题目连接
http://acm.hdu.edu.cn/showproblem.php?pid=1162
Eddy's picture
Description
Eddy begins to like painting pictures recently ,he is sure of himself to become a painter.Every day Eddy draws pictures in his small room, and he usually puts out his newest pictures to let his friends appreciate. but the result it can be imagined, the friends are not interested in his picture.Eddy feels very puzzled,in order to change all friends 's view to his technical of painting pictures ,so Eddy creates a problem for the his friends of you.
Problem descriptions as follows: Given you some coordinates pionts on a drawing paper, every point links with the ink with the straight line, causes all points finally to link in the same place. How many distants does your duty discover the shortest length which the ink draws?
Input
The first line contains 0 < n <= 100, the number of point. For each point, a line follows; each following line contains two real numbers indicating the (x,y) coordinates of the point.
Input contains multiple test cases. Process to the end of file.
Output
Your program prints a single real number to two decimal places: the minimum total length of ink lines that can connect all the points.
Sample Input
3
1.0 1.0
2.0 2.0
2.0 4.0
Sample Output
3.41
最小生成树。。
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<vector>
#include<queue>
#include<cmath>
#include<map>
using std::map;
using std::min;
using std::find;
using std::sqrt;
using std::vector;
using std::multimap;
using std::priority_queue;
#define pb(e) push_back(e)
#define sz(c) (int)(c).size()
#define mp(a, b) make_pair(a, b)
#define all(c) (c).begin(), (c).end()
#define iter(c) __typeof((c).begin())
#define cls(arr, val) memset(arr, val, sizeof(arr))
#define cpresent(c, e) (find(all(c), (e)) != (c).end())
#define rep(i, n) for(int i = 0; i < (int)n; i++)
#define tr(c, i) for(iter(c) i = (c).begin(); i != (c).end(); ++i)
const int N = 110;
const int INF = 0x3f3f3f3f;
struct P {
double x, y;
P(double i = 0.0, double j = 0.0) :x(i), y(j) {}
double calc(const P &t) const {
return sqrt((x - t.x) * (x - t.x) + (y - t.y) * (y - t.y));
}
}A[N];
struct edge { int to; double w; int next; }G[(N * N) << 1];
struct PII {
int v;
double w;
PII(int i = 0, double j = 0.0) :v(i), w(j) {}
inline bool operator<(const PII &x) const {
return w > x.w;
}
};
struct Prim {
bool vis[N];
int tot, head[N];
double mincost[N];
inline void init() {
tot = 0, cls(head, -1), cls(vis, false), cls(mincost, 0x3f);
}
inline void add_edge(int u, int v, double w) {
G[tot] = (edge){ v, w, head[u] }; head[u] = tot++;
}
inline void built(int m) {
rep(i, m) {
scanf("%lf %lf", &A[i].x, &A[i].y);
}
for(int i = 0; i < m; i++) {
for(int j = 0; j < m; j++) {
if(i == j) continue;
add_edge(i + 1, j + 1, A[i].calc(A[j]));
}
}
}
inline void prim(int s) {
double ans = 0.0;
priority_queue<PII> q;
q.push(PII(s, 0.0));
for(int i = head[s]; ~i; i = G[i].next) {
mincost[G[i].to] = G[i].w;
q.push(PII(G[i].to, G[i].w));
}
mincost[s] = 0, vis[s] = true;
while(!q.empty()) {
PII t = q.top(); q.pop();
int u = t.v;
if(vis[u]) continue;
vis[u] = true;
ans += t.w;
for(int i = head[u]; ~i; i = G[i].next) {
double &d = mincost[G[i].to];
if(d > G[i].w && !vis[G[i].to]) {
d = G[i].w;
q.push(PII(G[i].to, d));
}
}
}
printf("%.2lf\n", ans);
}
inline void solve(int n) {
init(), built(n), prim(1);
}
}go;
int main() {
#ifdef LOCAL
freopen("in.txt", "r", stdin);
freopen("out.txt", "w+", stdout);
#endif
int n;
while(~scanf("%d", &n)) {
go.solve(n);
}
return 0;
}
Eddy热爱绘画,但朋友对其作品反应冷淡。为改变这一现状,Eddy设计了一个数学问题:给定平面上的多个点,如何用最短的墨水线将所有点连接起来?本文通过实现Prim算法解决该问题,展示了如何找到连接所有点的最小生成树。
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