結果
問題 | No.235 めぐるはめぐる (5) |
ユーザー | anta |
提出日時 | 2015-08-26 00:43:43 |
言語 | C++11 (gcc 11.4.0) |
結果 |
AC
|
実行時間 | 485 ms / 10,000 ms |
コード長 | 18,340 bytes |
コンパイル時間 | 1,463 ms |
コンパイル使用メモリ | 112,420 KB |
実行使用メモリ | 43,408 KB |
最終ジャッジ日時 | 2024-07-18 14:38:14 |
合計ジャッジ時間 | 3,819 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 485 ms
42,296 KB |
testcase_01 | AC | 334 ms
43,408 KB |
testcase_02 | AC | 433 ms
42,260 KB |
コンパイルメッセージ
main.cpp: In function ‘int main()’: main.cpp:608:30: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result] 608 | scanf("%d", &S[i]); | ~~~~~^~~~~~~~~~~~~ main.cpp:615:30: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result] 615 | scanf("%d", &C[i]); | ~~~~~^~~~~~~~~~~~~ main.cpp:627:30: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result] 627 | scanf("%d%d", &A, &B), -- A, -- B; | ~~~~~^~~~~~~~~~~~~~~~ main.cpp:642:22: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result] 642 | scanf("%d", &Q); | ~~~~~^~~~~~~~~~ main.cpp:649:30: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result] 649 | scanf("%d", &ty); | ~~~~~^~~~~~~~~~~ main.cpp:656:38: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result] 656 | scanf("%d%d%d", &X, &Y, &Z), -- X, -- Y; | ~~~~~^~~~~~~~~~~~~~~~~~~~~~ main.cpp:670:38: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result] 670 | scanf("%d%d", &X, &Y), -- X, -- Y; | ~~~~~^~~~~~~~~~~~~~~~
ソースコード
#include <string> #include <vector> #include <algorithm> #include <numeric> #include <set> #include <map> #include <queue> #include <iostream> #include <sstream> #include <cstdio> #include <cmath> #include <ctime> #include <cstring> #include <cctype> #include <cassert> #include <limits> #include <functional> #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) #if defined(_MSC_VER) || __cplusplus > 199711L #define aut(r,v) auto r = (v) #else #define aut(r,v) __typeof(v) r = (v) #endif #define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it) #define all(o) (o).begin(), (o).end() #define pb(x) push_back(x) #define mp(x,y) make_pair((x),(y)) #define mset(m,v) memset(m,v,sizeof(m)) #define INF 0x3f3f3f3f #define INFL 0x3f3f3f3f3f3f3f3fLL using namespace std; typedef vector<int> vi; typedef pair<int,int> pii; typedef vector<pair<int,int> > vpii; typedef long long ll; template<typename T, typename U> inline void amin(T &x, U y) { if(y < x) x = y; } template<typename T, typename U> inline void amax(T &x, U y) { if(x < y) x = y; } #ifndef MY_LOCAL_RUN #undef assert #define assert(e) #endif template<int MOD> struct ModInt { static const int Mod = MOD; unsigned x; ModInt(): x(0) { } ModInt(signed sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; } ModInt(signed long long sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if((x += that.x) >= MOD) x -= MOD; return *this; } ModInt &operator-=(ModInt that) { if((x += MOD - that.x) >= MOD) x -= MOD; return *this; } ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } }; typedef ModInt<1000000007> mint; class SchieberVishkinLCA { public: typedef unsigned Word; typedef int Vertex; private: static inline Word lowestOneBit(Word v) { return v & (~v+1); } static inline Word highestOneBitMask(Word v) { v |= v >> 1; v |= v >> 2; v |= v >> 4; v |= v >> 8; v |= v >> 16; return v >> 1; } std::vector<Word> indices; //Vertex -> index std::vector<Word> maxHIndices; //Vertex -> index std::vector<Word> ancestorHeights; //Vertex -> Word std::vector<Vertex> pathParents; //index-1 -> Vertex public: void build(const std::vector<Vertex> &preorder, const