matsutaku-library

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:heavy_check_mark: test/yosupo/vertex_add_path_sum.test.cpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#include "include/mtl/hld.hpp"
#include "include/mtl/segment_tree.hpp"
#include <bits/stdc++.h>
using namespace std;

struct Sum {
    long long x;
    Sum(long long x=0):x(x) {}
    Sum operator*(const Sum& o) const { 
        return Sum(x+o.x);
    }
};

int main() {
    int n,q; cin>>n>>q;
    vector<int> A(n);
    for (int i = 0; i < n; i++) cin>>A[i];
    Hld T(n);
    for (int i = 0; i < n-1; i++) {
        int u,v; cin>>u>>v;
        T.add_edge(u,v);
    } 
    T.build();
    vector<int> B(n);
    for (int i = 0; i < n; i++) B[T.in[i]] = A[i];
    SegmentTree<Sum> path_sum(B.begin(), B.end());
    for (int i = 0; i < q; i++) {
        int t; cin>>t;
        if (t == 0) {
            int p,x; cin>>p>>x;
            auto tp = T.in[p];
            path_sum.set(tp, {path_sum.get(tp).x+x});
        } else {
            int u,v; cin>>u>>v;
            auto ret = T.query(u,v,[&](int l, int r) { 
                return path_sum.query(l, r); 
            }).x;
            cout << ret << endl;
        }
    }
}

#line 1 "test/yosupo/vertex_add_path_sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_add_path_sum"
#line 2 "include/mtl/hld.hpp"
#include <cstddef>
#include <vector>

struct Hld {
  int r,n;
  std::vector<std::vector<int>> edge;
  std::vector<int> size, in, out, head, rev, par, depth, clen;
 private:
  void dfs_sz(int v, int p, int d) {
    par[v] = p;
    size[v] = 1;
    if (!edge[v].empty() and edge[v][0] == p)
      std::swap(edge[v][0], edge[v].back());
    for (auto& t:edge[v]) {
      if (t == p) continue;
      dfs_sz(t, v, d+1);
      size[v] += size[t];
      if (size[edge[v][0]] < size[t])
        std::swap(edge[v][0], t);
    }
  }
  void dfs_hld(int v, int p, int& times) {
    in[v] = times++;
    rev[in[v]] = v;
    clen[v] = 1;
    if (!edge[v].empty() and edge[v][0] != p) {
      int t = edge[v][0];
      head[t] = head[v];
      depth[t] = depth[v];
      dfs_hld(t, v, times);
      clen[v] += clen[t];
    }
    for (size_t i = 1; i < edge[v].size(); i++) {
      int t = edge[v][i];
      if (t == p) continue;
      head[t] = t;
      depth[t] = depth[v] + 1;
      dfs_hld(t, v, times);
    }
    out[v] = times;
  }

 public:
  Hld(int n) : r(0), n(n), edge(n), size(n), in(n, -1), out(n, -1), head(n, -1), rev(n, -1), par(n, -1), depth(n, -1), clen(n) {}

  inline void add_edge(int a, int b) {
    edge[a].push_back(b);
    edge[b].push_back(a);
  }

  void build(int root = 0) {
    r = root;
    dfs_sz(root, -1, 0);
    int t = 0;
    head[root] = root;
    depth[root] = 0;
    dfs_hld(root, -1, t);
  }

  inline int lca(int a, int b) const {
    if (depth[a] > depth[b]) std::swap(a, b);
    while (depth[a] < depth[b]) {
      b = par[head[b]];
    }
    while (head[a] != head[b]) {
      a = par[head[a]];
      b = par[head[b]];
    }
    return in[a] < in[b] ? a : b;
  }

 private:
  template<class Query, class ReverseQuery>
  auto _query(int u, int v, Query Q, ReverseQuery RQ, bool include_lca) const -> decltype(Q(0,0)) {
    using T = decltype(Q(0,0));
    T um, vm;
    auto u_up = [&]() {
      um = um * (T)RQ(in[head[u]], in[u]+1);
      u = par[head[u]];
    };
    auto v_up = [&]() {
      vm = (T)Q(in[head[v]], in[v]+1) * vm;
      v = par[head[v]];
    };
    while (depth[u] > depth[v])
      u_up();
    while (depth[u] < depth[v])
      v_up();
    while (head[u] != head[v]) {
      u_up();
      v_up();
    }
    if (in[u] < in[v]) {
      int l = include_lca ? in[u] : in[u]+1;
      return um * (T)Q(l, in[v]+1) * vm;
    } else {
      int l = include_lca ? in[v] : in[v]+1;
      return um * (T)RQ(l, in[u]+1) * vm;
    }
  }

 public:
  template<class Query, class ReverseQuery>
  auto query(int u, int v, Query Q, ReverseQuery RQ, bool include_lca = true) const -> decltype(Q(0,0)) {
    return _query(u, v, Q, RQ, include_lca);
  }

