(第三种最小生成树算法) 在本题中,我们给出三种不同算法的伪代码。每种算法的输入都是一个连通图和一个权重函数,返回值都是-个边的集合T。对于每种算法,要么证明T是一棵最小生成树,要么证明T不是一棵最小生成树。同时给出每种算法的最有效的实现(不管该算法是否能够计算出最小生成树)。
a MA YBE-MST-A(G,w) 1 sort the edges into nonincreasing order of edge weights w 2 T=E 3 for each edge e, taken in nonincreasing order by weight 4if T - (e)is a connected graph 5T=T-(e) 6return T b. MAYBE-MST-B(G,w) 1 T=2 for each edge e, taken in arbitrary order 3if TU (e)has no cycles 4T= TU(e) 5return T c. MA YBE-MST-C(G,w) 1T=
2for each edge e, taken in arbitrary order 3T= . TU(e) 4if T has a cycle c 5 lete' be a maximum-weight edge on c 6T= T-(e) 7return T