【代码随想录Day58】图论Part09

dijkstra（堆优化版）精讲

题目链接/文章讲解：代码随想录

import java.util.*;class Edge {int to;  // 邻接顶点int val; // 边的权重Edge(int to, int val) {this.to = to;this.val = val;}
}class Pair<U, V> {public final U first;  // 节点public final V second; // 从源点到该节点的权重public Pair(U first, V second) {this.first = first;this.second = second;}
}public class Main {public static void main(String[] args) {Scanner scanner = new Scanner(System.in);// 读取节点数和边数int n = scanner.nextInt();int m = scanner.nextInt();// 创建图的邻接表List<List<Edge>> graph = new ArrayList<>(n + 1);for (int i = 0; i <= n; i++) {graph.add(new ArrayList<>());}// 读取边的信息for (int i = 0; i < m; i++) {int p1 = scanner.nextInt();int p2 = scanner.nextInt();int val = scanner.nextInt();graph.get(p1).add(new Edge(p2, val));}int start = 1;  // 起点int end = n;    // 终点// 存储从源点到每个节点的最短距离int[] minDist = new int[n + 1];Arrays.fill(minDist, Integer.MAX_VALUE);minDist[start] = 0;  // 起始点到自身的距离为0// 记录顶点是否被访问过boolean[] visited = new boolean[n + 1];// 优先队列，用于选择当前最短路径的节点PriorityQueue<Pair<Integer, Integer>> pq = new PriorityQueue<>(Comparator.comparingInt(pair -> pair.second));// 初始化队列，添加源点pq.add(new Pair<>(start, 0));while (!pq.isEmpty()) {// 取出当前距离源点最近的节点Pair<Integer, Integer> cur = pq.poll();int currentNode = cur.first;// 如果该节点已被访问，跳过if (visited[currentNode]) continue;// 标记该节点为已访问visited[currentNode] = true;// 更新与当前节点相连的邻接节点的路径for (Edge edge : graph.get(currentNode)) {// 如果该邻接节点未被访问且新路径更短，则更新最短路径if (!visited[edge.to] && minDist[currentNode] + edge.val < minDist[edge.to]) {minDist[edge.to] = minDist[currentNode] + edge.val;pq.add(new Pair<>(edge.to, minDist[edge.to])); // 将新路径加入优先队列}}}// 输出结果System.out.println(minDist[end] == Integer.MAX_VALUE ? -1 : minDist[end]);}
}

Bellman_ford 算法精讲

题目链接/文章讲解：代码随想录

import java.util.*;public class Main {// 定义边的内部类static class Edge {int from; // 起始节点int to;   // 结束节点int val;  // 边的权重public Edge(int from, int to, int val) {this.from = from;this.to = to;this.val = val;}}public static void main(String[] args) {// 输入处理Scanner scanner = new Scanner(System.in);int numberOfNodes = scanner.nextInt(); // 节点数量int numberOfEdges = scanner.nextInt();  // 边的数量List<Edge> edges = new ArrayList<>();// 读取每一条边的信息for (int i = 0; i < numberOfEdges; i++) {int from = scanner.nextInt();int to = scanner.nextInt();int val = scanner.nextInt();edges.add(new Edge(from, to, val));}// 存储从起点到各节点的最小距离int[] minDistance = new int[numberOfNodes + 1];Arrays.fill(minDistance, Integer.MAX_VALUE); // 初始化最小距离为无穷大minDistance[1] = 0; // 起点到自身的距离为0// 执行 Bellman-Ford 算法，放松所有边 n-1 次for (int i = 1; i < numberOfNodes; i++) {for (Edge edge : edges) {// 如果起始节点的距离不为无穷大，且通过当前边可以找到更短的路径if (minDistance[edge.from] != Integer.MAX_VALUE) {int newDistance = minDistance[edge.from] + edge.val;if (newDistance < minDistance[edge.to]) {minDistance[edge.to] = newDistance; // 更新最小距离}}}}// 输出结果if (minDistance[numberOfNodes] == Integer.MAX_VALUE) {System.out.println("unconnected"); // 如果目标节点不可达} else {System.out.println(minDistance[numberOfNodes]); // 输出目标节点的最小距离}scanner.close(); // 关闭扫描器以释放资源}
}