  /// Query for commutative monoid
  template<class Query>
  auto query(int u, int v, Query Q, bool include_lca = true) const -> decltype(Q(0,0)) {
    return _query(u, v, Q, Q, include_lca);
  }

  template<class Set, class T>
  void set(int i, Set S, T&& val) const {
    S(in[i], std::forward<T>(val));
  }

  template<typename Upd, typename T>
  void update(int u, int v, Upd U, const T& val, bool include_lca = true) const {
    if (depth[u] > depth[v]) std::swap(u,v);
    auto up = [&](int& v) {
      U(in[head[v]], in[v]+1, val);
      v = par[head[v]];
    };
    while (depth[u] < depth[v]) {
      up(v);
    }
    while (head[u] != head[v]) {
      up(u);
      up(v);
    }
    if (in[u] > in[v]) std::swap(u,v);
    int l = include_lca ? in[u] : in[u]+1;
    U(l, in[v]+1, val);
  }

public:
  template<class Add, class Sum>
  void subtree_build(Add A, Sum S) const {
    dfs_subtree_build(A, S, r);
  }
 private:
  template<class Add, class Sum>
  void dfs_subtree_build(Add A, Sum S, int u) const {
    for (size_t i = 0; i < edge[u].size(); i++) {
      auto v = edge[u][i];
      if (v == par[u]) continue;
      dfs_subtree_build(A, S, v);
      if (i > 0)
        A(in[u], S(in[v], in[v]+clen[v]));
    }
  }
 public:
  template<class T, class Sum>
  T subtree_sum(int r, Sum S) const {
    return (T)S(in[r], in[r]+clen[r]);
  }
  template<class T, class Add>
  void subtree_point_add(int u, Add A, const T& val) const {
    while (u != -1) {
      A(in[u], val);
      u = par[head[u]];
    }
  }
};
#line 2 "include/mtl/bit_manip.hpp"
#include <cstdint>
#include <cassert>
#if __cplusplus >= 202002L
#ifndef MTL_CPP20
#define MTL_CPP20
#endif
#include <bit>
#endif

