基于深度优先搜索，设计C语言算法，判断一个无向图是否为一棵树 ，并给出完整代码

下面是基于深度优先搜索的 C 语言算法，用于判断一个无向图是否为一棵树。

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>

#define MAX_VERTICES 100

// Graph structure using adjacency list
struct Graph {
    int V;
    struct Node* adjList[MAX_VERTICES];
};

// Node structure for adjacency list
struct Node {
    int dest;
    struct Node* next;
};

// Create a new node
struct Node* createNode(int dest) {
    struct Node* newNode = (struct Node*)malloc(sizeof(struct Node));
    newNode->dest = dest;
    newNode->next = NULL;
    return newNode;
}

// Create a graph with V vertices
struct Graph* createGraph(int V) {
    struct Graph* graph = (struct Graph*)malloc(sizeof(struct Graph));
    graph->V = V;

    for (int i = 0; i < V; i++) {
        graph->adjList[i] = NULL;
    }

    return graph;
}

// Add an edge between two vertices
void addEdge(struct Graph* graph, int src, int dest) {
    struct Node* newNode = createNode(dest);
    newNode->next = graph->adjList[src];
    graph->adjList[src] = newNode;

    newNode = createNode(src);
    newNode->next = graph->adjList[dest];
    graph->adjList[dest] = newNode;
}

// Check if there is a cycle in the graph
bool isCyclic(struct Graph* graph, int v, bool visited[], int parent) {
    visited[v] = true;

    for (struct Node* i = graph->adjList[v]; i != NULL; i = i->next) {
        int dest = i->dest;

        if (!visited[dest]) {
            if (isCyclic(graph, dest, visited, v)) {
                return true;
            }
        } else if (dest != parent) {
            return true;
        }
    }

    return false;
}

// Check if the graph is a tree
bool isTree(struct Graph* graph) {
    bool visited[MAX_VERTICES] = { false };

    // Check if there is a cycle in the graph
    if (isCyclic(graph, 0, visited, -1)) {
        return false;
    }

    // Check if all vertices are visited (i.e. connected graph)
    for (int i = 0; i < graph->V; i++) {
        if (!visited[i]) {
            return false;
        }
    }

    return true;
}

// Example usage
int main() {
    struct Graph* graph = createGraph(5);
    addEdge(graph, 1, 0);
    addEdge(graph, 0, 2);
    addEdge(graph, 2, 1);
    addEdge(graph, 0, 3);
    addEdge(graph, 3, 4);

    if (isTree(graph)) {
        printf("Graph is a tree\n");
    } else {
        printf("Graph is not a tree\n");
    }

    return 0;
}

这里使用了邻接表来存储图，`isCyclic()` 方法用来检查从节点 `v` 开始是否存在环，`isTree()` 方法则用来检查整个图是否是一棵树。