在技术面试中，大厂可能会要求候选人实现或优化一些与图相关的算法，比如深度优先搜索（DFS）、广度优先搜索（BFS）和拓扑排序等。以下是三道与这些算法相关的面试题目，以及它们的Java源码示例。
1. 实现深度优先搜索（DFS）
题目：实现一个深度优先搜索算法，用于递归地遍历一个图的所有顶点。
源码：
import java.util.ArrayList;
import java.util.List;public class DFSGraph {private final int V; // 顶点的数量private final List<List<Integer>> adj; // 邻接表public DFSGraph(int V) {this.V = V;adj = new ArrayList<>(V);for (int i = 0; i < V; i++) {adj.add(new ArrayList<>());}}public void addEdge(int source, int dest) {adj.get(source).add(dest);}public void DFS(int v) {boolean[] visited = new boolean[V];DFSUtil(v, visited);}private void DFSUtil(int v, boolean[] visited) {visited[v] = true;System.out.print(v + " ");for (int i : adj.get(v)) {if (!visited[i]) {DFSUtil(i, visited);}}}public static void main(String[] args) {DFSGraph graph = new DFSGraph(4);graph.addEdge(0, 1);graph.addEdge(1, 2);graph.addEdge(2, 3);graph.addEdge(3, 1);graph.DFS(0);}
}
2. 实现广度优先搜索（BFS）
题目：实现一个广度优先搜索算法，用于遍历一个图，并找到最短路径。
源码：
import java.util.*;public class BFSGraph {private final int V; // 顶点的数量private final List<List<Integer>> adj; // 邻接表public BFSGraph(int V) {this.V = V;adj = new ArrayList<>(V);for (int i = 0; i < V; i++) {adj.add(new ArrayList<>());}}public void addEdge(int source, int dest) {adj.get(source).add(dest);}public void BFS(int s) {boolean[] visited = new boolean[V];Queue<Integer> queue = new LinkedList<>();visited[s] = true;queue.offer(s);while (!queue.isEmpty()) {int v = queue.poll();System.out.print(v + " ");for (Integer i : adj.get(v)) {if (!visited[i]) {visited[i] = true;queue.offer(i);}}}}public static void main(String[] args) {BFSGraph graph = new BFSGraph(4);graph.addEdge(0, 1);graph.addEdge(1, 2);graph.addEdge(2, 3);graph.addEdge(3, 1);graph.BFS(0);}
}
3. 检测图是否包含环
题目：给定一个图，使用DFS实现一个算法来检测图中是否存在环。
源码：
import java.util.ArrayList;
import java.util.List;public class GraphCycleDetection {private final int V; // 顶点的数量private final List<List<Integer>> adj; // 邻接表private boolean[] visited;private boolean[] recStack;private boolean isCycle;public GraphCycleDetection(int V) {this.V = V;adj = new ArrayList<>(V);for (int i = 0; i < V; i++) {adj.add(new ArrayList<>());}}public void addEdge(int source, int dest) {adj.get(source).add(dest);}public boolean isGraphCyclic() {visited = new boolean[V];recStack = new boolean[V];isCycle = false;for (int i = 0; i < V; i++) {if (isCycle) break;if (!visited[i]) {detectCycle(i);}}return isCycle;}private void detectCycle(int v) {if (isCycle) return;visited[v] = true;recStack[v] = true;for (Integer neighbour : adj.get(v)) {if (!visited[neighbour] && detectCycle(neighbour)) {isCycle = true;return;} else if (recStack[neighbour]) {isCycle = true;return;}}recStack[v] = false;}public static void main(String[] args) {GraphCycleDetection graph = new GraphCycleDetection(4);graph.addEdge(0, 1);graph.addEdge(1, 2);graph.addEdge(2, 3);graph.addEdge(3, 1); // 此边创建环System.out.println("图中是否存在环: " + graph.isGraphCyclic());}
}
以上三道题目分别考察了DFS、BFS的实现以及如何使用DFS来检测图中的环。这些题目都是大厂面试中常见的题型，旨在考察候选人对图算法的理解和实现能力。在技术面试中，大厂可能会要求候选人实现或优化一些与图相关的算法，比如深度优先搜索（DFS）、广度优先搜索（BFS）和拓扑排序等。以下是三道与这些算法相关的面试题目，以及它们的Java源码示例。
