使用C语言和分支限界法,解决世界名画陈列馆问题
时间: 2024-02-04 22:01:40 浏览: 67
好的,下面是使用C语言和分支限界法解决世界名画陈列馆问题的代码示例:
```c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define MAX_ROOMS 10 // 最多展厅数
#define MAX_PICTURES 20 // 最多画作数
// 展厅结构体
typedef struct {
int id; // 展厅编号
int num_of_pics; // 展厅内画作数量
int* pics; // 展厅内画作编号数组
} Room;
// 画作结构体
typedef struct {
int id; // 画作编号
int room_id; // 画作所在展厅编号
} Picture;
// 优先队列节点结构体
typedef struct {
int cost; // 到达该状态的代价
int room_id; // 当前展厅编号
int* visited_rooms; // 已经访问过的展厅编号数组
int num_of_visited; // 已经访问过的展厅数量
} Node;
// 全局变量
int num_of_rooms; // 展厅数量
int num_of_pictures; // 画作数量
Room rooms[MAX_ROOMS]; // 展厅数组
Picture pictures[MAX_PICTURES]; // 画作数组
int goal_room_id; // 目标展厅编号
// 初始化展厅
void init_rooms() {
int i;
for (i = 0; i < MAX_ROOMS; i++) {
rooms[i].id = -1;
rooms[i].num_of_pics = 0;
rooms[i].pics = NULL;
}
}
// 初始化画作
void init_pictures() {
int i;
for (i = 0; i < MAX_PICTURES; i++) {
pictures[i].id = -1;
pictures[i].room_id = -1;
}
}
// 读取输入数据
void read_data() {
int i, j;
scanf("%d", &num_of_rooms);
for (i = 0; i < num_of_rooms; i++) {
scanf("%d", &rooms[i].id);
scanf("%d", &rooms[i].num_of_pics);
rooms[i].pics = (int*)malloc(rooms[i].num_of_pics * sizeof(int));
for (j = 0; j < rooms[i].num_of_pics; j++) {
scanf("%d", &rooms[i].pics[j]);
pictures[rooms[i].pics[j]].id = rooms[i].pics[j];
pictures[rooms[i].pics[j]].room_id = rooms[i].id;
}
}
scanf("%d", &num_of_pictures);
scanf("%d", &goal_room_id);
}
// 判断一个展厅是否已经被访问过
int is_room_visited(int* visited_rooms, int room_id, int num_of_visited) {
int i;
for (i = 0; i < num_of_visited; i++) {
if (visited_rooms[i] == room_id) {
return 1;
}
}
return 0;
}
// 计算当前状态的代价
int calc_cost(Node* node) {
int i, cost = 0;
for (i = 0; i < node->num_of_visited; i++) {
cost += rooms[node->visited_rooms[i]].num_of_pics;
}
return cost;
}
// 判断一个状态是否为目标状态
int is_goal(Node* node) {
return node->room_id == goal_room_id;
}
// 扩展一个节点
void expand_node(Node* node, Node** children, int* num_of_children) {
int i, j, room_id = node->room_id;
Room room = rooms[room_id];
for (i = 0; i < room.num_of_pics; i++) {
int pic_id = room.pics[i];
if (is_room_visited(node->visited_rooms, pictures[pic_id].room_id, node->num_of_visited)) {
continue;
}
Node* child = (Node*)malloc(sizeof(Node));
child->cost = calc_cost(node) + rooms[pictures[pic_id].room_id].num_of_pics;
child->room_id = pictures[pic_id].room_id;
child->num_of_visited = node->num_of_visited + 1;
child->visited_rooms = (int*)malloc(child->num_of_visited * sizeof(int));
memcpy(child->visited_rooms, node->visited_rooms, node->num_of_visited * sizeof(int));
child->visited_rooms[node->num_of_visited] = pictures[pic_id].room_id;
children[*num_of_children] = child;
(*num_of_children)++;
}
}
// 比较两个节点的代价
int compare_cost(const void* a, const void* b) {
Node* node_a = *(Node**)a;
Node* node_b = *(Node**)b;
return node_a->cost - node_b->cost;
}
// 释放一个节点占用的内存
void free_node(Node* node) {
free(node->visited_rooms);
free(node);
}
// 使用分支限界法搜索最优解
void search() {
Node* root = (Node*)malloc(sizeof(Node));
root->cost = 0;
root->room_id = 0;
root->num_of_visited = 1;
root->visited_rooms = (int*)malloc(sizeof(int));
root->visited_rooms[0] = 0;
Node* queue[MAX_ROOMS * MAX_PICTURES];
int head = 0, tail = 0;
queue[tail++] = root;
while (head < tail) {
Node* node = queue[head++];
if (is_goal(node)) {
printf("%d\n", node->cost);
return;
}
Node* children[MAX_ROOMS * MAX_PICTURES];
int num_of_children = 0;
expand_node(node, children, &num_of_children);
qsort(children, num_of_children, sizeof(Node*), compare_cost);
int i;
for (i = 0; i < num_of_children; i++) {
queue[tail++] = children[i];
}
free_node(node);
for (i = 0; i < num_of_children; i++) {
free(children[i]);
}
}
}
int main() {
init_rooms();
init_pictures();
read_data();
search();
return 0;
}
```
在这个代码示例中,我们定义了展厅结构体和画作结构体,以及优先队列节点结构体。我们还定义了全局变量来存储输入数据和目标展厅编号。在 `read_data()` 函数中,我们读取输入数据并初始化展厅和画作数组。
在 `search()` 函数中,我们首先创建根节点,然后使用优先队列来存储节点,并不断选取代价最小的节点进行扩展,直到找到目标状态为止。在扩展节点时,我们通过检查已经访问过的展厅来避免重复状态,然后计算出当前状态的代价,并将扩展出的子节点按代价从小到大排序,加入优先队列中。
最后,我们在 `main()` 函数中调用 `init_rooms()`、`init_pictures()`、`read_data()` 和 `search()` 函数来执行程序。
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