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Problem solution · C++

Point Set Tree Path Composite Sum

Point Set Tree Path Composite Sum: a C++ solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to NyaanNyaan Competitive Programming Library.

Technique
Direct simulation
Source
NyaanNyaan Competitive Programming Library
Length
71 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Direct simulation

For Point Set Tree Path Composite Sum, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 71 lines of C++ from the credited upstream file yosupo-point-set-tree-path-composite-sum.test.cpp.
  • The implementation visibly relies on sequence storage.
  • 6 loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from NyaanNyaan Competitive Programming Library by NyaanNyaan and is used under the CC0-1.0 licence.

Open problem ↗Original source ↗
Full codePoint Set Tree Path Composite Sum · C++C++
Use this to learn the idea, then write your own version.
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_tree_path_composite_sum"//#include "../../template/template.hpp"//#include "../../modint/montgomery-modint.hpp"//#include "../../tree/dynamic-rerooting.hpp"//using mint = LazyMontgomeryModInt<998244353>; struct Path {  mint a, b, s, x;};struct Point {  mint s, x;};struct Info {  bool vertex;  mint x, y;};Path vertex(const Info &i) {  if (i.vertex) return {1, 0, i.x, 1};  return {i.x, i.y, 0, 0};}Path compress(const Path &p, const Path &c) {  return {p.a * c.a, p.a * c.b + p.b, p.s + p.a * c.s + p.b * c.x, p.x + c.x};}Point rake(const Point &a, const Point &b) { return {a.s + b.s, a.x + b.x}; }Point add_edge(const Path &a) { return {a.s, a.x}; }Path add_vertex(const Point &a, const Info &i) {  if (i.vertex) return {1, 0, a.s + i.x, a.x + 1};  return {i.x, i.y, a.s * i.x + a.x * i.y, a.x};} using DR = DynamicRerooting<Path, Point, Info, vertex, compress, rake, add_edge,                            add_vertex>; using namespace Nyaan; void Nyaan::solve() {  int N, Q;  in(N, Q);  vector<int> A(N);  for (auto &x : A) in(x);  vector<int> U(N - 1), V(N - 1), B(N - 1), C(N - 1);  for (int i = 0; i < N - 1; i++) in(U[i], V[i], B[i], C[i]);   vector<Info> info(2 * N - 1);  for (int i = 0; i < N; i++) info[i] = {true, A[i], 0};  for (int i = 0; i < N - 1; i++) info[N + i] = {false, B[i], C[i]};   DR dr{2 * N - 1, info};  for (int i = 0; i < N - 1; i++) {    dr.add_edge(N + i, U[i]), dr.add_edge(N + i, V[i]);  }   while (Q--) {    int cmd, i, x;    in(cmd, i, x);    if (cmd == 0) {      dr.set_info(i, {true, x, 0});    } else {      int y;      in(y);      dr.set_info(N + i, {false, x, y});    }    ini(r);    out(dr.query(r).s.get());  }}

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