题目链接：https://vjudge.net/problem/POJ-2031
题目大意
给定 N 个空间站，每个空间站都有自己的三维坐标和半径，任意两个空间站都互相可达，如果两个空间接触或者有重叠，则记为无走廊可达；反之就是有走廊可达，问为了使空间站两两可达，最短需要修建的走廊长度为多少。分析
同 POJ 1789。代码如下
1 #include <cmath>
2 #include <ctime>
3 #include <iostream>
4 #include <string>
5 #include <vector>
6 #include <cstdio>
7 #include <cstdlib>
8 #include <cstring>
9 #include <queue>
10 #include <map>
11 #include <set>
12 #include <algorithm>
13 #include <cctype>
14 #include <stack>
15 #include <deque>
16 #include <list>
17 #include <sstream>
18 #include <cassert>
19 using namespace std;
20
21 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
22 #define Rep(i,n) for (int i = 0; i < (n); ++i)
23 #define For(i,s,t) for (int i = (s); i <= (t); ++i)
24 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)
25 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
26 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
27 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
28 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
29
30 #define pr(x) cout << #x << " = " << x << " "
31 #define prln(x) cout << #x << " = " << x << endl
32
33 #define LOWBIT(x) ((x)&(-x))
34
35 #define ALL(x) x.begin(),x.end()
36 #define INS(x) inserter(x,x.begin())
37 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
38 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c
39 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
40 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
41
42 #define ms0(a) memset(a,0,sizeof(a))
43 #define msI(a) memset(a,0x3f,sizeof(a))
44 #define msM(a) memset(a,-1,sizeof(a))
45
46 #define MP make_pair
47 #define PB push_back
48 #define ft first
49 #define sd second
50
51 template<typename T1, typename T2>
52 istream &operator>>(istream &in, pair<T1, T2> &p) {
53 in >> p.first >> p.second;
54 return in;
55 }
56
57 template<typename T>
58 istream &operator>>(istream &in, vector<T> &v) {
59 for (auto &x: v)
60 in >> x;
61 return in;
62 }
63
64 template<typename T1, typename T2>
65 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
66 out << "[" << p.first << ", " << p.second << "]" << "\n";
67 return out;
68 }
69
70 inline int gc(){
71 static const int BUF = 1e7;
72 static char buf[BUF], *bg = buf + BUF, *ed = bg;
73
74 if(bg == ed) fread(bg = buf, 1, BUF, stdin);
75 return *bg++;
76 }
77
78 inline int ri(){
79 int x = 0, f = 1, c = gc();
80 for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
81 for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
82 return x*f;
83 }
84
85 template<class T>
86 inline string toString(T x) {
87 ostringstream sout;
88 sout << x;
89 return sout.str();
90 }
91
92 inline int toInt(string s) {
93 int v;
94 istringstream sin(s);
95 sin >> v;
96 return v;
97 }
98
99 //min <= aim <= max
100 template<typename T>
101 inline bool BETWEEN(const T aim, const T min, const T max) {
102 return min <= aim && aim <= max;
103 }
104
105 typedef long long LL;
106 typedef unsigned long long uLL;
107 typedef pair< double, double > PDD;
108 typedef pair< int, int > PII;
109 typedef pair< int, PII > PIPII;
110 typedef pair< string, int > PSI;
111 typedef pair< int, PSI > PIPSI;
112 typedef set< int > SI;
113 typedef set< PII > SPII;
114 typedef vector< int > VI;
115 typedef vector< double > VD;
116 typedef vector< VI > VVI;
117 typedef vector< SI > VSI;
118 typedef vector< PII > VPII;
119 typedef map< int, int > MII;
120 typedef map< LL, int > MLLI;
121 typedef map< int, string > MIS;
122 typedef map< int, PII > MIPII;
123 typedef map< PII, int > MPIII;
124 typedef map< string, int > MSI;
125 typedef map< string, string > MSS;
126 typedef map< PII, string > MPIIS;
127 typedef map< PII, PII > MPIIPII;
128 typedef multimap< int, int > MMII;
129 typedef multimap< string, int > MMSI;
130 //typedef unordered_map< int, int > uMII;
131 typedef pair< LL, LL > PLL;
132 typedef vector< LL > VL;
133 typedef vector< VL > VVL;
134 typedef priority_queue< int > PQIMax;
135 typedef priority_queue< int, VI, greater< int > > PQIMin;
136 const double EPS = 1e-8;
137 const LL inf = 0x3fffffff;
138 const LL infLL = 0x3fffffffffffffffLL;
139 const LL mod = 1e9 + 7;
140 const int maxN = 1e2 + 7;
141 const LL ONE = 1;
142 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
143 const LL oddBits = 0x5555555555555555;
144
145 struct Cell{
146 double x, y, z, r;
147 };
148
149 istream& operator>> (istream& in, Cell &x) {
150 in >> x.x >> x.y >> x.z >> x.r;
151 return in;
152 }
153
154 int sgn(double x) {
155 if(fabs(x) < EPS) return 0;
156 return x > 0 ? 1 : -1;
157 }
158
159 int N;
160 double ans;
161 double adj[maxN][maxN], dist[maxN];
162 Cell cells[maxN];
163 bool vis[maxN];
164
165 void Prim(int S) {
166 ms0(vis);
167 vis[S] = 1;
168 For(i, 1, N) dist[i] = adj[S][i];
169
170 Rep(cnt, N - 1) {
171 int index;
172 double minW = inf;
173
174 For(i, 1, N) {
175 if(!vis[i] && sgn(minW - dist[i]) > 0) {
176 index = i;
177 minW = dist[i];
178 }
179 }
180
181 ans += minW;
182 vis[index] = 1;
183
184 For(i, 1, N) if(!vis[i] && sgn(dist[i] - adj[index][i]) > 0) dist[i] = adj[index][i];
185 }
186 }
187
188 int main(){
189 //freopen("MyOutput.txt","w",stdout);
190 //freopen("input.txt","r",stdin);
191 //INIT();
192 while(cin >> N && N) {
193 ans = 0;
194 For(i, 1, N) cin >> cells[i];
195 For(i, 1, N) {
196 For(j, i + 1, N) {
197 double x = cells[i].x - cells[j].x;
198 double y = cells[i].y - cells[j].y;
199 double z = cells[i].z - cells[j].z;
200 double d = sqrt(x * x + y * y + z * z);
201 d -= cells[i].r + cells[j].r;
202 if(sgn(d) <= 0) d = 0;
203
204 adj[i][j] = adj[j][i] = d;
205 }
206 }
207
208 Prim(1);
209
210 printf("%.3f\n", ans + EPS);
211 }
212 return 0;
213 }
View Code