#include #include #include #include #include #include #include using namespace std; const int LIM = 3005; const int MAXN = LIM * LIM; vector adj[MAXN]; unordered_set cutpoints; vector comp; vector> bcc, bcc_adj; void reset_edges() { for (int i = 0; i < MAXN; i++) { adj[i].clear(); } } void add_edge(int u, int v) { adj[u].push_back(v); adj[v].push_back(u); } void tarjan(int N) { cutpoints.clear(); bcc.clear(); comp.assign(N, -1); vector vis(N), parent(N, -1), children(N), tin(N), pushed(N), low(N); vector is_cut(N); int curr_root = 0; stack> dfs; stack st; for (int i = 0; i < N; i++) { if (vis[i]) { continue; } vis[i] = ++curr_root; tin[i] = 0; int timer = 1; dfs.push({i, 0, 0}); while (!dfs.empty()) { auto [u, j, t] = dfs.top(); low[u] = t; if (!pushed[u]) { st.push(u); pushed[u] = 1; } if (j == (int)adj[u].size()) { if ((parent[u] == -1 && children[u] >= 2) || (parent[u] != -1 && is_cut[u])) { cutpoints.insert(u); } if (t >= tin[u]) { vector component; do { int v = st.top(); component.push_back(v); comp[v] = bcc.size(); st.pop(); } while (comp[u] == -1); bcc.push_back(component); } dfs.pop(); continue; } int v = adj[u][j]; if (parent[u] == v) { get<1>(dfs.top())++; continue; } if (vis[v] == 0) { vis[v] = curr_root; parent[v] = u; children[u]++; dfs.push({v, 0, timer}); tin[v] = timer++; continue; } is_cut[u] = is_cut[u] || low[v] >= tin[u]; if (vis[v] == curr_root && comp[v] == -1 && low[v] < t) { get<2>(dfs.top()) = low[v]; } get<1>(dfs.top())++; } } bcc_adj.assign(bcc.size(), {}); for (int i = 0; i < N; i++) { for (int j = 0; j < (int)adj[i].size(); j++) { if (comp[i] != comp[adj[i][j]]) { bcc_adj[comp[i]].push_back(comp[adj[i][j]]); } } } } template class LinkCut { struct Node { int ch[2] = {0, 0}, p = 0; Value self = 0, path = 0; // Path aggregates Value sub = 0, vir = 0; // Subtree aggregates bool flip = 0; // Lazy tags }; vector T; void push(int x) { if (x == 0 || !T[x].flip) { return; } int l = T[x].ch[0], r = T[x].ch[1]; T[l].flip ^= 1; T[r].flip ^= 1; swap(T[x].ch[0], T[x].ch[1]); T[x].flip = 0; } void pull(int x) { int l = T[x].ch[0], r = T[x].ch[1]; push(l); push(r); T[x].path = T[l].path + T[x].self + T[r].path; T[x].sub = T[x].vir + T[l].sub + T[r].sub + T[x].self; } void set(int x, int d, int y) { T[x].ch[d] = y; T[y].p = x; pull(x); } void splay(int x) { auto dir = [&](int x) { int p = T[x].p; if (p == 0) { return -1; } return T[p].ch[0] == x ? 0 : T[p].ch[1] == x ? 1 : -1; }; auto rotate = [&](int x) { int y = T[x].p, z = T[y].p, dx = dir(x), dy = dir(y); set(y, dx, T[x].ch[!dx]); set(x, !dx, y); if (~dy) { set(z, dy, x); } T[x].p = z; }; for (push(x); ~dir(x);) { int y = T[x].p, z = T[y].p; push(z); push(y); push(x); int dx = dir(x), dy = dir(y); if (~dy) { rotate(dx != dy ? x : y); } rotate(x); } } int access(int x) { int v = 0; for (int u = x; u != 0; u = T[u].p) { splay(u); int &ov = T[u].ch[1]; T[u].vir += T[ov].sub; T[u].vir -= T[v].sub; ov = v; pull(u); v = u; } splay(x); return v; } void reroot(int x) { access(x); T[x].flip ^= 1; push(x); } public: LinkCut(int n = 0) : T(n + 1) {} void Init(int u, Value v) { T[++u].self = v; pull(u); } void Reset(int n) { T.clear(); T.resize(n + 1); } void Link(int u, int v) { if (u == v || LCA(u, v) != -1) { return; } reroot(++u); access(++v); T[v].vir += T[u].sub; T[u].p = v; pull(v); } void Cut(int u, int v) { if (u == v || LCA(u, v) == -1) { return; } reroot(++u); access(++v); T[v].ch[0] = T[u].p = 0; pull(v); } // Rooted tree LCA. Returns -1 if u and v aren't connected. int LCA(int u, int v) { if (++u == ++v) { return u; } access(u); int ret = access(v); return T[u].p ? ret : -1; } // Query subtree of u where v is outside the subtree. // Pass u = v to get the aggregate for the entire tree containing u. Value Subtree(int u, int v) { reroot(++v); access(++u); return T[u].vir + T[u].self; } Value Path(int u, int v) { reroot(++u); access(++v); return T[v].path; } void Update(int u, Value v) { access(++u); T[u].self = v; pull(u); } }; // Main algorithm. int R, C; int G[LIM][LIM]; LinkCut lcf; inline int getn(int r, int c) { return r * C + c; } inline int getr(int n) { return n / C; } inline int getc(int n) { return n % C; } // Size of group connected to (r2, c2) after swapping (r1, c1) to (r2, c2). int num_cleared(int r1, int c1, int r2, int c2) { int res = 0; int u = getn(r1, c1), cu = comp[u]; // If u is a cutpoint, disconnect it from all neighboring BCCs. if (cutpoints.count(u)) { for (int v : adj[u]) { int cv = comp[v]; if (cu != cv) { lcf.Cut(cu, cv); } } } // Get a representative for each neighboring group of (r2, c2). unordered_set seen_groups; bool seen_orig = false; // Whether we've seen the original group of cu. for (auto [dr, dc] : {pair{-1, 0}, {0, 1}, {1, 0}, {0, -1}}) { int r3 = r2 + dr, c3 = c2 + dc; if (r3 < 0 || r3 >= R || c3 < 0 || c3 >= C) { continue; } if (!(r1 == r3 && c1 == c3) && G[r1][c1] == G[r3][c3]) { int cv = comp[getn(r3, c3)]; bool seen = false; // Have we seen the same group? for (int cmp : seen_groups) { if (lcf.LCA(cv, cmp) != -1) { seen = true; break; } } if (!seen) { if (lcf.LCA(cu, cv) != -1) { seen_orig = true; } res += lcf.Subtree(cv, cv); seen_groups.insert(cv); } } } // If we didn't encounter the original component, add 1 for the cell itself. if (!seen_orig) { res++; } // Undo disconnections. if (cutpoints.count(u)) { for (int v : adj[u]) { int cv = comp[v]; if (cu != cv) { lcf.Link(cu, cv); } } } return res >= 3 ? res : 0; } long long solve() { reset_edges(); // Build graph. for (int r = 0; r < R; r++) { for (int c = 0; c < C; c++) { for (auto [dr, dc] : {pair{0, 1}, {1, 0}}) { int r2 = r + dr, c2 = c + dc; if (r2 < 0 || r2 >= R || c2 < 0 || c2 >= C) { continue; } if (G[r][c] == G[r2][c2]) { add_edge(getn(r, c), getn(r2, c2)); } } } } // Compute BCC and block forest. tarjan(R * C); int bcc_nodes = (int)bcc.size(); // Create link-cut forest from BCC. lcf.Reset(bcc_nodes); for (int i = 0; i < bcc_nodes; i++) { lcf.Init(i, bcc[i].size()); } for (int i = 0; i < bcc_nodes; i++) { for (int j : bcc_adj[i]) { lcf.Link(i, j); } } // Try swapping each neighbor. long long ans = 0; for (int r = 0; r < R; r++) { for (int c = 0; c < C; c++) { // Only check right and bottom for ordered pairs. for (auto [dr, dc] : {pair{0, 1}, {1, 0}}) { int r2 = r + dr, c2 = c + dc; if (r2 < 0 || r2 >= R || c2 < 0 || c2 >= C) { continue; } if (G[r][c] != G[r2][c2]) { ans += num_cleared(r, c, r2, c2) + num_cleared(r2, c2, r, c); } } } } return 2 * ans; } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int T; cin >> T; for (int t = 1; t <= T; t++) { memset(G, 0, sizeof G); cin >> R >> C; for (int r = 0; r < R; r++) { for (int c = 0; c < C; c++) { cin >> G[r][c]; } } cout << "Case #" << t << ": " << solve() << endl; } return 0; }