关于可达矩阵的O(N*N)算法和强分图的O(E)算法

#include<iostream>
#include<vector>
#include<stack>
#include<algorithm>
#include<set>using namespace std;/*
定义 N为图的节点数，E为边的数量(除去数组初始化)
步骤                  时间复杂度           空间复杂度
邻接矩阵                    O(E)                O(N*N)
关联矩阵                    O(E)                O(E*N)
强分图                 O(E)                O(E)
可达矩阵                    O(N*N)              O(N*N)
*///矩阵基类
class Matrix {protected:int**Data;int ColLength,RawLength;constexpr void SetValue(const int&col, const int&raw, const int&&val) {Data[col][raw] = val;}public:const int&GetColLength() { return this->ColLength; }const int&GetRawLength() { return this->RawLength; }Matrix(const int&Col, const int&Raw) :ColLength(Col), RawLength(Raw) {Data = new int*[Col + 1];for (int col = 1; col <= Col; ++col) {Data[col] = new int[Raw + 1];for (int raw = 1; raw <= Raw; ++raw) {Data[col][raw] = 0;}}}virtual void Output() {cout << '\t';for (int i = 1; i <= ColLength; ++i) {cout << 'v' << i << '\t';}cout << endl;for (int col = 1; col <= ColLength; ++col) {cout << 'v' << col << '\t';for (int raw = 1; raw <= RawLength; ++raw) {cout << Data[col][raw] << '\t';}cout << endl;}}~Matrix() {for (int i = 1; i <= ColLength; ++i) {delete[]Data[i];}delete[]Data;}
};//邻接矩阵
class AdjointMatrix :public Matrix {friend class StrongPartiteGraph;friend class ReachabilityMatrix;public:AdjointMatrix(const int&PointNumber) :Matrix(PointNumber, PointNumber) {  }void AddEdge(const int&from, const int&to) {this->SetValue(from, to, 1);}constexpr bool IsConnected(const int&from, const int&to) {return Data[from][to];}void Output()override {cout << '\t';for (int i = 1; i <= ColLength; ++i) {cout << 'v' << i << '\t';}cout << endl;for (int col = 1; col <= ColLength; ++col) {cout << 'v' << col << '\t';for (int raw = 1; raw <= RawLength; ++raw) {cout << Data[col][raw] << '\t';}cout << endl;}}AdjointMatrix*Clone() {AdjointMatrix*AM = new AdjointMatrix(this->ColLength);size_t&&Size = sizeof(int)*(ColLength + 1);for (int Index = 1; Index <= this->ColLength; ++Index) {memcpy(AM->Data[Index], this->Data[Index], Size);}return AM;}};//关联矩阵
class RelatedMatrix :public Matrix {public:RelatedMatrix(const int&PointNumber, const int&EdgeNumber) :Matrix(PointNumber, EdgeNumber) {  }void AddEdge(const int&EdgeIndex, const int&from, const int&to) {this->SetValue(from, EdgeIndex, 1);this->SetValue(to, EdgeIndex, -1);}void Output()override {cout << '\t';for (int i = 1; i <= RawLength; ++i) {cout << 'e' << i << '\t';}cout << endl;for (int col = 1; col <= ColLength; ++col) {cout << 'v' << col << '\t';for (int raw = 1; raw <= RawLength; ++raw) {cout << Data[col][raw] << '\t';}cout << endl;}}};//图
class Graph {vector<int>*G;struct Edge {const int from,to;Edge(const int&from, const int&to) :from(from), to(to) {  }};vector<Edge> Edges;int PointNumber;friend class StrongPartiteGraph;public:Graph(const int&N) :PointNumber(N) { G = new vector<int>[PointNumber + 1];}void AddEdge(const int&from, const int&to) {G[from].push_back(to);Edges.emplace_back(from, to);}AdjointMatrix* GetAdjointMatrix() {AdjointMatrix*M = new AdjointMatrix(PointNumber);for (int from = 1; from <= PointNumber; ++from) {for (const auto&to : G[from]) {M->AddEdge(from, to);}}return M;}RelatedMatrix* GetRelatedMatrix() {int&&EdgeNumber = 0;for (int from = 1; from <= PointNumber; ++from) {EdgeNumber += G[from].size();}RelatedMatrix*M = new RelatedMatrix(PointNumber, EdgeNumber);for (int Index = 0; Index < static_cast<int>(Edges.size()); ++Index) {M->AddEdge(Index + 1, Edges[Index].from, Edges[Index].to);}return M;}~Graph() {delete[] G;}};//并查集，用于算法优化
class DisjointSet {int MaxPoint;int *Father;public:DisjointSet(int MaxPoint) {this->Father = new int[MaxPoint + 1];for (int i = 1; i <= MaxPoint; ++i) {this->Father[i] = i;}}int Find(int x) {return this->Father[x] == x ? x : (this->Father[x] = Find(this->Father[x]));}void Merge(int x, int y) {this->Father[this->Find(x)] = this->Find(y);}bool isSameSet(int x, int y) {return Find(x) == Find(y);}~DisjointSet() {delete[]this->Father;}};//强分图,采用Gabow算法
