UVA 11380 - Down Went The Titanic（网络流）

UVA 11380 - Down Went The Titanic

题目链接

题意：给定一个图，上面有薄冰'.'或'*‘，厚冰'@',木块'#'，一开始人都在'*'上，薄冰只能走一次就会沉掉，厚冰次数不限，如果人走到木块上就获救了，但是一个木块的容量只有p，求最多能有多少人获救

思路：最大流，由于点有次数限制，所以可以进行拆点，然后建图每个4和四个方向建边，源点和'*'建边，'#'和汇点建边容量为p，然后跑一下最大流即可

代码：

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

const int MAXNODE = 2005;
const int MAXEDGE = 100005;

typedef int Type;
const Type INF = 0x3f3f3f3f;

struct Edge {
int u, v;
Type cap, flow;
Edge() {}
Edge(int u, int v, Type cap, Type flow) {
this->u = u;
this->v = v;
this->cap = cap;
this->flow = flow;
}
};

struct Dinic {
int n, m, s, t;
Edge edges[MAXEDGE];
int first[MAXNODE];
int next[MAXEDGE];
bool vis[MAXNODE];
Type d[MAXNODE];
int cur[MAXNODE];
vector<int> cut;

void init(int n) {
this->n = n;
memset(first, -1, sizeof(first));
m = 0;
}
void add_Edge(int u, int v, Type cap) {
edges[m] = Edge(u, v, cap, 0);
next[m] = first[u];
first[u] = m++;
edges[m] = Edge(v, u, 0, 0);
next[m] = first[v];
first[v] = m++;
}

bool bfs() {
memset(vis, false, sizeof(vis));
queue<int> Q;
Q.push(s);
d[s] = 0;
vis[s] = true;
while (!Q.empty()) {
int u = Q.front(); Q.pop();
for (int i = first[u]; i != -1; i = next[i]) {
Edge& e = edges[i];
if (!vis[e.v] && e.cap > e.flow) {
vis[e.v] = true;
d[e.v] = d[u] + 1;
Q.push(e.v);
}
}
}
return vis[t];
}

Type dfs(int u, Type a) {
if (u == t || a == 0) return a;
Type flow = 0, f;
for (int &i = cur[u]; i != -1; i = next[i]) {
Edge& e = edges[i];
if (d[u] + 1 == d[e.v] && (f = dfs(e.v, min(a, e.cap - e.flow))) > 0) {
e.flow += f;
edges[i^1].flow -= f;
flow += f;
a -= f;
if (a == 0) break;
}
}
return flow;
}

Type Maxflow(int s, int t) {
this->s = s; this->t = t;
Type flow = 0;
while (bfs()) {
for (int i = 0; i < n; i++)
cur[i] = first[i];
flow += dfs(s, INF);
}
return flow;
}

void MinCut() {
cut.clear();
for (int i = 0; i < m; i += 2) {
if (vis[edges[i].u] && !vis[edges[i].v])
cut.push_back(i);
}
}
} gao;

const int N = 35;
const int d[4][2] = {1, 0, -1, 0, 0, 1, 0, -1};

int x, y, p;
char str
;

int main() {
while (~scanf("%d%d%d", &x, &y, &p)) {
int tot = x * y;
gao.init(2 * tot + 2);
for (int i = 0; i < x; i++) {
scanf("%s", str);
for (int j = 0; j < y; j++) {
int u = i * y + j + 1;
if (str[j] == '*' || str[j] == '.') {
gao.add_Edge(u, u + tot, 1);
if (str[j] == '*')
gao.add_Edge(0, u, 1);
}
if (str[j] == '#') {
gao.add_Edge(u, u + tot, INF);
gao.add_Edge(u + tot, 2 * tot + 1, p);
}
if (str[j] == '@') gao.add_Edge(u, u + tot, INF);
for (int k = 0; k < 4; k++) {
int xx = i + d[k][0];
int yy = j + d[k][1];
if (xx < 0 || xx >= x || yy < 0 || yy >= y) continue;
int v = xx * y + yy + 1;
gao.add_Edge(u + tot, v, INF);
}
}
}
printf("%d\n", gao.Maxflow(0, 2 * tot + 1));
}
return 0;
}