UVA 1001 Say Cheese（dijkstra算法）

题意：

在实体空间中给出若干个空心的球，在球中可以瞬间移动， 在实体中移动花费与距离成正比的的时间，给出两点求到达的最短时间。

解题思路：

花样建图， 把起点和终点作为半径为0的球加入图中，使用dijkstra算法一搞就好啦！
https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=3442

Memory: 0 KB		Time: 3 MS
Language: C++ 4.8.2		Result: Accepted

#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<cctype>
#include<list>
#include<iostream>
#include<map>
#include<queue>
#include<set>
#include<stack>
#include<vector>

using namespace std;

#define FOR(i, s, t) for(int i = (s) ; i <= (t) ; ++i)
#define REP(i, n) for(int i = 0 ; i < (n) ; ++i)

int buf[10];
inline long long read()
{
long long x=0,f=1;
char ch=getchar();
while(ch<'0'||ch>'9')
{
if(ch=='-')f=-1;
ch=getchar();
}
while(ch>='0'&&ch<='9')
{
x=x*10+ch-'0';
ch=getchar();
}
return x*f;
}

inline void writenum(int i)
{
int p = 0;
if(i == 0) p++;
else while(i)
{
buf[p++] = i % 10;
i /= 10;
}
for(int j = p - 1 ; j >= 0 ; --j) putchar('0' + buf[j]);
}
/**************************************************************/
#define MAX_N 110
const int INF = 0x3f3f3f3f;
int n;
typedef pair<double, int> PP;
priority_queue<PP, vector<PP>, greater<PP> > que;
double d[MAX_N];
struct point
{
int x, y, z, r;
}P[MAX_N];
struct node
{
int to, next;
double w;
} edge[MAX_N * MAX_N];
int head[MAX_N];
int top = 0;
inline void add_edge(int u, int v, double w)
{
edge[top].to = v;
edge[top].w = w;
edge[top].next = head[u];
head[u] = top++;
}

double dist(point a, point b)
{
return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y) + (a.z - b.z) * (a.z - b.z)) - a.r - b.r;
}

void dijkstra(int s)
{
d[s] = 0.0;
que.push(PP(0.0, s));
while(!que.empty())
{
PP p = que.top();
que.pop();
int v = p.second;
if(d[v] < p.first) continue;
for(int k = head[v] ; k != -1 ; k = edge[k].next)
{
//            cout<<d[edge[k].to]<<" "<<d[v]<<" "<<edge[k].w<<endl;
if(d[edge[k].to] > d[v] + edge[k].w)
{
d[edge[k].to] = d[v] + edge[k].w;
que.push(PP(d[edge[k].to], edge[k].to));
}
}

}
}

inline void init()
{
for(int i = 0 ; i < MAX_N ; i ++)
{
d[i] = 1e10;
}
memset(head, -1, sizeof(head));
while(!que.empty()) que.pop();
top = 0;
}
int main()
{
int cas = 1;
while(scanf("%d",&n) && n != -1)
{
init();
for(int i = 1 ; i <= n ; i++)
{
P[i].x = read();
P[i].y = read();
P[i].z = read();
P[i].r = read();
}

P[0].x = read();
P[0].y = read();
P[0].z = read();
P[0].r = 0;

P[n + 1].x = read();
P[n + 1].y = read();
P[n + 1].z = read();
P[n + 1].r = 0;
//        cout<<endl<<endl;
for(int i = 0 ; i <= n + 1 ; i++)
{
for(int j = 0 ; j <= n + 1 ; j++)
{
if(i != j)
{
double w = dist(P[i], P[j]);
if(w < 1e-8) w = 0;
add_edge(i ,j, w);
//                    cout<<i<<" "<<j<<" "<<w<<endl;
}
}
}
//        cout<<endl<<endl;
//        for(int i = 0 ; i <= n + 1 ; i++)
//        {
//            for(int k = head[i] ; k != -1 ; k = edge[k].next)
//            {
//                cout<<i<<" "<<edge[k].to<<" "<<edge[k].w<<endl;
//            }
//        }
dijkstra(0);
//        cout<<endl<<endl;
//        for(int i = 0 ; i <= n + 1 ; i++)
//        {
//            cout<<d[i]<<endl;
//        }
int ans = (int)(d[n + 1] * 10 + 0.5);
printf("Cheese %d: Travel time = %d sec\n", cas++, ans);

}

return 0;
}