floyd算法的三重循环问题

2025-03-15 18:01:29
推荐回答(4个)
回答1:

三层循环的意思。第一层就是加入K的中间点,第二层和第三层循环是求每一对顶点在加入新的点后是否存在距离更近的路径,所以K只能放在最外层。也就是说你再加入新的点后,再进行判断每对顶点是否距离有变,就相当于一个前提条件。

回答2:

佛洛依德最短距离,算法就是这么计算的,如果不是在最外层,这就没逻辑了,求不出最短距离了。你需要仔细思考一下。

回答3:

floyd的根本思想是动态规划,最外层枚举的k是表示新加入一个可以作为中间点的顶点

回答4:

floyd的核心思路是
通过一个图的权值矩阵求出它的每两点间的最短路径矩阵。
从图的带权邻接矩阵A=[a(i,j)] n×n开始,递归地进行n次更新,即由矩阵D(0)=A,按一个公式,构造出矩阵D(1);又用同样地公式由D(1)构造出D(2);……;最后又用同样的公式由D(n-1)构造出矩阵D(n)。矩阵D(n)的i行j列元素便是i号顶点到j号顶点的最短路径长度,称D(n)为图的距离矩阵,同时还可引入一个后继节点矩阵path来记录两点间的最短路径。
采用的是(松弛技术),对在i和j之间的所有其他点进行一次松弛。所以时间复杂度为O(n^3);
其状态转移方程如下: map[i,j]:=min{map[i,k]+map[k,j],map[i,j]}
map[i,j]表示i到j的最短距离,K是穷举i,j的断点,map[n,n]初值应该为0,或者按照题目意思来做。
当然,如果这条路没有通的话,还必须特殊处理,比如没有map[i,k]这条路
详情请见:http://baike.baidu.com/view/14495.htm

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