#line 1 "template/template.hpp" #include #define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++) #define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--) #define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++) #define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() #line 2 "template/debug_template.hpp" #line 4 "template/debug_template.hpp" namespace ebi { #ifdef LOCAL #define debug(...) \ std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \ debug_out(__VA_ARGS__) #else #define debug(...) #endif void debug_out() { std::cerr << std::endl; } template void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cerr << " :"; debug_out(t...); } } // namespace ebi #line 2 "template/int_alias.hpp" #line 4 "template/int_alias.hpp" namespace ebi { using ld = long double; using std::size_t; using i8 = std::int8_t; using u8 = std::uint8_t; using i16 = std::int16_t; using u16 = std::uint16_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; } // namespace ebi #line 2 "template/io.hpp" #line 5 "template/io.hpp" #include #line 7 "template/io.hpp" namespace ebi { template std::ostream &operator<<(std::ostream &os, const std::pair &pa) { return os << pa.first << " " << pa.second; } template std::istream &operator>>(std::istream &os, std::pair &pa) { return os >> pa.first >> pa.second; } template std::ostream &operator<<(std::ostream &os, const std::vector &vec) { for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template std::istream &operator>>(std::istream &os, std::vector &vec) { for (T &e : vec) std::cin >> e; return os; } template std::ostream &operator<<(std::ostream &os, const std::optional &opt) { if (opt) { os << opt.value(); } else { os << "invalid value"; } return os; } void fast_io() { std::cout << std::fixed << std::setprecision(15); std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } } // namespace ebi #line 2 "template/utility.hpp" #line 5 "template/utility.hpp" #line 2 "graph/base.hpp" #line 5 "graph/base.hpp" #include #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 6 "data_structure/simple_csr.hpp" namespace ebi { template struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector start; std::vector elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template struct Edge { int from, to; T cost; int id; }; template struct Graph { using cost_type = E; using edge_type = Edge; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector> buff; std::vector edges; simple_csr csr; bool prepared = false; }; } // namespace ebi #line 8 "template/utility.hpp" namespace ebi { template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template T safe_ceil(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return (a / b) + 1; else return -((-a) / b); } template T safe_floor(T a, T b) { if (a % b == 0) return a / b; else if (a >= 0) return a / b; else return -((-a) / b) - 1; } constexpr i64 LNF = std::numeric_limits::max() / 4; constexpr int INF = std::numeric_limits::max() / 2; const std::vector dy = {1, 0, -1, 0, 1, 1, -1, -1}; const std::vector dx = {0, 1, 0, -1, 1, -1, 1, -1}; } // namespace ebi #line 2 "tree/centroid_decomposition.hpp" #line 7 "tree/centroid_decomposition.hpp" namespace ebi { namespace internal { template void centroid_decomposition_dfs_naive(const std::vector &par, const std::vector &original_vs, F f) { const int n = (int)par.size(); assert(par.size() == original_vs.size()); int center = -1; std::vector sz(n, 1); for (const int v : std::views::iota(0, n) | std::views::reverse) { if (sz[v] >= (n + 1) / 2) { center = v; break; } sz[par[v]] += sz[v]; } std::vector color(n, -1); std::vector vs = {center}; color[center] = 0; int c = 1; for (const int v : std::views::iota(1, n)) { if (par[v] == center) { vs.emplace_back(v); color[v] = c++; } } if (center > 0) { for (int v = par[center]; v != -1; v = par[v]) { vs.emplace_back(v); color[v] = c; } c++; } for (const int v : std::views::iota(0, n)) { if (color[v] == -1) { vs.emplace_back(v); color[v] = color[par[v]]; } } std::vector index_ptr(c + 1, 0); for (const int v : std::views::iota(0, n)) { index_ptr[color[v] + 1]++; } for (const int