Arctic Network最小生成树
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2022-06-16 08:57:48
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Arctic Network
原题链接https://vjudge.net/contest/352170#problem/F
有n 个信号站,有两种链接方式,一种是卫星,不需要通道,一种需要建立通道才行,问需要建立的最小通道。
Prim:
由于Prim是对于当前的点的最小值计算,所以我们需要先将最小生成树的路径求出,记录,排序,找到除去使用卫星链接的信号站的最大路径。
#include <algorithm>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <iostream>
#include <queue>
using namespace std;
const int INF = 0x3f3f3f3f;
bool vis[30005];
double dis[300005];
double map[3005][3005];
double sum[300005];
double ans;
long long z;
long long n, m;
double maxx;
struct node
{
long long x;
long long y;
} stu[30005];
void prim()
{
ans = 0.0;
long long i, j;
for (i = 1; i <= n; i++)
{
vis[i] = false;
dis[i] = map[1][i];
}
vis[1] = true;
z = 1;
for (i = 0; i < n - 1; i++)
{
double minn = INF;
long long p = 1;
for (j = 1; j <= n; j++)
{
if (!vis[j] && dis[j] < minn)
{
minn = dis[j];
p = j;
}
}
if (minn == INF)
{
ans = -1;
return;
}
ans += minn;
sum[z] = minn;
// cout << minn << " " << endl;
z++;
if (maxx > minn)
{
maxx = minn;
}
vis[p] = true;
for (j = 1; j <= n; j++)
{
if (!vis[j] && map[p][j] < dis[j])
{
dis[j] = map[p][j];
}
}
}
return;
}
int main()
{
long long t;
scanf("%lld", &t);
while (t--)
{
scanf("%lld %lld", &m, &n);
long long i, j;
for (i = 1; i <= n; i++)
{
scanf("%lld %lld", &stu[i].x, &stu[i].y);
}
for (i = 1; i <= n; i++)
{
for (j = 1; j <= n; j++)
{
map[i][j] = sqrt(1.0 * (stu[i].x - stu[j].x) * (stu[i].x - stu[j].x) + 1.0 * (stu[i].y - stu[j].y) * (stu[i].y - stu[j].y));
}
}
/* for (i = 1; i <= n; i++)
{
for (j = 1; j <= n; j++)
{
printf("%.2lf ", map[i][j]);
}
cout << endl;
}*/
prim();
sort(sum + 1, sum + z);
/* for (i = 1; i <= z; i++)
{
printf("%.2lf ", sum[i]);
}
cout << endl;*/
printf("%.2f\n", sum[n - m]);
}
return 0;
}
Kruskal:
这种算法是直接从最小路径开始计算的,一开始便排了序,所以只需要减去卫星链接的信号站,最小生成树计算剩下的信号站的路径,选取最大值即可。
#include <algorithm>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <fstream>
#include <iostream>
#include <queue>
using namespace std;
long long pre[300005];
double map[3005][3005];
struct node
{
long long u;
long long v;
double w;
} stu[300005];
struct id
{
long long x;
long long y;
} stuu[300005];
double ans;
long long cnt;
double maxx;
bool cmp(node x, node y)
{
return x.w < y.w;
}
long long find(long long x)
{
if (x == pre[x])
{
return x;
}
return pre[x] = find(pre[x]);
}
void join(long long x, long long y, double w)
{
long long ss1 = find(x);
long long ss2 = find(y);
if (ss1 != ss2)
{
pre[ss2] = ss1;
ans += w;
maxx = max(maxx, w);
cnt--;
}
}
int main()
{
long long n, i, j;
long long t;
scanf("%lld", &t);
while (t--)
{
long long sum1;
scanf("%lld %lld", &sum1, &n);
if (n == 0)
{
break;
}
ans = 0;
cnt = n - sum1+1;
maxx = -1;
for (i = 1; i <= n; i++)
{
scanf("%lld %lld", &stuu[i].x, &stuu[i].y);
}
for (i = 1; i <= n; i++)
{
for (j = 1; j <= n; j++)
{
double dis = 1.0*sqrt(1.0*(stuu[i].x - stuu[j].x) * (stuu[i].x - stuu[j].x) + 1.0*(stuu[i].y - stuu[j].y) * (stuu[i].y - stuu[j].y));
map[i][j] = dis;
}
}
/* for (i = 1; i <= n; i++)
{
for (j = 1; j <= n; j++)
{
printf("%.2lf ", map[i][j]);
}
cout << endl;
}*/
long long k = 0;
for (i = 1; i <= n; i++)
{
for (j = i + 1; j <= n; j++)
{
stu[k].u = i;
stu[k].v = j;
stu[k].w = map[i][j];
k++;
}
}
sort(stu, stu + k, cmp);
/* for (i = 0; i < k; i++)
{
printf("*%lld %lld %lld\n", stu[i].u, stu[i].v, stu[i].w);
}
for (i = 0; i <= n;i++)
{
cout << pre[i] << endl;
}
cout << endl;*/
for (i = 0; i <= n; i++)
{
pre[i] = i;
}
for (i = 0; i < k; i++)
{
join(stu[i].u, stu[i].v, stu[i].w);
if (cnt == 1)
{
break;
}
}
if (cnt > 1)
{
ans = -1;
}
printf("%.2f\n", maxx);
}
return 0;
}
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