匈牙利算法3（转载） - Something TO DO

匈牙利算法 2

A*算法

匈牙利算法3（转载）

Something TO DO posted @ 2016年11月06日 17:01 in math , 973 阅读

这是转载的文章，如果想要系统的看，可以从匈牙利算法1http://mario.is-programmer.com/posts/52265.html开始看起！！！

这是一种用增广路求二分图最大匹配的算法。它由匈牙利数学家Edmonds于1965年提出，因而得名。定义未盖点：设Vi是图G的一个顶点，如果Vi 不与任意一条属于匹配M的边相关联，就称Vi 是一个未盖点。

交错路：设P是图G的一条路，如果P的任意两条相邻的边一定是一条属于M而另一条不属于M，就称P是一条交错路。

可增广路：两个端点都是未盖点的交错路叫做可增广路。

流程图

伪代码：

bool 寻找从k出发的对应项出的可增广路
{
    while (从邻接表中列举k能关联到顶点j)
    {
        if (j不在增广路上)
        {
            把j加入增广路;
            if (j是未盖点 或者 从j的对应项出发有可增广路)
            {
                修改j的对应项为k;
                则从k的对应项出有可增广路,返回true;
            }
        }
    }
    则从k的对应项出没有可增广路,返回false;
}

void 匈牙利hungary()
{
    for i->1 to n
    {
        if (则从i的对应项出有可增广路)
            匹配数++;
    }
    输出 匹配数;
}

演示

转载链接：https://www.byvoid.com/blog/hungary/

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