KM算法的实现和封装

        自己在写一个小程序时，遇到了一个类似于“完备匹配下的最大权匹配”的优化问题。在网上搜了下相关资料，了解到对应的匈牙利算法与KM算法，而且已经都有大神进行了详细讲解和代码的编写。唯一的不同之处是我参考的文章中KM算法目标是匹配结果最大为目标，而我的程序中是以匹配结果最小为目标。自己把代码改写了下，并封装为类。验证结果表明代码没有问题~

        这里将代码放出，以供网友参考。不过具体到算法层，本人理解不深，还是观摩网上算法大神的讲解（见后面参考文献）吧。

1）KM.h

#ifndef _KM_H_
#define _KM_H_

#include 


class KM
{
public:
    KM();
    ~KM();
    void init(int size, std::vector> diff);
    bool dfs(int a);
    void KM_Calc(); 
    int* getMatch();
    double getdiffSum();

private:
    std::vector> diff;// 差异度矩阵(方阵)
    double* ex_a;// 每个a类对象的期望
    double* ex_b;// 每个b类对象的期望
    bool* vis_a;// 记录每一轮匹配过的a类对象
    bool* vis_b;// 记录每一轮匹配过的b类对象
    int* match;// 记录每一个b类对象匹配到的a类对象索引，如果没有匹配到则为-1
    double* slack;// 记录每个b类对象能被a类对象匹配到所需要减少的最小差异度
    int size;// 记录差异度矩阵的边长
    double diffSum;// 记录匹配结果的总体差异度大小
};



#endif

2）KM.cpp

#include "KM.h"

KM::KM()
{
    // 参数初始化
    ex_a = ex_b = NULL;
    slack = NULL;
    match = NULL;
    vis_a = vis_b = NULL;
    size = 0;
    diffSum = 0;
}

KM::~KM()
{
    /* 释放之前分配了的内存 */
    if(ex_a)
    {
        delete []ex_a;
        ex_a = NULL;
    }
    if(ex_b)
    {
        delete []ex_b;
        ex_b = NULL;
    }
    if(vis_a)
    {
        delete []vis_a;
        vis_a = NULL;
    }
    if(vis_b)
    {
        delete []vis_b;
        vis_b = NULL;
    }
    if(slack)
    {
        delete []slack;
        slack = NULL;
    }

    if(match)
    {
        delete []match;
        match = NULL;
    }
    
}

void KM::init(int size, std::vector> diff)
{
    /* 获取差异度矩阵，根据矩阵的边长为其他变量分配空间 */
    this->diff = diff;
    this->size = size;
    ex_a = new double[size];
    ex_b = new double[size];
    vis_a = new bool[size];
    vis_b = new bool[size];
    slack = new double[size];
    match = new int[size];
}

bool KM::dfs(int a)
{
    vis_a[a] = true;
    for(int b = 0; b < size; b++)
    {
        if(vis_b[b])// 每一轮匹配中b类每个对象只尝试一次
            continue;
        double c = diff[a][b];
        double gap = ex_a[a] + ex_b[b] - c;// 差异度符合要求
        if(fabs(gap) < 1e-6)
        {
            vis_b[b] = true;
            if(match[b] == -1 || dfs(match[b]))// 匹配成功
            {
                match[b] = a;
                return true;
            }
        }
        else
        {
            slack[b] = std::max(slack[b], gap);// 匹配失败，记录该b类对象若想成功匹配，其差异度减小的最小值
        }
    }

    return false;
}

void KM::KM_Calc()
{
    for(int i = 0; i < size; i++)
    {
        ex_b[i] = 0;// 每个b类对象的差异度初始为0
        match[i] = -1;
        ex_a[i] = (diff)[i][0];
        for(int j = 1; j < size; j++)
        {
            ex_a[i] = std::min(ex_a[i], (diff)[i][j]);// 每个a类对象的初始期望值是与之相连的每个b类对象差异度的最小值
        }

    }

    for(int i = 0; i < size; i++)
    {
        for(int m = 0; m < size; m++)
            slack[m] = -1000000.0;
        while(1)
        {
            for(int m = 0; m 

3）main.cpp提供调用示例，其中的数据来自http://blog.csdn.net/kevinjqy/article/details/54584114

#include 

#include "km.h"

int main()
{
    /* 构造差异度矩阵 */
    std::vector> diff;
    diff.resize(4);
    for(int i = 0; i < diff.size(); i++)
    {
        diff[i].resize(4);
    }
    diff[0][0] = 90;
    diff[0][1] = 75;
    diff[0][2] = 75;
    diff[0][3] = 80;
    diff[1][0] = 35;
    diff[1][1] = 85;
    diff[1][2] = 55;
    diff[1][3] = 65;
    diff[2][0] = 125;
    diff[2][1] = 95;
    diff[2][2] = 90;
    diff[2][3] = 105;
    diff[3][0] = 45;
    diff[3][1] = 110;
    diff[3][2] = 95;
    diff[3][3] = 115;

    /* 初始化算法对象 */
    KM km;
    km.init(diff.size(), diff);
    /* 计算结果并输出 */
    km.KM_Calc();
    std::cout<<"diffSum: "<

参考文章：

[1] http://www.cnblogs.com/wenruo/p/5264235.html KM算法详解+模板

[2] http://blog.csdn.net/kevinjqy/article/details/54584114 分配问题与匈牙利算法

[3] http://blog.csdn.net/dark_scope/article/details/8880547 趣写算法系列之匈牙利算法