std::vector<Vertex> &parents, Vertex root) { Vertex N = static_cast<Vertex>(preorder.size()); ancestorHeights.resize(N); maxHIndices.resize(N); indices.resize(N); pathParents.resize(N); for(Vertex ix = 0; ix < N; ++ ix) indices[preorder[ix]] = ix + 1; for(Vertex i = 0; i < N; ++ i) maxHIndices[i] = indices[i]; for(Vertex ix = N-1; ix > 0; -- ix) { Vertex v = preorder[ix], parent = parents[v]; if(lowestOneBit(maxHIndices[parent]) < lowestOneBit(maxHIndices[v])) maxHIndices[parent] = maxHIndices[v]; } ancestorHeights[root] = 0; for(Vertex ix = 1; ix < N; ++ ix) { Vertex v = preorder[ix], parent = parents[v]; ancestorHeights[v] = ancestorHeights[parent] | lowestOneBit(maxHIndices[v]); } pathParents[0] = root; for(Vertex ix = 1; ix < N; ++ ix) { Vertex v = preorder[ix], parent = parents[v]; if(maxHIndices[v] != maxHIndices[parent]) pathParents[indices[v]-1] = parent; else pathParents[indices[v]-1] = pathParents[indices[parent]-1]; } } Vertex query(Vertex v, Vertex u) const { Word Iv = maxHIndices[v], Iu = maxHIndices[u]; Word hIv = lowestOneBit(Iv), hIu = lowestOneBit(Iu); Word hbMask = highestOneBitMask((Iv ^ Iu) | hIv | hIu); Word j = lowestOneBit(ancestorHeights[v] & ancestorHeights[u] & ~hbMask); Vertex x, y; if(j == hIv) x = v; else { Word kMask = highestOneBitMask(ancestorHeights[v] & (j-1)); x = pathParents[(indices[v] & ~kMask | (kMask+1))-1]; } if(j == hIu) y = u; else { Word kMask = highestOneBitMask(ancestorHeights[u] & (j-1)); y = pathParents[(indices[u] & ~kMask | (kMask+1))-1]; } return indices[x] < indices[y] ? x : y; } }; struct HeavyLightDecomposition { vector<int> colors, positions; //Vertex -> Color, Vertex -> Offset vector<int> lengths, parents, branches; //Color -> Int, Color -> Color, Color -> Offset vector<int> parentnodes, depths; //Vertex -> Vertex, Vertex -> Int //vector<FenwickTree>とかを避けて1次元にしたい時に使う //sortednodesの[lefts[v], rights[v])はvのsubtreeとなっている vector<int> sortednodes, offsets; //Index -> Vertex, Color -> Index vector<int> lefts, rights; //Vertex -> Index struct BuildDFSState { int i, len, parent; BuildDFSState() { } BuildDFSState(int i_, int l, int p): i(i_), len(l), parent(p) { } }; //両方の辺があってもいいし、親から子への辺だけでもよい void build(const vector<vi> &g, int root) { int n = g.size(); colors.assign(n, -1); positions.assign(n, -1); lengths.clear(); parents.clear(); branches.clear(); parentnodes.assign(n, -1); depths.assign(n, -1); sortednodes.clear(); offsets.clear(); lefts.assign(n, -1); rights.assign(n, -1); vector<int> subtreesizes; measure(g, root, subtreesizes); typedef BuildDFSState State; depths[root] = 0; vector<State> s; s.push_back(State(root, 0, -1)); while(!s.empty()) { State t = s.back(); s.pop_back(); int i = t.i, len = t.len; int index = sortednodes.size(); int color = lengths.size(); if(t.parent == -3) { rights[i] = index; continue; } if(t.parent != -2) { assert(parents.size() == color); parents.push_back(t.parent); branches.push_back(len); offsets.push_back(index); len = 0; } colors[i] = color; positions[i] = len; lefts[i] = index; sortednodes.push_back(i); int maxsize = -1, maxj = -1; each(j, g[i]) if(colors[*j] == -1) { if(maxsize < subtreesizes[*j]) { maxsize = subtreesizes[*j]; maxj = *j; } parentnodes[*j] = i; depths[*j] = depths[i] + 1; } s.push_back(State(i, -1, -3)); if(maxj == -1) { lengths.push_back(len + 1); }else { each(j, g[i]) if(colors[*j] == -1 && *j != maxj) s.push_back(State(*j, len, color)); s.push_back(State(maxj, len + 1, -2)); } } } void get(int v, int &c, int &p) const { c = colors[v]; p = positions[v]; } bool