最大流算法

单源点单汇点的最大流算法，C++实现例子一枚。

/* * Graph.cpp * *  Created on: 2013-1-18 *      Author: qichi */#include "Graph.h"#include <string.h>#include <iostream>/* * DAG */Graph::Graph(int n, int s, int t) {m_nVertex = n;m_nStart = s;m_nTarget = t;m_nMaxFlow = 0;m_pEdges = new EDGE*[n];m_bVisited = new bool[n];m_pStack = new int[n];m_nTop = -1;// allocate continuous memory for 2-d arraym_pMatrix = new double*[n];m_pMatrix[0] = new double[n*n];for ( int i=1; i<n; i++ ) {m_pMatrix[i] = m_pMatrix[i-1]+n;}// initialize arraysmemset(m_pEdges,0,n*sizeof(EDGE*));memset(m_pMatrix[0],0,n*n*sizeof(double));memset(m_pStack,0,n*sizeof(int));}Graph::~Graph() {for ( int i=0; i<m_nVertex; i++ ) {EDGE *e= m_pEdges[i];while ( e ) {EDGE *p = e;e = e->next;delete p;}}delete m_pEdges;delete m_pMatrix[0];delete m_pMatrix;delete m_bVisited;}void Graph::insert(int i, int j, double volume, double price) {// insert an edgeEDGE *e = new EDGE();e->target = j;e->volum = volume;e->price = price;e->next = m_pEdges[i];m_pEdges[i] = e;// insert a reverse edgee = new EDGE();e->target = i;e->volum = 0;e->price = price;e->next = m_pEdges[j];m_pEdges[j] = e;// insert it to matrixm_pMatrix[i][j] = volume;}void Graph::print() {std::cout << "Adjacent matrix of graph : " << std::endl;for ( int i=0; i<m_nVertex; i++ ) {for ( int j=0; j<m_nVertex; j++ ) {std::cout << m_pMatrix[i][j] << " ";}std::cout << std::endl;}}bool Graph::explore(int u, int t) {m_pStack[++m_nTop] = u;m_bVisited[u] = true;bool res = false;if ( u == t ) {// search max flow allowed on pathdouble maxv = 1.0e+32;for ( int i=0; i<m_nTop; i++ ) {int x=m_pStack[i], y=m_pStack[i+1];if ( m_pMatrix[x][y] < maxv )maxv = m_pMatrix[x][y];}// reduce volume of edges along through pathfor ( int i=0; i<m_nTop; i++ ) {int x=m_pStack[i], y=m_pStack[i+1];m_pMatrix[x][y] -= maxv;m_pMatrix[y][x] += maxv;}// add to max flowm_nMaxFlow += maxv;res = true;} else {EDGE *e = m_pEdges[u];while ( e!=NULL ) {int v = e->target;// v is not visited && <u,v> has extra volumeif ( ! m_bVisited[v] && m_pMatrix[u][v] > 0 ) {res = explore(v, t);if ( res ) break;}e = e->next;}}m_nTop--;return res;}void Graph::maxflow() {bool res = false;do {for ( int i=0; i<m_nVertex; i++ ) {m_bVisited[i] = false;}m_nTop = -1;res = explore(m_nStart,m_nTarget);} while ( res );// show the max flow and flow on each edgestd::cout << "Max flow is : " << m_nMaxFlow << std::endl;for ( int i=0; i<m_nVertex; i++ ) {EDGE *e=m_pEdges[i];while ( e ) {if ( e->volum > 0 ) {int j = e->target;std::cout << "Flow on edge <" << i << "," << j ;std::cout << "> is " << e->volum - m_pMatrix[i][j] << std:: endl;}e = e->next;}}}

/* * Graph.h * *  Created on: 2013-1-18 *      Author: qichi */#ifndef GRAPH_H_#define GRAPH_H_typedef struct EDGE {double volum;double price;int target;EDGE *next;} EDGE ;class Graph {private:// link of edgesint m_nVertex;EDGE **m_pEdges;// adjacent matrix of volumedouble **m_pMatrix;// a stack to save pathint *m_pStack;intm_nTop;// a array to mark visited vertexbool*m_bVisited;// max flowint m_nStart;int m_nTarget;int m_nMaxFlow;public:Graph(int n, int s, int t);virtual ~Graph();void insert(int i, int j, double volume, double price);void print();bool explore(int s, int t);void maxflow();};#endif /* GRAPH_H_ */

//============================================================================// Name        : MaxFlowProblem.cpp// Author      : Qichi// Version     :// Copyright   : Your copyright notice// Description : Hello World in C++, Ansi-style//============================================================================#include <iostream>#include "Graph.h"using namespace std;int main() {int n, s, t;cout << "Enter number of vertex <n s t>: ";cin >> n >> s >> t;if ( n <= 0 ) {cout << "Invalid number!" << endl;return 1;}Graph *g = new Graph(n, s, t);int i, j;double v, p;cout << "Enter an edge <i j v p > : ";while ( cin >> i >> j >> v >> p ) {g->insert(i,j,v,p);cout << "Enter an edge <i j v p > : ";}cout << endl;g->maxflow();delete g;return 0;}