最大流练习：Parking，二分匹配

题目：http://community.topcoder.com/stat?c=problem_statement&pm=3530&rd=6535

先用BFS求出每辆车到每个停车场的最短距离，接下来就是二分匹配。逐渐增大最小时间D，知道能够找到一条增广路径，若找不到，则说明不能匹配，返回-1。

代码：

#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <iostream>
#include <sstream>
#include <iomanip>

#include <bitset>
#include <string>
#include <vector>
#include <stack>
#include <deque>
#include <queue>
#include <set>
#include <map>

#include <cstdio>
#include <cstdlib>
#include <cctype>
#include <cmath>
#include <cstring>
#include <ctime>
#include <climits>
using namespace std;

#define CHECKTIME() printf("%.2lf\n", (double)clock() / CLOCKS_PER_SEC)
typedef pair<int, int> pii;
typedef long long llong;
typedef pair<llong, llong> pll;
#define mkp make_pair

/*************** Program Begin **********************/
int g[105][105];
bool v_bfs[105][105];
int dx[] = {1, -1, 0, 0};
int dy[] = {0, 0, 1, -1};
const int INF = INT_MAX;
int D = 0;
const int MAX = 10000;
int park_match[105];
bool v_dfs[105];

class Parking {
public:
vector <string> park;
map <pii, int> car_mp;
map <pii, int> park_mp;

void BFS(pii start)
{
queue <pair<pii, int>> Q;
v_bfs[start.first][start.second] = true;
Q.push(mkp(start, 0));
while (!Q.empty()) {
pii where = Q.front().first;
int dist = Q.front().second;
Q.pop();
if (park_mp.find(where) != park_mp.end()) {
g[ car_mp[start] ][ park_mp[where] ] = dist;
}
for (int i = 0; i < 4; i++) {
int nx = where.first + dx[i];
int ny = where.second + dy[i];
if (nx < 0 || nx >= park.size() || ny < 0 || ny >= park[0].size()) {
continue;
}
if (v_bfs[nx][ny] || 'X' == park[nx][ny]) {
continue;
}
v_bfs[nx][ny] = true;
Q.push(mkp( mkp(nx, ny), dist + 1 ));
}
}
}

bool DFS(int where)
{
if (-1 == where) {
return true;
}

for (int i = 0; i < park_mp.size(); i++) {
if (g[where][i] > D || v_dfs[i]) {
continue;
}
v_dfs[i] = true;
if (DFS(park_match[i])) {
park_match[i] = where;
return true;
}
}
return false;
}

int minTime(vector <string> park) {
int res = 0;
this->park = park;
int cnt1 = 0, cnt2 = 0;

for (int i = 0; i < park.size(); i++) {
for (int j = 0; j < park[0].size(); j++) {
if ('C' == park[i][j]) {
car_mp[mkp(i, j)] = cnt1;
++cnt1;
} else if ('P' == park[i][j]) {
park_mp[mkp(i, j)] = cnt2;
++cnt2;
}
}
}
for (int i = 0; i < 105; i++) {
for (int j = 0; j < 105; j++) {
g[i][j] = INF;
}
}

for (map<pii, int>::iterator it = car_mp.begin(); it != car_mp.end(); it++) {
memset(v_bfs, 0, sizeof(v_bfs));
BFS( (*it).first );
}

D = 0;
memset(park_match, -1, sizeof(park_match));
for (int i = 0; i < car_mp.size(); i++) {
memset(v_dfs, 0, sizeof(v_dfs));
while (D < MAX && !DFS(i)) {
++D;
memset(v_dfs, 0, sizeof(v_dfs));
}
if (D >= MAX) {
break;
}
}
res = (D >= MAX ? -1 : D);
return res;
}
};

/************** Program End ************************/