实现Gabow缩放算法的Java程序

Gabow 算法是一种缩放算法，旨在通过最初仅考虑每个相关输入值(例如边缘权重)的最高位来解决问题。然后它通过查看两个最高位来细化初始解决方案。它逐渐查看越来越多的高阶位，在每次迭代中细化解，直到检查所有位并计算出正确的解。

Basically, Gabow’s scaling algorithm is a scaling algorithm that solves a problem by initially considering only the highest order bit of each input value as an edge weight, then it refines the initial solution by looking at two highest-order bits and then refines the solution iteratively until it has visited all bits(in the graph) and computes the correct solution

程序：

1. 在方法getSCComponents()或它命名为每CONV烯ience
   • 最初，我们通过使用Java集合中的列表声明了一个图，并且
   • 然后我们通过应用dfs() 方法找到强连通分量
2. 在上面的方法中，我们实现了一种深度优先搜索方法来考虑图中的每一位，同时考虑预排序和重计数。
3. 在 main 方法中，我们将顶点数和边数添加到数组列表中，然后打印 getSCComponents() 方法以打印出图形给定值的强连通分量。
4. 打印并显示表示图中没有强连通分量的输出

算法：

1. 仅使用权重的最高有效位的从 v0 到 v 的最小权重路径的权重是从 v0 到 v 的最小权重路径的权重的近似值。
2. 然后，增量地引入额外的权重位来改进我们对最小权重路径的近似。
3. 在每次迭代中，对于某些边 (u, v)，我们将近似距离 u.dist – v.dist 的差异定义为 (u, v) 上的电位。
4. 我们将边的成本定义为它在某些迭代中的细化权重加上它的潜力：
   • li(u, v) = wi(u, v) + u.dist − v.dist。
5. 由于成本与路径望远镜的总和，这些成本保留了图中的最小权重路径。
6. 我们保证边的成本总是非负的。
7. 我们可以在成本值图上重复找到最小权重路径。

例子：

Java

// Java Program to Implement Gabow Scaling Algorithm
  
// Impoting input output classes
import java.io.*;
import java.util.*;
  
// Main Class
// Implementation of Gabow Scaling Algorithm
public class GFG {
  
    // Declaring variables
  
    // 1. Number of vertices
    private int V;
    // 2. Preorder number counter
    private int preCount;
    private int[] preorder;
  
    // 3. To check if v is visited
    private boolean[] visited;
  
    // 4. To check strong componenet containing v
    private boolean[] chk;
  
    // 5. To store given graph
    private List[] graph;
  
    // 6. To store all Integer elements
    private List > sccComp;
    private Stack stack1;
    private Stack stack2;
  
    // Method 1
    // To get all strongly connected components
    public List >
        getSCComponents(List[] graph)
    {
        V = graph.length;
        this.graph = graph;
        preorder = new int[V];
        chk = new boolean[V];
        visited = new boolean[V];
        stack1 = new Stack();
        stack2 = new Stack();
        sccComp = new ArrayList<>();
  
        for (int v = 0; v < V; v++)
            if (!visited[v])
                dfs(v);
  
        return sccComp;
    }
  
    // Method 2
    // Depth first search algorithm
    public void dfs(int v)
    {
        preorder[v] = preCount++;
        visited[v] = true;
        stack1.push(v);
        stack2.push(v);
  
        for (int w : graph[v]) {
            if (!visited[w])
                dfs(w);
            else if (!chk[w])
                while (preorder[stack2.peek()]
                       > preorder[w])
                    stack2.pop();
        }
        if (stack2.peek() == v) {
            stack2.pop();
            List component
                = new ArrayList();
            int w;
            do {
                w = stack1.pop();
                component.add(w);
                chk[w] = true;
            } while (w != v);
            sccComp.add(component);
        }
    }
  
    // Method 3
    // Main driver method
    public static void main(String[] args)
    {
  
        // Declaring and initializing variable to
        // number of vertices
        int V = 8;
  
        // Creating a graph
        @SuppressWarnings("unchecked")
        List[] g = new List[V];
        for (int i = 0; i < V; i++)
            g[i] = new ArrayList();
  
        // Accpeting all edges
        int E = 14;
  
        // Custom integers inputs for all edges
        int[] x = new int[] { 0, 1, 2, 3, 3, 7, 2,
                              7, 5, 6, 1, 4, 4, 1 };
        int[] y = new int[] { 1, 2, 3, 2, 7, 3, 6,
                              6, 6, 5, 5, 5, 0, 4 };
  
        for (int i = 0; i < E; i++) {
            int x1 = x[i];
            int y1 = y[i];
            g[x1].add(y1);
        }
  
        // Creating an object of main class i the main()
        // method
        GFG gab = new GFG();
  
        // Display message only
        System.out.println(
            "\nStrongly Connected Components for given edges : ");
  
        // now, printing all the strongly connected
        // components
        List > scComponents
            = gab.getSCComponents(g);
        System.out.println(scComponents);
    }
}

输出

Strongly Connected Components for give edges : 
[[5, 6], [7, 3, 2], [4, 1, 0]]

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