1. 实现深度优先搜索（DFS）
题目：实现一个深度优先搜索算法，用于递归地遍历一个图的所有顶点。
源码：
import java.util.ArrayList;
import java.util.List;public class DFSGraph {private final int V; // 顶点的数量private final List<List<Integer>> adj; // 邻接表public DFSGraph(int V) {this.V = V;adj = new ArrayList<>(V);for (int i = 0; i < V; i++) {adj.add(new ArrayList<>());}}public void addEdge(int source, int dest) {adj.get(source).add(dest);}public void DFS(int v) {boolean[] visited = new boolean[V];DFSUtil(v, visited);}private void DFSUtil(int v, boolean[] visited) {visited[v] = true;System.out.print(v + " ");for (int i : adj.get(v)) {if (!visited[i]) {DFSUtil(i, visited);}}}public static void main(String[] args) {DFSGraph graph = new DFSGraph(4);graph.addEdge(0, 1);graph.addEdge(1, 2);graph.addEdge(2, 3);graph.addEdge(3, 1);graph.DFS(0);}
}
2. 实现广度优先搜索（BFS）
题目：实现一个广度优先搜索算法，用于遍历一个图，并找到最短路径。
源码：
import java.util.*;public class BFSGraph {private final int V; // 顶点的数量private final List<List<Integer>> adj; // 邻接表public BFSGraph(int V) {this.V = V;adj = new ArrayList<>(V);for (int i = 0; i < V; i++) {adj.add(new ArrayList<>());}}public void addEdge(int source, int dest) {adj.get(source).add(dest);}public void BFS(int s) {boolean[] visited = new boolean[V];Queue<Integer> queue = new LinkedList<>();visited[s] = true;queue.offer(s);while (!queue.isEmpty()) {int v = queue.poll();System.out.print(v + " ");for (Integer i : adj.get(v)) {if (!visited[i]) {visited[i] = true;queue.offer(i);}}}}public static void main(String[] args) {BFSGraph graph = new BFSGraph(4);graph.addEdge(0, 1);graph.addEdge(1, 2);graph.addEdge(2, 3);graph.addEdge(3, 1);graph.BFS(0);}
}
3. 检测图是否包含环
题目：给定一个图，使用DFS实现一个算法来检测图中是否存在环。
源码：
import java.util.ArrayList;
import java.util.List;public class GraphCycleDetection {private final int V; // 顶点的数量private final List<List<Integer>> adj; // 邻接表private boolean[] visited;private boolean[] recStack;private boolean isCycle;public GraphCycleDetection(int V) {this.V = V;adj = new ArrayList<>(V);for (int i = 0; i < V; i++) {adj.add(new ArrayList<>());}}public void addEdge(int source, int dest) {adj.get(source).add(dest);}public boolean isGraphCyclic() {visited = new boolean[V];recStack = new boolean[V];isCycle = false;for (int i = 0; i < V; i++) {if (isCycle) break;if (!visited[i]) {detectCycle(i);}}return isCycle;}private void detectCycle(int v) {if (isCycle) return;visited[v] = true;recStack[v] = true;for (Integer neighbour : adj.get(v)) {if (!visited[neighbour] && detectCycle(neighbour)) {isCycle = true;return;} else if (recStack[neighbour]) {isCycle = true;return;}}recStack[v] = false;}public static void main(String[] args) {GraphCycleDetection graph = new GraphCycleDetection(4);graph.addEdge(0, 1);graph.addEdge(1, 2);graph.addEdge(2, 3);graph.addEdge(3, 1); // 此边创建环System.out.println("图中是否存在环: " + graph.isGraphCyclic());}
}
以上三道题目分别考察了DFS、BFS的实现以及如何使用DFS来检测图中的环。这些题目都是大厂面试中常见的题型，旨在考察候选人对图算法的理解和实现能力。
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