go_up(int &c, int &p) const { p = branches[c]; c = parents[c]; return c != -1; } inline const int *nodesBegin(int c) const { return &sortednodes[0] + offsets[c]; } inline const int *nodesEnd(int c) const { return &sortednodes[0] + (c+1 == offsets.size() ? sortednodes.size() : offsets[c+1]); } private: void measure(const vector<vi> &g, int root, vector<int> &out_subtreesizes) const { out_subtreesizes.assign(g.size(), -1); vector<int> s; s.push_back(root); while(!s.empty()) { int i = s.back(); s.pop_back(); if(out_subtreesizes[i] == -2) { int s = 1; each(j, g[i]) if(out_subtreesizes[*j] != -2) s += out_subtreesizes[*j]; out_subtreesizes[i] = s; }else { s.push_back(i); each(j, g[i]) if(out_subtreesizes[*j] == -1) s.push_back(*j); out_subtreesizes[i] = -2; } } } }; struct Val { mint val, coef; explicit Val(): val(), coef() { } explicit Val(mint val_, mint coef_): val(val_), coef(coef_) { } }; struct PathSum { mint sum, coefsum; PathSum(): sum(), coefsum() { } explicit PathSum(const Val &val): sum(val.val), coefsum(val.coef) { } PathSum &operator+=(const PathSum &that) { sum += that.sum; coefsum += that.coefsum; return *this; } PathSum operator+(const PathSum &that) const { return PathSum(*this) += that; } PathSum reverse() const { return *this; } }; struct PathAdd { mint add; PathAdd() { } explicit PathAdd(mint add_): add(add_) { } PathAdd &operator+=(const PathAdd &that) { add += that.add; return *this; } void addToVal(Val &val) const { val.val += add * val.coef; } void addToSum(PathSum &sum) const { sum.sum += add * sum.coefsum; } }; struct Node { Node *parent; Node *pathLeft, *pathRight; Val val; PathSum pathSum; PathAdd pathAdd; Node(): parent(NULL), pathLeft(NULL), pathRight(NULL), val(), pathSum(), pathAdd() { } bool isPathRoot() const { return !parent || (parent->pathLeft != this && parent->pathRight != this); } static PathSum getPathSum(const Node *p) { if(!p) return PathSum(); PathSum pathSum = p->pathSum; p->pathAdd.addToSum(pathSum); return pathSum; } static mint getPathSum2(const Node *p) { if(!p) return mint(); return p->pathSum.sum + p->pathAdd.add * p->pathSum.coefsum; } static void addToPath(Node *p, const PathAdd &add) { if(p != NULL) p->pathAdd += add; } PathSum getSingletonPathSum() const { return PathSum(val); } void propagate() { if(pathAdd.add.x != 0) { if(pathLeft != NULL) pathLeft->pathAdd += pathAdd; if(pathRight != NULL) pathRight->pathAdd += pathAdd; pathAdd.addToVal(val); pathAdd.addToSum(pathSum); pathAdd = PathAdd(); } } void update() { pathSum = getPathSum(pathLeft) + getSingletonPathSum() + getPathSum(pathRight); } bool debugCheckUpdated() const { Node tmp = *this; tmp.update(); return memcmp(this, &tmp, sizeof(Node)) == 0; } }; struct BiasedHeavyLightDecompositionPathOnly { vector<Node> nodes; vector<int> pathRoots; //ノード に対して、それが属するパスの path tree 上の根のノード vector<int> subpathLeft, subpathRight; //path tree 上でそのノードが表す subpath の offset の区間 [left, right] vector<int> globalOrder; HeavyLightDecomposition hld; SchieberVishkinLCA lca; void build(const vector<vi> &g, int root, const vector<Val> &initVal) { hld.build(g, root); int n = g.size(); nodes.assign(n, Node()); vector<int> subtreeSize(n, 1); for(int ix = n-1; ix > 0; -- ix) { int i = hld.sortednodes[ix], p = hld.parentnodes[i]; subtreeSize[p] += subtreeSize[i]; } vector<int> childrenSize = subtreeSize; for(int ix = 1; ix < n; ++ ix) { int i = hld.sortednodes[ix], p = hld.parentnodes[i]; if(hld.colors[i] == hld.colors[p]) childrenSize[p] -= subtreeSize[i]; } buildPathTrees(childrenSize); getGlobalOrder(root); subpathLeft.resize(n); subpathRight.resize(n); for(int