HDU 4744 Starloop System（最小费用最大流）（2013 ACM/ICPC Asia Regional Hangzhou Online）

Description

At the end of the 200013 th year of the Galaxy era, the war between Carbon-based lives and Silicon civilization finally comes to its end with the Civil Union born from the ruins. The shadow fades away, and the new-born Union is opening a new page.

Although the war ended, the affect of the war is far from over. Now the council is busy fixing the transportation system. Before the war, all the stars were connected with artificial wormholes which were destroyed during the war. At the same time, natural wormholes are breaking down with the growing traffic. A new traffic system is on the schedule.

As two civilizations combine, the technology integrates. Scientists find a new traffic system called the Starloop System.

This system is made up of several starloops. People build a starway to connect two stars. A startloop is a closed path with no repetitions of stars or starways allowed, other than the repetition of the starting and ending star. And a starloop contains at least two starts and two starways. A startloop's cost is the sum of the length of all the starways in it. Length of a starway connecting two stars is floor(x), which x is the euclidean distance between two stars. You can build more than one starway between any two stars, but one starway can only belongs to one starloop.

#include <cstdio>
#include <queue>
#include <cstring>
#include <cmath>
using namespace std;

const int MAXN = 210;
const int MAXE = 210 * 210 * 2;
const int INF = 0x3f3f3f3f;

struct ZKW_flow{
int st, ed, ecnt, n;
int head[MAXN];
int cap[MAXE], cost[MAXE], to[MAXE], next[MAXE];

void init(){
memset(head, 0, sizeof(head));
ecnt = 2;
}

void addEdge(int u, int v, int cc, int ww){
cap[ecnt] = cc; cost[ecnt] = ww; to[ecnt] = v;
next[ecnt] = head[u]; head[u] = ecnt++;
cap[ecnt] = 0; cost[ecnt] = -ww; to[ecnt] = u;
next[ecnt] = head[v]; head[v] = ecnt++;
}

int dis[MAXN];

void SPFA(){
for(int i = 1; i <= n; ++i) dis[i] = INF;
priority_queue<pair<int, int> > Q;
dis[st] = 0;
Q.push(make_pair(0, st));
while(!Q.empty()){
int u = Q.top().second, d = -Q.top().first;
Q.pop();
if(dis[u] != d) continue;
for(int p = head[u]; p; p = next[p]){
int &v = to[p];
if(cap[p] && dis[v] > d + cost[p]){
dis[v] = d + cost[p];
Q.push(make_pair(-dis[v], v));
}
}
}
for(int i = 1; i <= n; ++i) dis[i] = dis[ed] - dis[i];
}

int minCost, maxFlow;
bool use[MAXN];

int add_flow(int u, int flow){
if(u == ed){
maxFlow += flow;
minCost += dis[st] * flow;
return flow;
}
use[u] = true;
int now = flow;
for(int p = head[u]; p; p = next[p]){
int &v = to[p];
if(cap[p] && !use[v] && dis[u] == dis[v] + cost[p]){
int tmp = add_flow(v, min(now, cap[p]));
cap[p] -= tmp;
cap[p^1] += tmp;
now -= tmp;
if(!now) break;
}
}
return flow - now;
}

bool modify_label(){
int d = INF;
for(int u = 1; u <= n; ++u) if(use[u])
for(int p = head[u]; p; p = next[p]){
int &v = to[p];
if(cap[p] && !use[v]) d = min(d, dis[v] + cost[p] - dis[u]);
}
if(d == INF) return false;
for(int i = 1; i <= n; ++i) if(use[i]) dis[i] += d;
return true;
}

int min_cost_flow(int ss, int tt, int nn){
st = ss, ed = tt, n = nn;
minCost = maxFlow = 0;
SPFA();
while(true){
while(true){
for(int i = 1; i <= n; ++i) use[i] = 0;
if(!add_flow(st, INF)) break;
}
if(!modify_label()) break;
}
return minCost;
}
} G;

struct Point {
int x, y, z, w;
void read() {
scanf("%d%d%d%d", &x, &y, &z, &w);
}
int operator * (const Point &rhs) const {
double xx = x - rhs.x, yy = y - rhs.y, zz = z - rhs.z;
return (int)sqrt(xx * xx + yy * yy + zz * zz);
}
};

Point a[MAXN];
int n;

int main() {
while(scanf("%d", &n) != EOF && n) {
int sumw = 0;
for(int i = 1; i <= n; ++i) a[i].read(), sumw += a[i].w;
G.init();
int ss = 2 * n + 1, tt = ss + 1;
for(int i = 1; i <= n; ++i) {
G.addEdge(ss, i, a[i].w, 0);
G.addEdge(i + n, tt, a[i].w, 0);
for(int j = i + 1; j <= n; ++j) {
int cost = a[i] * a[j];
G.addEdge(i, j + n, INF, cost);
G.addEdge(j, i + n, INF, cost);
}
}
int ans = G.min_cost_flow(ss, tt, tt);
if(sumw != G.maxFlow) ans = -1;
printf("%d\n", ans);
}
}

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