旅行商问题的分支限界算法C语言和伪代码

旅行商问题（Traveling Salesman Problem, TSP）是一个经典的组合优化问题，涉及找到一条经过所有城市恰好一次然后返回起点的最短路径。分支限界算法是一种搜索策略，常用于解决这类NP完全问题。

在C语言中实现旅行商问题的分支限界法，首先需要设计数据结构（如邻接矩阵或向量表示城市），以及函数来计算节点的价值、剪枝等操作。以下是简单的伪代码描述：

// Pseudo-code for Branch-and-Bound algorithm for TSP in C

typedef struct Node {
    int city;
    int cost; // Cost to reach this city from the previous one
    bool visited;
    Node* next;
} Node;

Node* create_node(int city) {
    // Create a new node with given city and initialize values
}

void tsp_branch_bound(Node** current, int& best_cost) {
    if (current->visited == true) { // All cities visited
        update_best_path(current, best_cost);
        return prune_tree(current); // Prune branches with higher costs
    }
    
    for (int i = 0; i < num_cities; i++) {
        if (!current->next[i].visited) {
            current->next[i].visited = true;
            tsp_branch_bound(&current->next[i], best_cost); // Recursive call
            current->next[i].visited = false; // Backtracking
        }
    }
}

// Function to calculate value of a solution and update best_cost
void update_best_path(Node* path, int& best_cost) {
    // Calculate cost of the path and compare with best_cost
    if (path->cost + get_city_cost(path->city) < best_cost) {
        best_cost = path->cost;
    }
}

// Prune branches where lower bound exceeds current best cost
bool prune_tree(Node* node) {
    // Calculate lower bound and prune if it's worse than best_cost
    if (lower_bound(node) > best_cost) {
        return true;
    }
    return false;
}