PAT顶级 1003.Universal Travel Sites

181

基础网络流问题

题目


原题链接
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After finishing her tour around the Earth, CYLL is now planning a universal travel sites development project. After a careful investigation, she has a list of capacities of all the satellite transportation stations in hand. To estimate a budget, she must know the minimum capacity that a planet station must have to guarantee that every space vessel can dock and download its passengers on arrival.

Input Specification:
Each input file contains one test case. For each case, the first line contains the names of the source and the destination planets, and a positive integer N (<=500). Then N lines follow, each in the format:

source~i~ destination~i~ capacity~i~

where source~i~ and destination~i~ are the names of the satellites and the two involved planets, and capacity~i~ > 0 is the maximum number of passengers that can be transported at one pass from source~i~ to destination~i~. Each name is a string of 3 uppercase characters chosen from {A-Z}, e.g., ZJU.

Note that the satellite transportation stations have no accommodation facilities for the passengers. Therefore none of the passengers can stay. Such a station will not allow arrivals of space vessels that contain more than its own capacity. It is guaranteed that the list contains neither the routes to the source planet nor that from the destination planet.

Output Specification:

For each test case, just print in one line the minimum capacity that a planet station must have to guarantee that every space vessel can dock and download its passengers on arrival.

Sample Input:
EAR MAR 11
EAR AAA 300
EAR BBB 400
AAA BBB 100
AAA CCC 400
AAA MAR 300
BBB DDD 400
AAA DDD 400
DDD AAA 100
CCC MAR 400
DDD CCC 200
DDD MAR 300


Sample Output:
700



解析


基础的网络流题,不卡题意,不卡时间。
然而因为自己手写网络流,还是坑了很久。

具体踩的坑见:new、sizeof与指针
网络流算法见:EK、Dinic和ISAP

数据读入结合了string和map。
为了能在建图前获得节点个数,使用vector先把输入数据存了起来,在输入完成后重新插入到图中。

代码


C++解法


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#include <cstdio>
#include <cstring>
#include <map>
#include <queue>
#include <string>
#include <vector>
using namespace std;

#define Log(format, ...) // printf(format, ##__VA_ARGS__)

map<string, int> hashTable;
map<int, string> unHashTable;

int makeHash(char t[4]) {
static int idx = 0;
if (idx == 0) {
hashTable.clear();
unHashTable.clear();
}
string s = string(t);
if (hashTable.count(s) == 0) {
hashTable.insert(make_pair(s, idx));
unHashTable.insert(make_pair(idx, s));
++idx;
}
int hashCode = hashTable.find(s)->second;
Log("%s ---> %d\n", s.c_str(), hashCode);
return hashCode;
}
string unHash(int idx) {
auto iter = unHashTable.find(idx);
if (iter == unHashTable.end())
return "";
return iter->second;
}

class maxFlow {
struct Edge {
int cap, flow;
Edge(int _cap = 0, int _flow = 0) : cap(_cap), flow(_flow) {}
};
static const int INF = 0x7FFFFFFF;
static const bool DEBUG = false;
int s, v, n;

Edge **edges;
int *dis, *num, *pre, *cur;

public:
void addEdge(int from, int to, int cap) {
Log("%d -> %d cap = %d\n", from, to, cap);
edges[from][to].cap += cap;
}

int ISAP() {
bfs();
layerCalc();
return dfs();
}
maxFlow(int s, int v, int n) {
this->s = s;
this->v = v;
this->n = n;