class StrongPartiteGraph {vector<int> *G;AdjointMatrix*StrongPartiteMatrix;vector<int>*PointSet;vector<int>*StrongPartiteList;const int&PointNumber;int *Belongs,Color,*TimeTag,*Stack1,*Stack2;bool *Visable;void InitAdjointMatrix() {int&&CurrentSet = 1;this->PointSet = new vector<int>[Color + 1];this->StrongPartiteList = new vector<int>[Color + 1];this->StrongPartiteMatrix = new AdjointMatrix(Color);for (int Index = 1; Index <= PointNumber; ++Index) {this->PointSet[this->Belongs[Index]].push_back(Index);}DisjointSet DS(PointNumber);for (int Index = 1; Index <= Color; ++Index) {if (this->PointSet[Index].size() == 1)continue;auto it = this->PointSet[Index].begin();const int&temp = *(++it);for (; it != this->PointSet[Index].end(); ++it) {DS.Merge(*it, temp);}}for (int Index = 1; Index <= Color; ++Index) {for (const auto&Point : this->PointSet[Index]) {for (const auto&to : this->G[Point]) {if (!DS.isSameSet(Point, to)) {this->StrongPartiteMatrix->AddEdge(Index, this->Belongs[to]);if (Index != this->Belongs[to]) {this->StrongPartiteList[Index].push_back(this->Belongs[to]);}}}}}}void Visit(int cur, int&sig, int&scc_num){TimeTag[cur] = ++sig;Stack1[++Stack1[0]] = cur;Stack2[++Stack2[0]] = cur;for (const auto&to : this->G[cur]){if (!TimeTag[to]){Visit(to, sig, scc_num);}else if (!Belongs[to]){while (TimeTag[Stack2[Stack2[0]]] > TimeTag[to]) {--Stack2[0];}}}if (Stack2[Stack2[0]] == cur){--Stack2[0]; ++scc_num;do{Belongs[Stack1[Stack1[0]]] = scc_num;} while (Stack1[Stack1[0]--] != cur);}}void GabowCompute(){int sig;this->TimeTag = new int[PointNumber + 1];this->Stack1 = new int[PointNumber + 1];this->Stack2 = new int[PointNumber + 1];memset(this->Belongs, 0, sizeof(int)*(PointNumber + 1));memset(TimeTag, 0, sizeof(int)*(PointNumber + 1));sig = 0; Color = 0;Stack1[0] = 0; Stack2[0] = 0;for (int Point = 1; Point <= PointNumber; ++Point){if (!TimeTag[Point])Visit(Point, sig, Color);}delete[]this->TimeTag;delete[]this->Stack1;delete[]this->Stack2;this->InitAdjointMatrix();}public:StrongPartiteGraph(const Graph&G) :G(G.G), PointNumber(G.PointNumber) {this->Belongs = new int[PointNumber + 1];this->Visable = new bool[PointNumber + 1];memset(this->Belongs, 0x0, sizeof(int)*(PointNumber + 1));memset(this->Visable, 0x0, sizeof(bool)*(PointNumber + 1));this->GabowCompute();}AdjointMatrix*GetReachabilityMatrix() {AdjointMatrix*AM = new AdjointMatrix(PointNumber);int cnt = 0;auto Translate = [&AM,this](const int&FromSetIndex, const int&ToSetIndex)->void {for (const auto&from : this->PointSet[FromSetIndex]) {for (const auto&to : this->PointSet[ToSetIndex]) {AM->AddEdge(from, to); }}};bool**Vis = new bool*[PointNumber + 1];for (int Index = 1; Index <= PointNumber; ++Index) {Vis[Index] = new bool[PointNumber + 1];memset(Vis[Index], 0x0, sizeof(bool)*(PointNumber + 1));}stack<int>Stack;for (int Point = 1; Point <= Color; ++Point) {Stack.push(Point);vector<int>Froms;while (!Stack.empty()) {int from = Stack.top();Stack.pop();Froms.push_back(from);for (const auto&Precursor : Froms) {if (Vis[Precursor][from])break;Vis[Precursor][from] = true;Translate(Precursor, from);}for (const auto&to : this->StrongPartiteList[from]) {Stack.push(to);}}}for (int Index = 1; Index <= PointNumber; ++Index) {delete[]Vis[Index];}delete[]Vis;return AM;}void Output() {cout << "强分图共有" << Color << "个强连通分量" << endl<< "强分图为" << endl;this->StrongPartiteMatrix->Output();cout << "其中：" << endl;for (int Index = 1; Index <= Color; ++Index) {cout << "v" << Index << " = {";for (const auto&Point : this->PointSet[Index]) {cout << Point << ',';}cout << '\b' << '}' << endl;}}~StrongPartiteGraph() {delete[]this->Belongs;delete[]this->PointSet;delete this->StrongPartiteMatrix;delete[]this->Visable;}};int main() {int N;cout << "请输入点的数量N（编号从1到N）:" << endl;cin >> N;Graph G(N);int M;cout << "请输入有向边的数量M:" << endl;cin >> M;cout << "依次输入有向边:" << endl<< "from\tto" << endl;while (M--) {int from, to;cin >> from >> to;G.AddEdge(from, to);}Matrix* matrix;cout << "邻接矩阵：" << endl;matrix = G.GetAdjointMatrix();matrix->Output();delete matrix;cout << "关联矩阵：" << endl;matrix = G.GetRelatedMatrix();matrix->Output();delete matrix;cout << "强分图：" << endl;StrongPartiteGraph SPG(G);SPG.Output();cout << "可达矩阵：" << endl;matrix = SPG.GetReachabilityMatrix();matrix->Output();delete matrix;system("pause");return 0;}

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