hdu 4756 Install Air Conditioning
非正规做法，一个一个的暴，减一下枝，还得采用sort，qsort居然过不了……
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <algorithm>
using namespace std;
#define LL long long
struct node{
int u, v, no;
LL dis;
};
int n, len, pos, p[1010], num[1010][2];
double maxx;
node v[500010], cnt[1010];
LL dist(int i, int j){
return (LL)(num[i][0] - num[j][0]) * (num[i][0] - num[j][0]) + (LL)(num[i][1] - num[j][1]) * (num[i][1] - num[j][1]);
}
bool cmp(const node &p1, const node &p2) {
return p1.dis < p2.dis;
}
int find(int x) {
return p[x] == x ? x : p[x] = find(p[x]);
}
void Kruskal(){
sort(v, v + len, cmp);
maxx = 0;
pos = 0;
int k = n - 1;
for(int i = 0; i < n; ++i) p[i] = i;
for(int i = 0; i < len; ++i){
int x = find(v[i].u);
int y = find(v[i].v);
if(x!=y){
maxx += sqrt((double)v[i].dis);
p[x] = y;
cnt[pos] = v[i];
cnt[pos++].no = i;
--k;
if(!k) break;
}
}
}
void solve(){
double t = maxx;
for(int k = 0; k < pos; ++k){
if(!cnt[k].u) continue;
double e = t - sqrt((double)cnt[k].dis);
for(int i = 0; i < n; ++i) p[i] = i;
for(int i = 0; i < pos; ++i)
if(i != k){
int x = find(cnt[i].u);
int y = find(cnt[i].v);
p[x] = y;
}
for(int i = cnt[k].no + 1; i < len; ++i){
int x1 = find(v[i].u);
int y1 = find(v[i].v);
if(x1 != y1){
e += sqrt((double)v[i].dis);
if(maxx < e) maxx = e;
break;
}
}
}
}
int main()
{
//freopen("in.txt", "r", stdin);
int t, k;
scanf("%d", &t);
while(t--){
scanf("%d %d", &n, &k);
for(int i = 0; i < n; ++i)
scanf("%d %d", &num[i][0], &num[i][1]);
len = 0;
for(int i = 0; i < n; ++i)
for(int j = i+1; j < n; ++j){
v[len].dis = dist(i, j);
v[len].u = i;
v[len++].v = j;
}
Kruskal();
solve();
printf("%.2lf\n", maxx * k);
}
return 0;
}
第二次做：用dfs+并查集，速度果然提高了许多
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <algorithm>
using namespace std;
#define LL long long
struct node{
int u, v;
LL dis;
};
int n, len, pos, p[1010], num[1010][2], head[1010], next[2010][3];
double maxx, cnt;
node v[500010];
LL dist(int i, int j){
return (LL)(num[i][0] - num[j][0]) * (num[i][0] - num[j][0]) + (LL)(num[i][1] - num[j][1]) * (num[i][1] - num[j][1]);
}
bool cmp(const node &p1, const node &p2) {
return p1.dis < p2.dis;
}
int find(int x) {
return p[x] == x ? x : p[x] = find(p[x]);
}
void add(int u, int v, int i){
next[pos][1] = v;
next[pos][2] = i;
next[pos][0] = head[u];
head[u] = pos++;
}
void Kruskal(){
sort(v, v + len, cmp);
maxx = 0;
pos = 0;
int k = n - 1;
for(int i = 0; i < n; ++i) p[i] = i;
for(int i = 0; i < len; ++i){
int x = find(v[i].u);
int y = find(v[i].v);
if(x!=y){
maxx += sqrt((double)v[i].dis);
p[x] = y;
add(v[i].u, v[i].v, i);
add(v[i].v, v[i].u, i);
--k;
if(!k) break;
}
}
}
void dfs(int cur, int fa){
for(int i = head[cur]; i != -1; i = next[i][0]){
int u = next[i][1];
int no = next[i][2];
if(u != fa){
dfs(u, cur);
int x = find(cur);
int y = find(u);
if(u && cur){
double t = maxx - sqrt(double(v[no].dis));
for(int j = no + 1; j < len; ++j){
int x1 = find(v[j].u);
