06-图4. Saving James Bond - Hard Version (30)
06-图4. Saving James Bond - Hard Version (30)
This time let us consider the situation in the movie "Live and Let Die" in which James Bond, the world's most famous spy, was captured by a group of drug dealers. He was sent to a small piece of land at the center of a lake filled with crocodiles. There he performed the most daring action to escape -- he jumped onto the head of the nearest crocodile! Before the animal realized what was happening, James jumped again onto the next big head... Finally he reached the bank before the last crocodile could bite him (actually the stunt man was caught by the big mouth and barely escaped with his extra thick boot).
Assume that the lake is a 100 by 100 square one. Assume that the center of the lake is at (0,0) and the northeast corner at (50,50). The central island is a disk centered at (0,0) with the diameter of 15. A number of crocodiles are in the lake at various positions. Given the coordinates of each crocodile and the distance that James could jump, you must tell him a shortest path to reach one of the banks. The length of a path is the number of jumps that James has to make.
Input Specification:
Each input file contains one test case. Each case starts with a line containing two positive integers N (<=100), the number of crocodiles, and D, the maximum distance that James could jump. Then N lines follow, each containing the (x, y) location of a crocodile. Note that no two crocodiles are staying at the same position.
Output Specification:
For each test case, if James can escape, output in one line the minimum number of jumps he must make. Then starting from the next line, output the position (x, y) of each crocodile on the path, each pair in one line, from the island to the bank. If it is impossible for James to escape that way, simply give him 0 as the number of jumps. If there are many shortest paths, just output the one with the minimum first jump, which is guaranteed to be unique.
Sample Input 1:17 15 10 -21 10 21 -40 10 30 -50 20 40 35 10 0 -10 -25 22 40 -40 -30 30 -10 22 0 11 25 21 25 10 10 10 10 35 -30 10Sample Output 1:
4 0 11 10 21 10 35Sample Input 2:
4 13 -12 12 12 12 -12 -12 12 -12Sample Output 2:
0
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
typedef struct {
double x, y;
int pre; //记录路径上该节点的前一个节点，初始化为-1
int escape; //记录该节点能否直接跳上岸逃生
}Vertex;
struct Node {
int val;
struct Node *next;
};
int inLake(double x, double y) { //判断鳄鱼是否在湖里面；在岛上或岸上的鳄鱼不与任何节点相连
if (7.5 * 7.5 >= x * x + y * y)
return 0;
if (fabs(x) >= 50 || fabs(y) >= 50)
return 0;
return 1;
}
void createGraph(struct Node *table, Vertex *vertex, int n, int d) {
for (int i = 1; i <= n; ++i) { //将第一跳能跳到的节点链接到下标0，升序排序
if (inLake(vertex[i].x, vertex[i].y) && (d + 7.5)*(d + 7.5) >= vertex[i].x * vertex[i].x + vertex[i].y * vertex[i].y) {
struct Node *p = (struct Node *)malloc(sizeof(struct Node));
p->val = i;
struct Node *pre = &table[0]; //寻找插入位置的前一个节点
while (pre->next && vertex[i].x * vertex[i].x + vertex[i].y * vertex[i].y > vertex[pre->next->val].x * vertex[pre->next->val].x + vertex[pre->next->val].y * vertex[pre->next->val].y) {
pre = pre->next;
}
p->next = pre->next;
pre->next = p;
}
}
for (int i = 1; i <= n; ++i) { //将鳄鱼的节点连成网络
if (!inLake(vertex[i].x, vertex[i].y))
continue;
for (int j = 1; j <= n; ++j) {
if (j != i && inLake(vertex[j].x, vertex[j].y) && d * d >= (vertex[i].x - vertex[j].x)*(vertex[i].x - vertex[j].x) + (vertex[i].y - vertex[j].y) * (vertex[i].y - vertex[j].y)) {
struct Node *p = (struct Node *)malloc(sizeof(struct Node));
p->val = j;
p->next = table[i].next;
table[i].next = p;
}
}
}
}
int BFS(struct Node *table, Vertex *vertex, int n, int d) {
struct Node *p = &table[0];
while (p = p->next) { //以第一跳能跳到的节点为起始点广度优先搜索
// int pace = 0; //深度，对应跳的次数
int v = p->val; //起始节点
int queue[101] = {}, head = 0, rear = 0; //队列
int visited[101] = {}; //用于标记节点是否已访问
visited[v] = 1;
queue[rear++] = v; //第一个节点入队
vertex[v].pre = 0; //起始节点的前一个节点为中心岛
while (rear - head) { //队列不为空，循环
v = queue[head++]; //出队
if (vertex[v].escape) { //如果当前节点能跳到岸上，返回逃跑成功
return v;
}
struct Node *q = &table[v]; //否则，将该节点所有没有被访问的邻节点都入队
while (q = q->next) { //遍历每个邻接点
int u = q->val;
if (!visited[u]) { //如果该邻节点没有被访问，入队
visited[u] = 1;
queue[rear++] = u;
vertex[u].pre = v; //记录当前入队节点的前一个节点
}
}
}
}
return 0; //无法逃离
}
void destroyGraph(struct Node* table, int n) { //释放堆内空间
for (int i = 0; i <= n; ++i) {
struct Node* p = table[i].next;
while (p) {
struct Node* tmp = p;
p = p->next;
free(tmp);
}
}
}
int main() {
// freopen("test.txt", "r", stdin);
int n;
double d;
scanf("%d%lf", &n, &d);
if (d >= 50 - 7.5) { //可以直接跳上岸
printf("1\n");
return 0;
}
Vertex vertex[101];
for (int i = 1; i <= n; ++i) { //初始化节点信息，下标1开始分别对应每只鳄鱼，下标0对应中心小岛
scanf("%lf%lf", &vertex[i].x, &vertex[i].y);
vertex[i].pre = -1;
if (fabs(50 - fabs(vertex[i].x)) <= d || fabs(50 - fabs(vertex[i].y)) <= d) //判断该节点能否直接跳上岸逃生
vertex[i].escape = 1;
else
vertex[i].escape = 0;
}
struct Node table[101] = {}; //邻接表形式储存图结构
createGraph(table, vertex, n, d); //构造图
int escape = BFS(table, vertex, n, d); //广度优先搜索图，返回逃跑成功的最后一个节点，不能逃跑返回0
if (escape) { //如果能逃生，回溯寻找路径
int pace = 1;
int stack[100] = {}, top = 0; //栈
int v = escape;
while (v) { //回溯路径，依次压栈
++pace;
stack[top++] = v;
v = vertex[v].pre;
}
printf("%d\n", pace);
while (top) { //依次弹出栈内元素
v = stack[--top];
printf("%d %d\n", (int)vertex[v].x, (int)vertex[v].y);
}
}
else {
printf("0\n");
}
destroyGraph(table, n);
return 0;
}
注意：
测试点3：有鳄鱼在岸上或中心岛；
测试点4：有多条路径，选择其中第一跳最短的路径；
测试点5：可以直接从中心岛跳到岸上。