namespace bm {

/// Count 1s for each 8 bits
inline constexpr uint64_t popcnt_e8(uint64_t x) {
  x = (x & 0x5555555555555555) + ((x>>1) & 0x5555555555555555);
  x = (x & 0x3333333333333333) + ((x>>2) & 0x3333333333333333);
  x = (x & 0x0F0F0F0F0F0F0F0F) + ((x>>4) & 0x0F0F0F0F0F0F0F0F);
  return x;
}
/// Count 1s
inline constexpr unsigned popcnt(uint64_t x) {
#ifdef MTL_CPP20
  return std::popcount(x);
#else
  return (popcnt_e8(x) * 0x0101010101010101) >> 56;
#endif
}
/// Alias to mtl::popcnt(x)
constexpr unsigned popcount(uint64_t x) {
  return popcnt(x);
}
/// Count trailing 0s. s.t. *11011000 -> 3
inline constexpr unsigned ctz(uint64_t x) {
#ifdef MTL_CPP20
  return std::countr_zero(x);
#else
  return popcnt((x & (-x)) - 1);
#endif
}
/// Alias to mtl::ctz(x)
constexpr unsigned countr_zero(uint64_t x) {
  return ctz(x);
}
/// Count trailing 1s. s.t. *11011011 -> 2
inline constexpr unsigned cto(uint64_t x) {
#ifdef MTL_CPP20
  return std::countr_one(x);
#else
  return ctz(~x);
#endif
}
/// Alias to mtl::cto(x)
constexpr unsigned countr_one(uint64_t x) {
  return cto(x);
}
inline constexpr unsigned ctz8(uint8_t x) {
  return x == 0 ? 8 : popcnt_e8((x & (-x)) - 1);
}
/// [00..0](8bit) -> 0, [**..*](not only 0) -> 1
inline constexpr uint8_t summary(uint64_t x) {
  constexpr uint64_t hmask = 0x8080808080808080ull;
  constexpr uint64_t lmask = 0x7F7F7F7F7F7F7F7Full;
  auto a = x & hmask;
  auto b = x & lmask;
  b = hmask - b;
  b = ~b;
  auto c = (a | b) & hmask;
  c *= 0x0002040810204081ull;
  return uint8_t(c >> 56);
}
/// Extract target area of bits
inline constexpr uint64_t bextr(uint64_t x, unsigned start, unsigned len) {
  uint64_t mask = len < 64 ? (1ull<<len)-1 : 0xFFFFFFFFFFFFFFFFull;
  return (x >> start) & mask;
}
/// 00101101 -> 00111111 -count_1s-> 6
inline constexpr unsigned log2p1(uint8_t x) {
  if (x & 0x80)
    return 8;
  uint64_t p = uint64_t(x) * 0x0101010101010101ull;
  p -= 0x8040201008040201ull;
  p = ~p & 0x8080808080808080ull;
  p = (p >> 7) * 0x0101010101010101ull;
  p >>= 56;
  return p;
}
/// 00101100 -mask_mssb-> 00100000 -to_index-> 5
inline constexpr unsigned mssb8(uint8_t x) {
  assert(x != 0);
  return log2p1(x) - 1;
}
/// 00101100 -mask_lssb-> 00000100 -to_index-> 2
inline constexpr unsigned lssb8(uint8_t x) {
  assert(x != 0);
  return popcnt_e8((x & -x) - 1);
}
/// Count leading 0s. 00001011... -> 4
inline constexpr unsigned clz(uint64_t x) {
#ifdef MTL_CPP20
  return std::countl_zero(x);
#else
  if (x == 0)
    return 64;
  auto i = mssb8(summary(x));
  auto j = mssb8(bextr(x, 8 * i, 8));
  return 63 - (8 * i + j);
#endif
}
/// Alias to mtl::clz(x)
constexpr unsigned countl_zero(uint64_t x) {
  return clz(x);
}
/// Count leading 1s. 11110100... -> 4
inline constexpr unsigned clo(uint64_t x) {
#ifdef MTL_CPP20
  return std::countl_one(x);
#else
  return clz(~x);
#endif
}
/// Alias to mtl::clo(x)
constexpr unsigned countl_one(uint64_t x) {
  return clo(x);
}

inline constexpr unsigned clz8(uint8_t x) {
  return x == 0 ? 8 : 7 - mssb8(x);
}
inline constexpr uint64_t bit_reverse(uint64_t x) {
  x = ((x & 0x00000000FFFFFFFF) << 32) | ((x & 0xFFFFFFFF00000000) >> 32);
  x = ((x & 0x0000FFFF0000FFFF) << 16) | ((x & 0xFFFF0000FFFF0000) >> 16);
  x = ((x & 0x00FF00FF00FF00FF) << 8) | ((x & 0xFF00FF00FF00FF00) >> 8);
  x = ((x & 0x0F0F0F0F0F0F0F0F) << 4) | ((x & 0xF0F0F0F0F0F0F0F0) >> 4);
  x = ((x & 0x3333333333333333) << 2) | ((x & 0xCCCCCCCCCCCCCCCC) >> 2);
  x = ((x & 0x5555555555555555) << 1) | ((x & 0xAAAAAAAAAAAAAAAA) >> 1);
  return x;
}

/// Check if x is power of 2. 00100000 -> true, 00100001 -> false
constexpr bool has_single_bit(uint64_t x) noexcept {
#ifdef MTL_CPP20
  return std::has_single_bit(x);
#else
  return x != 0 && (x & (x - 1)) == 0;
#endif
}

/// Bit width needs to represent x. 00110110 -> 6
constexpr int bit_width(uint64_t x) noexcept {
#ifdef MTL_CPP20
  return std::bit_width(x);
#else
  return 64 - clz(x);
#endif
}

/// Ceil power of 2. 00110110 -> 01000000
constexpr uint64_t bit_ceil(uint64_t x) {
#ifdef MTL_CPP20
  return std::bit_ceil(x);
#else
  if (x == 0) return 1;
  return 1ull << bit_width(x - 1);
#endif
}

