#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; template struct LiChaoTree { private: struct Line { T a,b; Line(T a,T b) : a(a),b(b) {} inline T eval(T x) const { return a * x + b; } }; struct Node { Line x; Node *l, *r; Node(const Line &x) : x(x),l(nullptr),r(nullptr) {} }; Node *root; Node *add_line(Node *node,Line &x,const T &lower,const T &upper,const T &lower_value,const T &upper_value) { if(!node) { return new Node(x); } T node_lower_value = node -> x.eval(lower); T node_upper_value = node -> x.eval(upper); if(node_lower_value <= lower_value && node_upper_value <= upper_value) { return node; } else if(node_lower_value >= lower_value && node_upper_value >= upper_value) { node -> x = x; return node; } else { T mid = (lower + upper) / 2; if(mid == upper) { mid--; } T node_mid_value = node -> x.eval(mid),mid_value = x.eval(mid); T nxt_lower_value = lower_value; T nxt_mid_value = mid_value; T nxt_upper_value = upper_value; if(node_mid_value > mid_value) { swap(node -> x,x); swap(node_lower_value,nxt_lower_value); swap(node_mid_value,nxt_mid_value); swap(node_upper_value,nxt_upper_value); } if(node_lower_value >= nxt_lower_value) { node -> l = add_line(node -> l,x,lower,mid,nxt_lower_value,nxt_mid_value); } else { node -> r = add_line(node -> r,x,mid + 1,upper,nxt_mid_value + x.a,nxt_upper_value); } return node; } } Node *add_segment(Node *node,Line &x,const T &x_l,const T &x_r,const T &lower,const T &upper,const T &lower_value,const T &upper_value) { if(upper < x_l || x_r < lower) { return node; } if(x_l <= lower && upper <= x_r) { Line y = x; return add_line(node,y,lower,upper,lower_value,upper_value); } if(node) { T node_lower_value = node -> x.eval(lower); T node_upper_value = node -> x.eval(upper); if(node_lower_value <= lower_value && node_upper_value <= upper_value) { return node; } } else { node = new Node(Line(0,id)); } T mid = (lower + upper) / 2; if(mid == upper) { mid--; } T mid_value = x.eval(mid); node -> l = add_segment(node -> l,x,x_l,x_r,lower,mid,lower_value,mid_value); node -> r = add_segment(node -> r,x,x_l,x_r,mid + 1,upper,mid_value + x.a,upper_value); return node; } T query(const Node *node,const T &x_l,const T &x_r,const T &x) const { if(!node) { return id; } T res = node -> x.eval(x); if(x_l == x_r) { return res; } T x_m = (x_l + x_r) / 2; if(x_m == x_r) { x_m--; } if(x <= x_m) { res = min(res,query(node -> l,x_l,x_m,x)); } else { res = min(res,query(node -> r,x_m + 1,x_r,x)); } return res; } public: LiChaoTree() : root(nullptr) {} void add_line(const T &a,const T &b) { Line x(a,b); root = add_line(root,x,lower_limit,upper_limit,x.eval(lower_limit),x.eval(upper_limit)); } //[l,r) void add_segment(const T &l,const T &r,const T &a,const T &b) { Line x(a,b); root = add_segment(root,x,l,r - 1,lower_limit,upper_limit,x.eval(lower_limit),x.eval(upper_limit)); } T query(const T &x) const { assert(lower_limit <= x && x <= upper_limit); return query(root,lower_limit,upper_limit,x); } }; #include #include #include using namespace std; struct UnionFind { private: int n; vector par,siz; public: UnionFind(int n) :n(n),par(n,-1),siz(n,1) {} int root(int u) { assert(0 <= u && u < n); return (par[u] < 0 ? u:par[u] = root(par[u])); } bool same(int u,int v) { assert(0 <= u && u < n && 0 <= v && v < n); return root(u) == root(v); } bool unite(int u,int v) { assert(0 <= u && u < n && 0 <= v && v < n); u = root(u),v = root(v); if(u == v) return false; if(siz[u] < siz[v]) swap(u,v); siz[u] += siz[v]; par[v] = u; return true; } int size(int u) { assert(0 <= u && u < n); return siz[root(u)]; } vector> components() { vector> ret(n); for(int u = 0;u < n;u++) ret[root(u)].push_back(u); ret.erase(remove_if(ret.begin(),ret.end(),[](vector v) { return v.empty();}),ret.end()); return ret; } }; void Main() { int H,W; cin >> H >> W; vector S(H); for(int i = 0;i < H;i++) { cin >> S[i]; } vector dp(W); for(int i = H - 2;i >= 0;i--) { vector n_dp(W,(int)1e9); UnionFind uf(2 * W); for(int j = 0;j < W;j++) { if(S[i][j] == '.') { if(j + 1 < W && S[i][j + 1] == '.') { uf.unite(j,j + 1); } if(S[i + 1][j] == '.') { uf.unite(j,j + W); } } if(S[i + 1][j] == '.') { if(j + 1 < W && S[i + 1][j + 1] == '.') { uf.unite(j + W,j + 1 + W); } } } vector L(2 * W,(int)1e9),R(2 * W,-1); for(int j = 0;j < W;j++) { int p = uf.root(j); L[p] = min(L[p],j); R[p] = max(R[p],j); } for(int j = 0;j < W;j++) { if(S[i][j] == '#') { dp[j] = (int)1e9; } } { LiChaoTree LCT; for(int j = 0;j < W;j++) { if(S[i + 1][j] != '#') { int p = uf.root(j + W); int l = L[p],r = R[p]; if(l != (int)1e9) { LCT.add_segment(l,min(r + 1,j + dp[j]),0,dp[j]); if(j + dp[j] < r + 1) { LCT.add_segment(j + dp[j],r + 1,1,-j); } } } n_dp[j] = min(n_dp[j],LCT.query(j)); } } { LiChaoTree LCT; for(int j = W - 1;j >= 0;j--) { if(S[i + 1][j] != '#') { int p = uf.root(j + W); int l = L[p],r = R[p]; if(l != (int)1e9) { if(j - dp[j] > l) { LCT.add_segment(l,min(r + 1,j - dp[j]),-1,j); } LCT.add_segment(max(l,j - dp[j]),r + 1,0,dp[j]); } } n_dp[j] = min(n_dp[j],LCT.query(j)); } } swap(dp,n_dp); } for(int i = 0;i < W;i++) { cout << dp[i] << "\n"; } } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int tt = 1; /* cin >> tt; */ while(tt--) Main(); }