int y1 = find(v[j].v);
if(x1 != y1 && (x1 == y || y1 == y)){
cnt = max(cnt, t + sqrt(double(v[j].dis)));
break;
}
}
}
p[x] = y;
}
}
}
int main()
{
// freopen("in.txt", "r", stdin);
int t, k;
scanf("%d", &t);
while(t--){
scanf("%d %d", &n, &k);
for(int i = 0; i < n; ++i)
scanf("%d %d", &num[i][0], &num[i][1]), head[i] = -1;
len = 0;
for(int i = 0; i < n; ++i)
for(int j = i+1; j < n; ++j){
v[len].dis = dist(i, j);
v[len].u = i;
v[len++].v = j;
}
Kruskal();
for(int i = 0; i < n; ++i) p[i] = i;
cnt = maxx;
dfs(0, -1);
printf("%.2lf\n", cnt * k);
}
return 0;
}
第三次做：采用普里姆算法，果然快了很多，适用于稠密图，也就是边比较多的图，N^2的算法，网上大多数采用普里姆算法+树形dp，我是采用普里姆算法然后dfs优化做的，c++也照样过
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <algorithm>
using namespace std;
#define LL long long
LL inf = 10000000000000000LL;
int n, dfs_cnt, p[1010], num[1010][2], head[1010], next[2010][2];
double maxx, q;
bool flag;
LL v[1005][1005], cnt[1010], arr[1005][1005];
LL dist(int i, int j)
{
return (LL)(num[i][0] - num[j][0]) * (num[i][0] - num[j][0]) + (LL)(num[i][1] - num[j][1]) * (num[i][1] - num[j][1]);
}
void add(int u, int v){
next[dfs_cnt][1] = v;
next[dfs_cnt][0] = head[u];
head[u] = dfs_cnt++;
}
void prim()
{
maxx = 0, dfs_cnt = 0;
for(int i = 1; i < n; ++i){
cnt[i] = v[0][i];
p[i] = 0;
}
cnt[0] = 0, p[0] = 0;
for(int i = 1; i < n; ++i){
int k = 0;
LL c = inf;
for(int j = 1; j < n; ++j)
if(cnt[j] != 0 && cnt[j] < c){
c = cnt[j];
k = j;
}
add(p[k], k);
add(k, p[k]);
maxx += sqrt(double(c));
cnt[k] = 0;
for(int j = 1; j < n; ++j)
if(cnt[j] != 0 && v[k][j] < cnt[j]){
cnt[j] = v[k][j];
p[j] = k;
}
}
}
double tarjan(int cur, int fa, int pos, LL f){
double c = inf;
for(int i = head[cur]; i != -1; i = next[i][0]){
int u = next[i][1];
if(u != fa){
c = min(c, tarjan(u, cur, pos, f));
if(arr[u][pos] != f) c = min(c, sqrt(double(arr[u][pos])) - sqrt(double(f)));
else if(flag) c = min(c, 0.0);
else flag = 1;
//printf("%.2lf ", c);
}
}
return c;
}
void dfs(int cur, int fa){
for(int i = head[cur]; i != -1; i = next[i][0]){
int u = next[i][1];
if(u != fa){
dfs(u, cur);
if(u && cur){
double c = inf;
for(int j = 0; j < n; ++j)
if(j != cur)
c = min(c, sqrt(double(v[u][j])) - sqrt(double(v[u][cur])));
flag = 0;
if(arr[u][cur] == v[u][cur]) flag = 1;
else c = min(c, sqrt(double(arr[u][cur])));
c = min(c, tarjan(u, cur, cur, v[u][cur]));
maxx = max(maxx, q + c);
}
v[u][cur] = v[cur][u] = inf;
for(int j = 0; j < n; ++j)
if(v[cur][j] == inf || v[u][j] == inf) v[cur][j] = inf;
else v[cur][j] = min(v[cur][j], v[u][j]);
}
}
}
int main()
{
// freopen("in.txt", "r", stdin);
int t, k;
scanf("%d", &t);
while(t--){
scanf("%d %d", &n, &k);
for(int i = 0; i < n; ++i)
scanf("%d %d", &num[i][0], &num[i][1]), head[i] = -1;
for(int i = 0; i < n; ++i){
arr[i][i] = v[i][i] = inf;
for(int j = i + 1; j < n; ++j)
if(i != j) arr[i][j] = arr[j][i] = v[i][j] = v[j][i] = dist(i, j);
}
prim();
q = maxx;
dfs(0, -1);
printf("%.2lf\n", maxx * k);
}
return 0;
}