/// Floor power of 2. 00110110 -> 00100000
constexpr uint64_t bit_floor(uint64_t x) {
#ifdef MTL_CPP20
  return std::bit_floor(x);
#else
  if (x == 0) return 0;
  return 1ull << (bit_width(x) - 1);
#endif
}

} // namespace bm
#line 5 "include/mtl/segment_tree.hpp"
#include <stack>
#if __cplusplus >= 202002L
#include <concepts>

template<class M>
concept SegmentTreeMonoid = requires (M m) {
  {m * m} -> std::same_as<M>;
};
#endif

template <class M>
class SegmentTree {
#if __cplusplus >= 202002L
  static_assert(SegmentTreeMonoid<M>);
#endif
 public:
  using monoid_type = M;
  using value_type = monoid_type;
 private:
  size_t size_;
  std::vector<value_type> tree_;

 public:
  explicit SegmentTree(size_t size) : size_(size), tree_(size*2) {}

  template <class Iter>
  explicit SegmentTree(Iter begin, Iter end) : SegmentTree(std::distance(begin, end)) {
    if (size_==0) return;
    std::copy(begin, end, tree_.begin() + size_);
    for (size_t i = size_-1; i > 0; i--)
      tree_[i] = tree_[i<<1] * tree_[(i<<1)+1];
  }

  value_type get(size_t index) const {
    return tree_[size_ + index];
  }
  value_type operator[](size_t index) const {
    return get(index);
  }

 private:
  template<class T>
  void _set(size_t index, T&& val) {
    auto i = size_ + index;
    tree_[i] = std::forward<T>(val);
    i >>= 1;
    while (i > 0) {
      tree_[i] = tree_[i<<1] * tree_[(i<<1)+1];
      i >>= 1;
    }
  }
 public:
  template<class T>
  void set(size_t index, T&& val) {
    return _set(index, std::forward<T>(val));
  }
  void set(size_t index, const value_type& val) {
    _set(index, val);
  }
  void set(size_t index, value_type&& val) {
    _set(index, std::move(val));
  }

  value_type query(size_t l, size_t r) const {
    value_type lhs,rhs;
    for (auto _l = l+size_, _r = r+size_; _l < _r; _l>>=1, _r>>=1) {
      if (_l&1) lhs = lhs * tree_[_l++];
      if (_r&1) rhs = tree_[--_r] * rhs;
    }
    return lhs * rhs;
  }

  template<class F>
  size_t max_right(size_t begin, size_t end, F f) const {
    if (begin == end) return end;
    monoid_type p;
    std::stack<std::pair<size_t, monoid_type>> rps;
    auto l = size_ + begin;
    auto r = size_ + end;
    while (l < r and f(p * tree_[l])) {
      if (l&1) p = p * tree_[l++];
      if (r&1) {
        rps.emplace(r, tree_[r-1]);
        r--;
      }
      l>>=1; r>>=1;
    }
    if (l >= r) {
      while (rps.size()) {
        auto& [r, rp] = rps.top();
        if (!f(p * rp)) {
          l = r-1;
          break;
        }
        p = p * rp;
        rps.pop();
      }
      if (rps.empty()) return end;
    }
    while (l < size_) {
      assert(!f(p * tree_[l]));
      l <<= 1;
      if (f(p * tree_[l]))
        p = p * tree_[l++];
    }
    return l - size_;
  }

  template<class F>
  size_t min_left(size_t begin, size_t end, F f) const {
    if (end == begin) return begin;
    monoid_type p;
    std::stack<std::pair<size_t, monoid_type>> lps;
    auto l = size_ + begin;
    auto r = size_ + end;
    while (l < r and f(tree_[r-1] * p)) {
      if (l&1) {
        lps.emplace(l, tree_[l]);
        l++;
      }
      if (r&1) p = tree_[r-1] * p;
      l>>=1; r>>=1;
    }
    if (l >= r) {
      while (lps.size()) {
        auto& [l, lp] = lps.top();
        if (!f(lp * p)) {
          r = l+1;
          break;
        }
        p = lp * p;
        lps.pop();
      }
      if (lps.empty()) return begin;
    }
    while (r <= size_) {
      assert(!f(tree_[r-1] * p));
      r <<= 1;
      if (f(tree_[r-1] * p)) 
        p = tree_[--r] * p;
    }
    return r - size_;
  }
  template<bool (*F)(value_type)>
  size_t min_left(size_t begin, size_t end) const {
    return min_left(begin, [](value_type x) { return F(x); });
  }

