結果
問題 | No.650 行列木クエリ |
ユーザー |
![]() |
提出日時 | 2018-02-09 22:51:12 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 213 ms / 2,000 ms |
コード長 | 7,663 bytes |
コンパイル時間 | 2,807 ms |
コンパイル使用メモリ | 218,572 KB |
最終ジャッジ日時 | 2025-01-05 08:14:47 |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 |
other | AC * 10 |
ソースコード
#include<bits/stdc++.h>using namespace std;struct CentroidPathDecomposition{struct Centroid{int ParIndex, ParDepth, Deep;vector< int > node;Centroid(int idx, int dep, int deep) : ParIndex(idx), ParDepth(dep), Deep(deep) {}inline size_t size(){return (node.size());}inline int &operator[](int k){return (node[k]);}inline pair< int, int > Up(){return (make_pair(ParIndex, ParDepth));}};vector< vector< int > > graph;vector< int > SubTreeSize, NextPath;vector< int > TreeIndex, TreeDepth;vector< Centroid > Centroids;void BuildSubTreeSize(){stack< pair< int, int > > s;s.emplace(0, -1);while(!s.empty()) {auto p = s.top();s.pop();if(~SubTreeSize[p.first]) {NextPath[p.first] = -1;for(auto &to : graph[p.first]) {if(p.second == to) continue;SubTreeSize[p.first] += SubTreeSize[to];if(NextPath[p.first] == -1 || SubTreeSize[NextPath[p.first]] < SubTreeSize[to]) {NextPath[p.first] = to;}}} else {s.push(p);SubTreeSize[p.first] = 1;for(auto &to : graph[p.first]) {if(p.second != to) s.emplace(to, p.first);}}}}void BuildPath(){stack< pair< int, int > > s;Centroids.emplace_back(-1, -1, 0);s.emplace(0, -1);TreeIndex[0] = 0;while(!s.empty()) {auto p = s.top();s.pop();TreeDepth[p.first] = (int) Centroids[TreeIndex[p.first]].size();for(auto &to : graph[p.first]) {if(p.second == to) continue;if(to == NextPath[p.first]) { // Centroid-PathTreeIndex[to] = TreeIndex[p.first];} else { // Not Centroid-PathTreeIndex[to] = (int) Centroids.size();Centroids.emplace_back(TreeIndex[p.first], TreeDepth[p.first], Centroids[TreeIndex[p.first]].Deep + 1);}s.emplace(to, p.first);}Centroids[TreeIndex[p.first]].node.emplace_back(p.first);}}void AddEdge(int x, int y){graph[x].push_back(y);graph[y].push_back(x);}virtual void Build(){BuildSubTreeSize();BuildPath();}inline size_t size(){return (Centroids.size());}inline pair< int, int > Information(int idx){return (make_pair(TreeIndex[idx], TreeDepth[idx]));}inline Centroid &operator[](int k){return (Centroids[k]);}inline int LCA(int a, int b){int TreeIdxA, TreeDepthA, TreeIdxB, TreeDepthB;tie(TreeIdxA, TreeDepthA) = Information(a);tie(TreeIdxB, TreeDepthB) = Information(b);while(TreeIdxA != TreeIdxB) {if(Centroids[TreeIdxA].Deep > Centroids[TreeIdxB].Deep) {tie(TreeIdxA, TreeDepthA) = Centroids[TreeIdxA].Up();} else {tie(TreeIdxB, TreeDepthB) = Centroids[TreeIdxB].Up();}}if(TreeDepthA > TreeDepthB) swap(TreeDepthA, TreeDepthB);return (Centroids[TreeIdxA][TreeDepthA]);}inline virtual void query(int a, int b, const function< void(int, int, int) > &f){int TreeIdxA, TreeDepthA, TreeIdxB, TreeDepthB;tie(TreeIdxA, TreeDepthA) = Information(a);tie(TreeIdxB, TreeDepthB) = Information(b);while(TreeIdxA != TreeIdxB) {if(Centroids[TreeIdxA].Deep > Centroids[TreeIdxB].Deep) {f(TreeIdxA, 0, TreeDepthA + 1);tie(TreeIdxA, TreeDepthA) = Centroids[TreeIdxA].Up();} else {f(TreeIdxB, 0, TreeDepthB + 1);tie(TreeIdxB, TreeDepthB) = Centroids[TreeIdxB].Up();}}if(TreeDepthA > TreeDepthB) swap(TreeDepthA, TreeDepthB);f(TreeIdxA, TreeDepthA, TreeDepthB + 1);}CentroidPathDecomposition(int SZ){graph.resize(SZ);SubTreeSize.assign(SZ, -1);NextPath.resize(SZ);TreeIndex.resize(SZ);TreeDepth.resize(SZ);}};struct TreeArray : CentroidPathDecomposition{TreeArray(int sz) : CentroidPathDecomposition(sz) {}vector< int > index;void Build(){CentroidPathDecomposition::Build();int ptr = 0;for(auto ¢roid : Centroids) {index.emplace_back(ptr);ptr += centroid.size();}}inline int get(int a){auto p = Information(a);return (index[p.first] + p.second);}inline void query(int a, int b, const function< void(int, int) > &f){int TreeIdxA, TreeDepthA, TreeIdxB, TreeDepthB;tie(TreeIdxA, TreeDepthA) = Information(a);tie(TreeIdxB, TreeDepthB) = Information(b);while(TreeIdxA != TreeIdxB) {if(Centroids[TreeIdxA].Deep > Centroids[TreeIdxB].Deep) {f(index[TreeIdxA], index[TreeIdxA] + TreeDepthA + 1);tie(TreeIdxA, TreeDepthA) = Centroids[TreeIdxA].Up();} else {f(index[TreeIdxB], index[TreeIdxB] + TreeDepthB + 1);tie(TreeIdxB, TreeDepthB) = Centroids[TreeIdxB].Up();}}if(TreeDepthA > TreeDepthB) swap(TreeDepthA, TreeDepthB);f(index[TreeIdxA] + TreeDepthA + 1, index[TreeIdxA] + TreeDepthB + 1);}};const int mod = 1e9 + 7;struct Matrix{int a[2][2];Matrix operator+(const Matrix &kj){Matrix ret;for(int i = 0; i < 2; i++) {for(int j = 0; j < 2; j++) {ret.a[i][j] = a[i][j] + kj.a[i][j];ret.a[i][j] %= mod;}}return (ret);}Matrix operator*(const Matrix &kj){Matrix ret = Matrix::Zero();for(int i = 0; i < 2; i++) {for(int j = 0; j < 2; j++) {for(int k = 0; k < 2; k++) {ret.a[i][j] = (ret.a[i][j] + 1LL * a[i][k] * kj.a[k][j]) % mod;}}}return (ret);}Matrix operator^(int n){Matrix ret = Matrix::I();Matrix x = *this;while(n > 0) {if(n & 1) (ret = ret * x);x = x * x;n >>= 1;}return (ret);}static Matrix Zero(){Matrix ret;memset(ret.a, 0, sizeof(ret.a));return (ret);}static Matrix I(){Matrix ret;memset(ret.a, 0, sizeof(ret.a));for(int i = 0; i < 2; i++) ret.a[i][i] = 1;return (ret);}};struct SegmentTree{vector< Matrix > seg, add;int sz;SegmentTree(int n){sz = 1;while(sz < n) sz <<= 1;seg.assign(2 * sz - 1, Matrix::I());}Matrix query(int a, int b, int k, int l, int r){if(a >= r || b <= l) return (Matrix::I());if(a <= l && r <= b) return (seg[k]);Matrix L = query(a, b, 2 * k + 1, l, (l + r) >> 1);Matrix R = query(a, b, 2 * k + 2, (l + r) >> 1, r);return (L * R);}void update(int k, Matrix x){k += sz - 1;seg[k] = x;while(k > 0) {k = (k - 1) >> 1;seg[k] = seg[2 * k + 1] * seg[2 * k + 2];}}Matrix query(int a, int b){return (query(a, b, 0, 0, sz));}};int main(){int N, X[100000], Y[100000];cin >> N;TreeArray g(N);for(int i = 1; i < N; i++) {cin >> X[i] >> Y[i];g.AddEdge(X[i], Y[i]);}g.Build();for(int i = 1; i < N; i++) {int a = g.get(X[i]);int b = g.get(Y[i]);if(a > b) swap(X[i], Y[i]);}SegmentTree seg(N);int Q;cin >> Q;while(Q--) {char x;cin >> x;if(x == 'x') {int v;cin >> v;++v;Matrix m;cin >> m.a[0][0] >> m.a[0][1] >> m.a[1][0] >> m.a[1][1];seg.update(g.get(Y[v]), m);} else {int y, z;cin >> y >> z;Matrix mat = Matrix::I();g.query(y, z, [&](int a, int b){mat = seg.query(a, b) * mat;});cout << mat.a[0][0] << " " << mat.a[0][1] << " " << mat.a[1][0] << " " << mat.a[1][1] << endl;}}}