连续最短路算法(Successive Shortest Path)(最小费用最大流)

时间:2023-03-08 22:17:40
连续最短路算法(Successive Shortest Path)(最小费用最大流)
 #include <cstdio>
#include <cstring>
#include <queue>
#include <vector>
#include <algorithm>
using namespace std;
#define N 205
#define INF 0x3f3f3f3f
struct node {
int x, y;
node () {}
node (int x, int y) : x(x), y(y) {}
};
struct Edge {
int cap, u, v, cost;
Edge() {}
Edge(int u, int v, int cap, int cost) : u(u), v(v), cap(cap), cost(cost) {}
}edge[N*N];
vector<node> p, h;
vector<int> G[N];
int tot, dis[N], inq[N], pre[N], S, T; void AddEdge(int u, int v, int cap, int cost) {
edge[tot] = Edge(u, v, cap, cost);
G[u].push_back(tot++);
edge[tot] = Edge(v, u, , -cost);
G[v].push_back(tot++);
} int CalDis(int x1, int y1, int x2, int y2) {
return abs(x1 - x2) + abs(y1 - y2);
} bool SPFA() {
memset(inq, , sizeof(inq));
memset(dis, INF, sizeof(dis));
queue<int> que; que.push(S);
dis[S] = ; inq[S] = ;
while(!que.empty()) {
int u = que.front(); que.pop(); inq[u] = ;
for(int i = ; i < G[u].size(); i++) {
Edge &e = edge[G[u][i]];
if(e.cap > && dis[e.v] > e.cost + dis[u]) {
// 当可以增广并且费用更小的时候
dis[e.v] = e.cost + dis[u];
pre[e.v] = G[u][i]; // 记录路径
if(inq[e.v]) continue;
que.push(e.v); inq[e.v] = ;
}
}
}
return dis[T] < INF;
} void MFMC(int &mincost, int &maxflow) {
int ans = , flow = INF, p;
// 从汇点沿着此次增广的路径往回走,当找到源点的时候退出
for(int u = T; u; u = edge[p].u) {
p = pre[u]; // 找增广的流量
if(edge[p].cap < flow) flow = edge[p].cap;
}
for(int u = T; u; u = edge[p].u) {
p = pre[u];
edge[p].cap -= flow; // 更新每条边的流量
edge[p^].cap += flow;
ans += flow * edge[p].cost; // 费用 = 单位费用 * 流量
}
mincost += ans, maxflow += flow;
} int main() {
int n, m;
char s[];
while(scanf("%d%d", &n, &m), n + m) {
p.clear(); h.clear();
for(int i = ; i < n; i++) {
scanf("%s", s);
for(int j = ; j < m; j++) {
if(s[j] == 'H') h.push_back(node(i, j));
if(s[j] == 'm') p.push_back(node(i, j));
}
}
tot = ; int sz1 = p.size(), sz2 = h.size();
S = , T = sz1 + sz2 + ;
for(int i = ; i <= T; i++) G[i].clear();
for(int i = ; i < sz1; i++) // S到man
AddEdge(S, i + , , );
for(int i = ; i < sz2; i++) // house到T
AddEdge(i + + sz1, T, , );
for(int i = ; i < sz1; i++) {
for(int j = ; j < sz2; j++) {
int c = CalDis(p[i].x, p[i].y, h[j].x, h[j].y);
AddEdge(i + , j + + sz1, , c);
}
} int mincost = , maxflow = ;
while(SPFA()) MFMC(mincost, maxflow);
printf("%d\n", mincost);
}
return ;
}