UVA 10888 - Warehouse
题意：就是推箱子游戏，问最少要几步
思路：每一个箱子和目标位置建边。权值为负权值，然后进行二分图完美匹配就可以，注意不能到达的位置权值应该置为最小
代码：
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <queue>
using namespace std; const int MAXNODE = 45; typedef int Type;
const Type INF = 0x3f3f3f3f; struct KM {
int n;
Type g[MAXNODE][MAXNODE];
Type Lx[MAXNODE], Ly[MAXNODE], slack[MAXNODE];
int left[MAXNODE];
bool S[MAXNODE], T[MAXNODE]; void init(int n) {
this->n = n;
} void add_Edge(int u, int v, Type val) {
g[u][v] = val;
} bool dfs(int i) {
S[i] = true;
for (int j = 0; j < n; j++) {
if (T[j]) continue;
Type tmp = Lx[i] + Ly[j] - g[i][j];
if (!tmp) {
T[j] = true;
if (left[j] == -1 || dfs(left[j])) {
left[j] = i;
return true;
}
} else slack[j] = min(slack[j], tmp);
}
return false;
} void update() {
Type a = INF;
for (int i = 0; i < n; i++)
if (!T[i]) a = min(a, slack[i]);
for (int i = 0; i < n; i++) {
if (S[i]) Lx[i] -= a;
if (T[i]) Ly[i] += a;
}
} int km() {
for (int i = 0; i < n; i++) {
left[i] = -1;
Lx[i] = -INF; Ly[i] = 0;
for (int j = 0; j < n; j++)
Lx[i] = max(Lx[i], g[i][j]);
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) slack[j] = INF;
while (1) {
for (int j = 0; j < n; j++) S[j] = T[j] = false;
if (dfs(i)) break;
else update();
}
}
int ans = 0;
for (int i = 0; i < n; i++)
ans -= g[left[i]][i];
return ans;
}
} gao; #define MP(a,b) make_pair(a,b)
const int d[4][2] = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}}; typedef pair<int, int> pii; const int N = 45; int t, n, m;
char g[N][N];
int idb[N][N], idx[N][N], bn, xn, vis[N][N];
pii tob[N], tox[N]; int dis(pii a, pii b) {
return abs(a.first - b.first) + abs(a.second - b.second);
} void bfs(int xs, int ys) {
queue<pii> Q;
Q.push(MP(xs, ys));
memset(vis, INF, sizeof(vis));
vis[xs][ys] = 0;
while (!Q.empty()) {
pii u = Q.front();
if (g[u.first][u.second] == 'X')
gao.add_Edge(idb[xs][ys], idx[u.first][u.second], -vis[u.first][u.second]);
Q.pop();
for (int i = 0; i < 4; i++) {
int x = u.first + d[i][0];
int y = u.second + d[i][1];
if (x < 0 || x >= n || y < 0 || y >= m || g[x][y] == '#') continue;
if (vis[x][y] <= vis[u.first][u.second] + 1) continue;
vis[x][y] = vis[u.first][u.second] + 1;
Q.push(MP(x, y));
}
}
} int main() {
scanf("%d", &t);
while (t--) {
scanf("%d%d", &n, &m);
bn = xn = 0;
memset(gao.g, -INF, sizeof(gao.g));
for (int i = 0; i < n; i++) {
scanf("%s", g[i]);
for (int j = 0; j < m; j++) {
if (g[i][j] == 'B') {
tob[bn] = MP(i, j);
idb[i][j] = bn++;
}
if (g[i][j] == 'X') {
tox[xn] = MP(i, j);
idx[i][j] = xn++;
}
}
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (g[i][j] == 'B') {
bfs(i, j);
}
}
}
gao.init(bn);
printf("%d\n", gao.km());
}
return 0;
}