N};
        matrix[3] = new int[]{N, 9, N, 0, N, 4, N};
        matrix[4] = new int[]{N, N, 8, N, 0, 5, 4};
        matrix[5] = new int[]{N, N, N, 4, 5, 0, 6};
        matrix[6] = new int[]{2, 3, N, N, 4, 6, 0};

        //创建 Graph 对象
        Graph graph = new Graph(matrix, vertex);
        //调用弗洛伊德算法
        graph.floyd();
        graph.print();
    }
}

class Graph {
    char[] vertexs; // 存放顶点
    int[][] dis;    // 保存从各个顶点出发到其他顶点的距离
    int[][] pre;    // 保存到达目标顶点的前驱顶点

    public Graph(int[][] matrix, char[] vertexs) {
        this.dis = matrix;
        this.vertexs = vertexs;
        this.pre = new int[vertexs.length][vertexs.length];
        // 初始化pre,存放前驱顶点下标
        for (int i = 0; i < vertexs.length; i++) {
//            for (int j = 0; j < vertexs.length; j++) {
//                pre[i][j] = i;
//            }
            Arrays.fill(pre[i], i);
        }
    }

    public void print() {
        for (int[] di : dis) {
            for (int i : di) {
                System.out.printf("%12d", i);
            }
            System.out.println();
        }
        System.out.println("从i到j的中间顶点:");
        for (int[] ints : pre) {
            for (int i : ints) {
                System.out.printf("%12c", this.vertexs[i]);
            }
            System.out.println();
        }

        System.out.println("即:");
        for (int i = 0; i < pre.length; i++) {
            for (int j = 0; j < pre.length; j++) {
                System.out.print(vertexs[i] + "-->" + vertexs[pre[i][j]] + "-->" + vertexs[j]+"    ");
            }
            System.out.println();
        }
    }

    // 弗洛伊德算法
    public void floyd() {
        // 保存距离(权值)
        int len = 0;
        // 从中间顶点k遍历[A,B,C,D,E,F.G]
        for (int k = 0; k < dis.length; k++) {
            // 从i顶点开始出发[A,B,C,D,E,F.G]
            for (int i = 0; i < dis.length; i++) {
                // j是到达的终点[A,B,C,D,E,F.G]
                for (int j = 0; j < dis.length; j++) {
                    // 从i顶点出发经过k中间顶点到达j顶点的距离
                    len = dis[i][k] + dis[k][j];
                    // 如果i,k,j连通距离小于i,j直连的距离
                    if (len < dis[i][j]) {
                        // 将小的更新给dis矩阵(两点距离)
                        dis[i][j] = len;
                        // 更新终点的前驱点
                        pre[i][j] = pre[k][j];
                    }
                }
            }
        }
    }
}

GitHub: data structure and algorithm source code