};
#line 4 "test/yosupo/vertex_add_path_sum.test.cpp"
#include <bits/stdc++.h>
using namespace std;

struct Sum {
    long long x;
    Sum(long long x=0):x(x) {}
    Sum operator*(const Sum& o) const { 
        return Sum(x+o.x);
    }
};

int main() {
    int n,q; cin>>n>>q;
    vector<int> A(n);
    for (int i = 0; i < n; i++) cin>>A[i];
    Hld T(n);
    for (int i = 0; i < n-1; i++) {
        int u,v; cin>>u>>v;
        T.add_edge(u,v);
    } 
    T.build();
    vector<int> B(n);
    for (int i = 0; i < n; i++) B[T.in[i]] = A[i];
    SegmentTree<Sum> path_sum(B.begin(), B.end());
    for (int i = 0; i < q; i++) {
        int t; cin>>t;
        if (t == 0) {
            int p,x; cin>>p>>x;
            auto tp = T.in[p];
            path_sum.set(tp, {path_sum.get(tp).x+x});
        } else {
            int u,v; cin>>u>>v;
            auto ret = T.query(u,v,[&](int l, int r) { 
                return path_sum.query(l, r); 
            }).x;
            cout << ret << endl;
        }
    }
}

Test cases

Env Name Status Elapsed Memory
g++ almost_line_00 :heavy_check_mark: AC 1236 ms 185 MB
g++ almost_line_01 :heavy_check_mark: AC 1647 ms 169 MB
g++ example_00 :heavy_check_mark: AC 6 ms 3 MB
g++ line_00 :heavy_check_mark: AC 1203 ms 165 MB
g++ line_01 :heavy_check_mark: AC 1504 ms 219 MB
g++ long-path-decomposition_killer_00 :heavy_check_mark: AC 1163 ms 58 MB
g++ max_random_00 :heavy_check_mark: AC 1133 ms 58 MB
g++ max_random_01 :heavy_check_mark: AC 1272 ms 58 MB
g++ max_random_02 :heavy_check_mark: AC 1336 ms 58 MB
g++ random_00 :heavy_check_mark: AC 895 ms 46 MB
g++ random_01 :heavy_check_mark: AC 1112 ms 54 MB
g++ random_02 :heavy_check_mark: AC 642 ms 9 MB
g++ random_03 :heavy_check_mark: AC 446 ms 51 MB
g++ random_04 :heavy_check_mark: AC 373 ms 34 MB
g++ small_00 :heavy_check_mark: AC 7 ms 4 MB
g++ small_01 :heavy_check_mark: AC 6 ms 3 MB
g++ small_02 :heavy_check_mark: AC 6 ms 3 MB
g++ small_03 :heavy_check_mark: AC 6 ms 3 MB
g++ small_04 :heavy_check_mark: AC 7 ms 4 MB
clang++ almost_line_00 :heavy_check_mark: AC 1111 ms 80 MB
clang++ almost_line_01 :heavy_check_mark: AC 1108 ms 77 MB
clang++ example_00 :heavy_check_mark: AC 6 ms 3 MB
clang++ line_00 :heavy_check_mark: AC 1071 ms 77 MB
clang++ line_01 :heavy_check_mark: AC 1246 ms 86 MB
clang++ long-path-decomposition_killer_00 :heavy_check_mark: AC 1095 ms 58 MB
clang++ max_random_00 :heavy_check_mark: AC 1144 ms 58 MB
clang++ max_random_01 :heavy_check_mark: AC 1561 ms 58 MB
clang++ max_random_02 :heavy_check_mark: AC 2896 ms 58 MB
clang++ random_00 :heavy_check_mark: AC 900 ms 46 MB
clang++ random_01 :heavy_check_mark: AC 1025 ms 54 MB
clang++ random_02 :heavy_check_mark: AC 524 ms 9 MB
clang++ random_03 :heavy_check_mark: AC 441 ms 51 MB
clang++ random_04 :heavy_check_mark: AC 375 ms 34 MB
clang++ small_00 :heavy_check_mark: AC 7 ms 4 MB
clang++ small_01 :heavy_check_mark: AC 6 ms 3 MB
clang++ small_02 :heavy_check_mark: AC 6 ms 3 MB
clang++ small_03 :heavy_check_mark: AC 6 ms 3 MB
clang++ small_04 :heavy_check_mark: AC 7 ms 4 MB
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