网络流分配问题Java

网络流分配问题是一类经典的组合优化问题，可以通过建立网络流模型来求解。以下是一个Java实现示例：

import java.util.*;

public class NetworkFlowAllocation {
    static int[][] capacity;
    static int[][] flow;
    static int[] parent;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        // 输入顶点个数和边数
        int n = sc.nextInt();
        int m = sc.nextInt();

        // 初始化capacity和flow数组
        capacity = new int[n][n];
        flow = new int[n][n];

        // 输入边的信息
        for (int i = 0; i < m; i++) {
            int u = sc.nextInt();
            int v = sc.nextInt();
            int c = sc.nextInt();
            capacity[u][v] = c;
        }

        // 计算最大流量
        int maxFlow = 0;
        while (bfs(0, n - 1)) {
            int pathFlow = Integer.MAX_VALUE;
            for (int v = n - 1; v != 0; v = parent[v]) {
                int u = parent[v];
                pathFlow = Math.min(pathFlow, capacity[u][v] - flow[u][v]);
            }
            for (int v = n - 1; v != 0; v = parent[v]) {
                int u = parent[v];
                flow[u][v] += pathFlow;
                flow[v][u] -= pathFlow;
            }
            maxFlow += pathFlow;
        }

        System.out.println("最大流量为：" + maxFlow);
    }

    // 广度优先搜索查找增广路径
    static boolean bfs(int s, int t) {
        Queue<Integer> queue = new LinkedList<>();
        boolean[] visited = new boolean[capacity.length];
        parent = new int[capacity.length];
        Arrays.fill(parent, -1);

        queue.offer(s);
        visited[s] = true;

        while (!queue.isEmpty()) {
            int u = queue.poll();
            for (int v = 0; v < capacity.length; v++) {
                if (!visited[v] && capacity[u][v] > flow[u][v]) {
                    parent[v] = u;
                    visited[v] = true;
                    queue.offer(v);
                }
            }
        }

        return visited[t];
    }
}

以上代码实现了一个最大流量计算器，通过输入顶点个数、边数和每条边的容量来计算最大流量。该实现采用了广度优先搜索算法来查找增广路径，并使用了一个parent数组来记录每个顶点在增广路径中的父节点。