Ultraviolet A 10888-warehouse (perfect match in a bipartite graph)

Ultraviolet A 10888-Warehouse

Question Link

It is a box-pushing game. It takes at least a few steps to ask.

Idea: Create an edge for each box and target location, and set the weight value to negative weight. Then perform a perfect match for the bipartite graph. Note that the location weight cannot be reached should be set to the minimum value.

Code:

#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;}

Ultraviolet A 10888-warehouse (perfect match in a bipartite graph)