UVA10397 - Connect the Campus(最小生成樹)
題目大意:給你n個點,然後再給你m個已經連接的邊,問如何使得所有的點都相連並且新建的邊長度之和最小。
解題思路:最小生成樹,但是有m條邊是已經建好的,就將這些邊的權值變成0,然後用kruskal的方法來求長度。
代碼:
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 755;
const int maxm = 3e5;
struct Node {
int x, y;
}node[maxn];
double w[maxm];
int p[maxn], u[maxm], v[maxm];
int vis[maxn][maxn], r[maxm];
double dist (int i, int j) {
double x = node[i].x - node[j].x;
double y = node[i].y - node[j].y;
return sqrt(x * x + y * y);
}
void init (int n) {
for (int i = 0; i < n; i++)
p[i] = i;
}
int getParent (int x) {
return (x == p[x]) ? p[x] : p[x] = getParent(p[x]);
}
int cmp (int i, int j) {
return w[i] < w[j];
}
double Kruskal (int n, int m) {
double ans = 0;
init(n);
for (int i = 0; i < m; i++)
r[i] = i;
sort(r, r + m, cmp);
for (int i = 0; i < m; i++) {
int P = getParent(u[r[i]]);
int Q = getParent(v[r[i]]);
if (P == Q) continue;
ans += w[r[i]];
p[P] = Q;
}
return ans;
}
int main () {
int n, m;
while (scanf ("%d", &n) != EOF) {
for (int i = 0; i < n; i++)
scanf ("%d%d", &node[i].x, &node[i].y);
int x, y;
memset (vis, 0, sizeof(vis));
scanf ("%d", &m);
for (int i = 0; i < m; i++) {
scanf ("%d%d", &x, &y);
vis[x - 1][y - 1] = vis[y - 1][x - 1] = 1;
}
int pos = 0;
for (int i = 0; i < n; i++)
for (int j = i + 1; j < n; j++) {
u[pos] = i;
v[pos] = j;
if (vis[i][j])
w[pos++] = 0;
else
w[pos++] = dist(i, j);
}
printf ("%.2lf\n", Kruskal(n, pos));
}
return 0;
}