Log("init %d -> %d n = %d\n", s, v, n);

edges = new Edge *[n];
for (int i = 0; i < n; ++i) {
edges[i] = new Edge[n];
memset(edges[i], 0, sizeof(Edge) * n);
}

dis = new int[n];
num = new int[n + 1];
pre = new int[n];
cur = new int[n];
}
~maxFlow() {
for (int i = 0; i < n; ++i)
delete[] edges[i];
delete[] edges;

delete[] dis;
delete[] num;
delete[] pre;
delete[] cur;
}

private:
queue<int> Q;

void bfs() {
while (!Q.empty())
Q.pop();
memset(dis, 0, sizeof(int) * n);
Q.push(v);
dis[v] = 1;
while (!Q.empty()) {
int t = Q.front();
Q.pop();
for (int i = 0; i < n; ++i) {
Edge &e = edges[i][t];
if (e.cap > e.flow && !dis[i]) {
dis[i] = dis[t] + 1;
Q.push(i);
}
}
}
}

void layerCalc() {
memset(num, 0, sizeof(int) * (n + 1));
for (int i = 0; i < n; ++i)
++num[dis[i]];
}

int Augumemt() {
int t = v, delta = INF;
while (t != s) {
int &lastNode = pre[t];
Edge &e = edges[lastNode][t];
delta = min(delta, e.cap - e.flow);
t = lastNode;
}
t = v;
while (t != s) {
int &lastNode = pre[t];
Edge &e = edges[lastNode][t];
Edge &e2 = edges[t][lastNode];
e.flow += delta;
e2.flow -= delta;
t = lastNode;
}
return delta;
}

int dfs() {
memset(pre, 0, sizeof(int) * n);
memset(cur, 0, sizeof(int) * n);

int flow = 0;
int t = s;

while (dis[s] <= n) {
if (DEBUG)
test(t);

if (t == v) {
flow += Augumemt();
t = s;
Log("At the destnation flow = %d\n", flow);
}

int finish = true;
for (int i = cur[t]; i < n; ++i) {
Edge &e = edges[t][i];
if (e.cap > e.flow && dis[t] == dis[i] + 1) {
finish = false;
pre[i] = t;
cur[t] = i;
t = i;
break;
}
}

if (finish) {
Log("finish\n");
int m = n;
for (int i = 0; i < n; i++) {
Edge &e = edges[t][i];
if (e.cap > e.flow)
m = min(m, dis[i]);
}
if (--num[dis[t]] == 0)
break;
++num[dis[t] = m + 1];
cur[t] = 0;
if (t != s)
t = pre[t];
}
}
return flow;
}

void test(int t) {
Log("At %d\n", t);
Log("idx:\t");
for (int i = 0; i < n; ++i)
Log("%4d ", i);
Log("\n");
disTest();
preTest();
numTest();
curTest();
edgeTest();
Log("\n\n");
}
void disTest() {
Log("dis:\t");
for (int i = 0; i <= n; ++i)
Log("%4d ", dis[i]);
Log("\n");
}

void preTest() {
Log("pre:\t");
for (int i = 0; i < n; ++i)
Log("%4d ", pre[i]);
Log("\n");
}

void numTest() {
Log("num:\t");
for (int i = 0; i <= n; ++i)
Log("%4d ", num[i]);
Log("\n");
}
void curTest() {
Log("cur:\t");
for (int i = 0; i < n; ++i)
Log("%4d ", cur[i]);
Log("\n");
}

void edgeTest() {
Log("\t");
for (int i = 0; i < n; ++i)
Log("%6d ", i);
Log("\n");
for (int i = 0; i < n; ++i) {
Log("%d\t", i);
for (int j = 0; j < n; ++j) {
Log("(%3d,%3d) ", edges[i][j].cap, edges[i][j].flow);
}
Log("\n");
}
}
};

const int maxn = 505;
struct Node {
int from, to, cap;
Node(int _from, int _to, int _cap) : from(_from), to(_to), cap(_cap) {}
};
vector<Node> vec;

int main() {
int n;
char a[4], b[4];
scanf("%s%s%d", a, b, &n);
int s = makeHash(a), v = makeHash(b);
vec.clear();
for (int i = 0; i < n; ++i) {
int cap;
scanf("%s%s%d", a, b, &cap);
int from = makeHash(a), to = makeHash(b);
vec.push_back(Node(from, to, cap));
}

maxFlow ans = maxFlow(s, v, hashTable.size());
for (auto it = vec.begin(); it != vec.end(); ++it)
ans.addEdge(it->from, it->to, it->cap);

printf("%d\n", ans.ISAP());

return 0;
}




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