ix = n-1; ix >= 0; -- ix) { int i = globalOrder[ix]; Node *a = &nodes[i]; a->val = initVal[i]; a->update(); subpathLeft[i] = a->pathLeft == NULL ? hld.positions[i] : subpathLeft[getNodeIndex(a->pathLeft)]; subpathRight[i] = a->pathRight == NULL ? hld.positions[i] : subpathRight[getNodeIndex(a->pathRight)]; if(pathRoots[i] == i) { int c, p; hld.get(i, c, p); if(hld.go_up(c, p)) { assert(a->parent == NULL); a->parent = &nodes[hld.nodesBegin(c)[p]]; } } } lca.build(hld.sortednodes, hld.parentnodes, root); } //x -> y mint sumPath(int x, int y) { int z = lca.query(x, y); const Node *ceiling = nodes[pathRoots[z]].parent; globalPropagate(&nodes[x], ceiling); globalPropagate(&nodes[y], ceiling); mint sum; sum += sumPathFromRoot(x, ceiling); sum += sumPathFromRoot(y, ceiling); sum -= sumPathFromRoot(z, ceiling) * 2; sum += nodes[z].val.val; return sum; } mint sumPathFromRoot(int x, const Node *ceiling) const { const Node *a = &nodes[x]; mint sum; while(a != ceiling) { sum += Node::getPathSum2(a->pathLeft); sum += a->val.val; while(a->parent != NULL && a->parent->pathLeft == a) a = a->parent; a = a->parent; } return sum; } //x -> y void addToPath(int x, int y, const PathAdd &add) { int z = lca.query(x, y); const Node *ceiling = nodes[pathRoots[z]].parent; addToPathFromRoot(x, add, ceiling); addToPathFromRoot(y, add, ceiling); add.addToVal(nodes[z].val); addToPathFromRoot(z, PathAdd(add.add * -2), ceiling); globalUpdate(&nodes[x], ceiling); globalUpdate(&nodes[y], ceiling); } void addToPathFromRoot(int x, const PathAdd &add, const Node *ceiling) { Node *a = &nodes[x]; while(a != ceiling) { Node::addToPath(a->pathLeft, add); add.addToVal(a->val); while(a->parent != NULL && a->parent->pathLeft == a) a = a->parent; a = a->parent; } } private: int getNodeIndex(const Node *a) const { return static_cast<int>(a - &nodes[0]); } Node *goUpToParentPath(const Node *a) { int c, p; hld.get(getNodeIndex(a), c, p); if(!hld.go_up(c, p)) return NULL; else return &nodes[hld.nodesBegin(c)[p]]; } void globalPropagate(Node *a, const Node *ceiling) { Node *r = a, *q = a->parent; while(q != ceiling) { Node *p = q; q = p->parent; p->parent = r; r = p; } while(r != a) { Node *c = r->parent; r->parent = q; q = r; r->propagate(); r = c; } a->propagate(); } void globalUpdate(Node *a, const Node *ceiling) { while(a != ceiling) { a->update(); a = a->parent; } } void buildPathTrees(const vector<int> &sizes) { vector<int> weights, childL, childR; pathRoots.resize(nodes.size()); int C = hld.lengths.size(); for(int c = 0; c < C; ++ c) { int len = hld.lengths[c]; const int *path = hld.nodesBegin(c); weights.resize(len); for(int j = 0; j < len; ++ j) weights[j] = sizes[path[j]]; int rootj = makeBiasedBinarySearchTree(weights, childL, childR); int rootNode = path[rootj]; for(int j = 0; j < len; ++ j) pathRoots[path[j]] = rootNode; nodes[rootNode].parent = NULL; for(int j = 0; j < len; ++ j) { Node *a = &nodes[path[j]]; Node *l = childL[j] == -1 ? NULL : &nodes[path[childL[j]]]; Node *r = childR[j] == -1 ? NULL : &nodes[path[childR[j]]]; if((a->pathLeft = l) != NULL) l->parent = a; if((a->pathRight = r) != NULL) r->parent = a; } } } //weightsは破壊される int makeBiasedBinarySearchTree(vector<int> &weights, vector<int> &resL, vector<int> &resR) { int n = weights.size(); weights.resize(n + 1); int sum = 0; for(int i = 0; i < n; ++ i) { int w = weights[i]; weights[i] = sum; sum += w; } weights[n] = sum; resL.resize(n); resR.resize(n); return makeBiasedBinarySearchTreeRec(-1, 0, n, weights, resL, resR); } //最初2倍してく2分探索でうまくコストを log(小さい方のサイズ) にすませるようにすれば O(n) にできる。 //けど、ここではやってない。この単純な2分探索でも、任意の重みで呼ばれるわけではないのであんまりコストがかかることはない気がする。 int makeBiasedBinarySearchTreeRec(int p, int i, int j, const vector<int> &prefixSums, vector<int> &resL, vector<int> &resR) { if(i == j) return -1; //prefixSums[mid+1] - prefixSums[i] >= prefixSums[j] - prefixSums[mid] //prefixSums[mid] + prefixSums[mid+1] >= prefixSums[i] + prefixSums[j] int mid; if(i + 1 == j) { mid = i; }else { int t = prefixSums[i] + prefixSums[j]; int l = i, u = j-1; while(u - l > 0) { int m = (l + u) / 2; if(prefixSums[m] + prefixSums[m+1] >= t) u = m; else l = m + 1; } mid = u; } assert(mid < j); resL[mid] = makeBiasedBinarySearchTreeRec(mid * 2 + 0, i, mid, prefixSums, resL, resR); resR[mid] = makeBiasedBinarySearchTreeRec(mid * 2 + 1, mid + 1, j, prefixSums, resL, resR); return mid; } void getGlobalOrder(int globalRoot) { globalOrder.clear(); globalOrder.reserve(nodes.size()); vector<const Node *> stk; int C = hld.lengths.size(); for(int c = 0; c < C; ++ c) { stk.push_back(&nodes[pathRoots[hld.nodesBegin(c)[0]]]); while(!stk.empty()) { const Node *a = stk.back(); stk.pop_back(); if(a == NULL) continue; globalOrder.push_back(getNodeIndex(a)); stk.push_back(a->pathLeft); stk.push_back(a->pathRight); } } assert(globalOrder.size() == nodes.size()); } }; bool naivegetpath(int i, int p, int t, const vector<vi> &g, vi &path) { bool r = false; if(i == t) { r = true; }else { each(j, g[i]) if(*j != p) r = r || naivegetpath(*j, i, t, g, path); } if(r) path.push_back(i); return r; } #ifdef MY_LOCAL_RUN #include "C:\Dropbox\backup\implements\Util\MyAssert.hpp" #undef assert #define assert my_assert #define TEST #endif int main() { int N; for(int iii = 0; ; ++ iii) { #ifndef TEST if(!~scanf("%d", &N)) break; #else if(iii % 100 == 0) cerr << iii << "\r", cerr.flush(); N=rand()%10+1; #endif vector<int> S(N), C(N); rep(i, N) { #ifndef TEST scanf("%d", &S[i]); #else S[i]=rand()%100; #endif } rep(i, N) { #ifndef TEST scanf("%d", &C[i]); #else C[i]=rand()%100; #endif } vector<Val> initVals(N); rep(i, N) initVals[i] = Val(S[i], C[i]); vector<vi> g(N); rep(i, N-1) { int A, B; #ifndef TEST scanf("%d%d", &A, &B), -- A, -- B; #else A=i+1,B=rand()%(i+1); #endif g[A].push_back(B); g[B].push_back(A); } BiasedHeavyLightDecompositionPathOnly bhld; bhld.build(g, 0, initVals); #ifdef TEST vector<mint> naiveval(all(S)); #endif int Q; #ifndef TEST scanf("%d", &Q); #else Q=rand()%100+1; #endif rep(ii, Q) { int ty; #ifndef TEST scanf("%d", &ty); #else ty=rand()%2; #endif if(ty == 0) { int X, Y, Z; #ifndef TEST scanf("%d%d%d", &X, &Y, &Z), -- X, -- Y; #else X=rand()%N,Y=rand()%N,Z=rand()%100; #endif bhld.addToPath(X, Y, PathAdd(Z)); #ifdef TEST vi naivepath; naivegetpath(X, -1, Y, g, naivepath); each(j, naivepath) naiveval[*j] += mint(Z) * C[*j]; #endif }else { int X, Y; #ifndef TEST scanf("%d%d", &X, &Y), -- X, -- Y; #else X=rand()%N,Y=rand()%N; #endif mint ans = bhld.sumPath(X, Y); #ifndef TEST printf("%d\n", ans.get()); #else vi naivepath; naivegetpath(X, -1, Y, g, naivepath); mint naivesum, naivecoefsum; each(j, naivepath) naivecoefsum += C[*j], naivesum += naiveval[*j]; if(ans.get() != naivesum.get()) cerr << ans.get() << " != " << naivesum.get() << endl; #endif } #ifdef TEST // rep(i, N) bhld.getVal(i); // rep(i, N) bhld.setVal(i, bhld.getVal(i)); rep(i, N) assert(bhld.nodes[i].debugCheckUpdated()); // rep(i, N) assert(bhld.getVal(i).val.x == naiveval[i].x); #endif } } return 0; }