graph-algorithm - 最大路径问题

Question

给定定向未加权图，问题是找到最大长度的简单路径
(起始顶点和结束顶点不固定)。显然可以在 O(n^2 * 2 ^n) 中解决，但我听说有 O(n * 2 ^ n) 算法，我不知道。那么如何在 O(n * 2 ^n) 中解决它呢？//n = |V|

Answer 1

如果您的问题确实是 Longest Path Problem在 DAG ，来自维基百科的算法如下，运行时间为 O(|V| + |E|):

algorithm dag-longest-path is
    input: 
         Directed acyclic graph G
    output: 
         Length of the longest path

    length_to = array with |V(G)| elements of type int with default value 0

    for each vertex v in topOrder(G) do
        for each edge (v, w) in E(G) do
            if length_to[w] <= length_to[v] + weight(G,(v,w)) then
                length_to[w] = length_to[v] + weight(G, (v,w))

    return max(length_to[v] for v in V(G))