i : std::views::iota(0, c)) { index_ptr[i + 1] += index_ptr[i]; } auto counter = index_ptr; std::vector ord(n); for (auto v : vs) { ord[counter[color[v]]++] = v; } std::vector relabel(n); for (const int v : std::views::iota(0, n)) { relabel[ord[v]] = v; } std::vector original_vs2(n); for (const int v : std::views::iota(0, n)) { original_vs2[relabel[v]] = original_vs[v]; } std::vector relabel_par(n, -1); for (int v : std::views::iota(1, n)) { int a = relabel[v]; int b = relabel[par[v]]; if (a > b) std::swap(a, b); relabel_par[b] = a; } f(relabel_par, original_vs2, index_ptr); for (const int i : std::views::iota(1, c)) { int l = index_ptr[i], r = index_ptr[i + 1]; std::vector par1(r - l, -1); std::vector original_vs1(r - l, -1); for (int v : std::views::iota(l, r)) { par1[v - l] = (relabel_par[v] == 0 ? -1 : relabel_par[v] - l); original_vs1[v - l] = original_vs2[v]; } centroid_decomposition_dfs_naive(par1, original_vs1, f); } return; } template void one_third_centroid_decomposition(const std::vector &par, const std::vector &original_vs, F f) { const int n = (int)par.size(); assert(n > 1); if (n == 2) return; int center = -1; std::vector sz(n, 1); for (const int v : std::views::iota(0, n) | std::views::reverse) { if (sz[v] >= (n + 1) / 2) { center = v; break; } sz[par[v]] += sz[v]; } std::vector color(n, -1); std::vector ord(n, -1); ord[center] = 0; int t = 1; int red = n - sz[center]; for (int v = par[center]; v != -1; v = par[v]) { ord[v] = t++; color[v] = 0; } for (const int v : std::views::iota(1, n)) { if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) { red += sz[v]; ord[v] = t++; color[v] = 0; } } for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1 && color[par[v]] == 0) { ord[v] = t++; color[v] = 0; } } const int n0 = t - 1; for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1) { ord[v] = t++; color[v] = 1; } } assert(t == n); const int n1 = n - 1 - n0; std::vector par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1); std::vector original_vs0(n0 + 1), original_vs1(n1 + 1), original_vs2(n); for (const int i : std::views::iota(0, n)) { int v = ord[i]; original_vs2[v] = original_vs[i]; if (color[i] != 1) { original_vs0[v] = original_vs[i]; } if (color[i] != 0) { int idx = std::max(v - n0, 0); original_vs1[idx] = original_vs[i]; } } for (const int v : std::views::iota(1, n)) { int a = ord[v], b = ord[par[v]]; if (a > b) std::swap(a, b); par2[b] = a; if (color[v] != 1 && color[par[v]] != 1) { par0[b] = a; } if (color[v] != 0 && color[par[v]] != 0) { par1[b - n0] = std::max(a - n0, 0); } } f(par2, original_vs2, n0, n1); one_third_centroid_decomposition(par0, original_vs0, f); one_third_centroid_decomposition(par1, original_vs1, f); return; } template void one_third_centroid_decomposition_virtual_real( const std::vector &par, const std::vector &original_vs, const std::vector &is_real, F f) { const int n = (int)par.size(); assert(n > 1); if (n == 2) { if (is_real[0] && is_real[1]) { f(par, original_vs, {0, 1}); } return; } int center = -1; std::vector sz(n, 1); for (const int v : std::views::iota(0, n) | std::views::reverse) { if (sz[v] >= (n + 1) / 2) { center = v; break; } sz[par[v]] += sz[v]; } std::vector color(n, -1); std::vector ord(n, -1); ord[center] = 0; int t = 1; int red = n - sz[center]; for (int v = par[center]; v != -1; v = par[v]) { ord[v] = t++; color[v] = 0; } for (const int v : std::views::iota(1, n)) { if (par[v] == center && 3 * (red + sz[v]) <= 2 * (n - 1)) { red += sz[v]; ord[v] = t++; color[v] = 0; } } for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1 && color[par[v]] == 0) { ord[v] = t++; color[v] = 0; } } const int n0 = t - 1; for (const int v : std::views::iota(1, n)) { if (v != center && color[v] == -1) { ord[v] = t++; color[v] = 1; } } assert(t == n); const int n1 = n - 1 - n0; std::vector par0(n0 + 1, -1), par1(n1 + 1, -1), par2(n, -1); std::vector original_vs0(n0 + 1), original_vs1(n1 + 1), original_vs2(n); std::vector is_real0(n0 + 1), is_real1(n1 + 1), is_real2(n); for (const int i : std::views::iota(0, n)) { int v = ord[i]; original_vs2[v] = original_vs[i]; is_real2[v] = is_real[i]; if (color[i] != 1) { original_vs0[v] = original_vs[i]; is_real0[v] = is_real[i]; } if (color[i] != 0) { int idx = std::max(v - n0, 0); original_vs1[idx] = original_vs[i]; is_real1[idx] = is_real[i]; } } for (const int v : std::views::iota(1, n)) { int a = ord[v], b = ord[par[v]]; if (a > b) std::swap(a, b); par2[b] = a; if (color[v] != 1 && color[par[v]] != 1) { par0[b] = a; } if (color[v] != 0 && color[par[v]] != 0) { par1[b - n0] = std::max(a - n0, 0); } } if (is_real[center]) { color.assign(n, -1); color[0] = 0; for (const int v : std::views::iota(1, n)) { if (is_real2[v]) color[v] = 1; } f(par2, original_vs2, color); is_real0[0] = is_real1[0] = is_real2[0] = 0; } color.assign(n, -1); for (const int v : std::views::iota(1, n)) { if (is_real2[v]) { color[v] = int(v > n0); } } f(par2, original_vs2, color); one_third_centroid_decomposition_virtual_real(par0, original_vs0, is_real0, f); one_third_centroid_decomposition_virtual_real(par1, original_vs1, is_real1, f); return; } } // namespace internal template void centroid_decomposition(const Graph &tree, F f) { int n = (int)tree.size(); if (n == 1) return; std::vector bfs_order(n), par(n, -1); bfs_order[0] = 0; int l = 0, r = 1; while (l < r) { int v = bfs_order[l++]; for (auto e : tree[v]) { int nv = e.to; if (nv == par[v]) continue; bfs_order[r++] = nv; par[nv] = v; } } assert(l == n && r == n); { std::vector relabel(n); for (int i : std::views::iota(0, n)) { relabel[bfs_order[i]] = i; } std::vector relabel_par(n, -1); for (int i : std::views::iota(1, n)) { relabel_par[relabel[i]] = relabel[par[i]]; } std::swap(par, relabel_par); } static_assert(MODE == 0 || MODE == 1 || MODE == 2); if constexpr (MODE == 0) { internal::centroid_decomposition_dfs_naive(par, bfs_order, f); } else if constexpr (MODE == 1) { internal::one_third_centroid_decomposition(par, bfs_order, f); } else { internal::one_third_centroid_decomposition_virtual_real( par, bfs_order, std::vector(n, 1), f); } } } // namespace ebi #line 2 "data_structure/fenwick_tree.hpp" #line 5 "data_structure/fenwick_tree.hpp" namespace ebi { template struct fenwick_tree { private: int n; std::vector data; public: fenwick_tree(int _n) : n(_n), data(std::vector(_n + 1, T(0))) {} void add(int i, T val) { i++; for (int x = i; x <= n; x += x & -x) { data[x] += val; } } T prefix_sum(int i) const { assert(0 <= i && i <= n); T ret = 0; for (int x = i; x > 0; x -= x & -x) { ret += data[x]; } return ret; } T sum(int l, int r) const { return prefix_sum(r) - prefix_sum(l); } T all_sum() const { return prefix_sum(n); } // prefix_sum(x) >= key となる最小のxを返す関数 O(log N) int lower_bound(T key) { if (key <= 0) return 0; int x = 0; int max = 1; while ((max << 1) <= n) max <<= 1; for (int k = max; k > 0; k >>= 1) { if (x + k <= n && data[x + k] < key) { x += k; key -= data[x]; } } return x + 1; } }; } // namespace ebi #line 4 "a.cpp" namespace ebi { void main_() { int n; std::cin >> n; Graph g(n); g.read_tree(); std::string s; std::cin >> s; int zero = n + 5; i64 ans = 0; fenwick_tree ftree0(2 * n + 10), ftree1(2 * n + 10); auto calc = [&](const std::vector &par, const std::vector &vs, int n0, int n1) -> void { int sz = (int)par.size(); assert(sz - 1 == n0 + n1); std::vector a(sz, 0); for(const int v: std::views::iota(1, sz)) { a[v] = a[par[v]] + (s[vs[v]] == '1' ? 1 : -1); } for(const int v: std::views::iota(1, sz)) { if(v < 1 + n0) { ftree0.add(zero + a[v], 1); } else { ftree1.add(zero + a[v], 1); } } for(const int v: std::views::iota(1, sz)) { if(v < 1 + n0) { int x = zero - (a[v] + (s[vs[0]] == '1' ? 1 : -1)); ans += ftree1.sum(x + 1, 2 * n + 10); } else { int x = zero - (a[v] + (s[vs[0]] == '1' ? 1 : -1)); ans += ftree0.sum(x + 1, 2 * n + 10); } } for(const int v: std::views::iota(1, sz)) { if(v < 1 + n0) { ftree0.add(zero + a[v], -1); } else { ftree1.add(zero + a[v], -1); } } }; rep(i,0,n) { if(s[i] != '1') continue; for(auto e: g[i]) { if(s[e.to] == '1') ans++; } } centroid_decomposition<1>(g, calc); ans /= 2; rep(i,0,n) if(s[i] == '1') ans++; std::cout << ans << '\n'; } } // namespace ebi int main() { ebi::fast_io(); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }