有环有向图中的最长路径

问题描述

我正在尝试编写一个 CLI 工具来查找启用了 go 模块的项目中最长依赖链的长度。为此，我获取 go mod graph 的输出并从中删除依赖版本，然后以 map[string][]string 的形式创建图形的邻接列表表示。代码如下：

depGraph := make(map[string][]string)
        scanner := bufio.NewScanner(strings.NewReader(goModGraphOutputString))

        // deps will store all the dependencies
        // since can't do slice.contains so better to use map
        deps := make(map[string]bool)
        mainModule := "notset"

        for scanner.Scan() {
            line := scanner.Text()
            words := strings.Fields(line)
            // remove versions
            words[0] = (strings.Split(words[0],"@"))[0]
            words[1] = (strings.Split(words[1],"@"))[0]
            if mainModule == "notset" {
                mainModule = words[0]
            }
            deps[words[0]] = true
            deps[words[1]] = true

            // we don't want to add the same dep again
            if !contains(depGraph[words[0]],words[1]) {
                depGraph[words[0]] = append(depGraph[words[0]],words[1])
            }
        }

之后为了得到最长链的长度，我使用动态编程运行了一个 DFS：

    dp := make(map[string]int)
        // visited array will make sure we don't have infinite recursion
        visited := make(map[string]bool)

        // values not in map will have their respective 0 value by default
        // so need to worry about terminal nodes
        for k := range deps {
            dp[k] = 0
            visited[k] = false
        }

        for k := range deps {
            if visited[k] == false {
                dfs(k,depGraph,dp,visited)
            }
        }

// perform depth first search from current dependency
func dfs(k string,graph map[string][]string,dp map[string]int,visited map[string]bool) {
    visited[k] = true
    // for terminal deps we won't go into this for loop
    // and so vis for them would be true and dp would be 0
    // since in maps non existent keys have 0 value by default
    for _,u := range graph[k] {
        if visited[u] == false {
            dfs(u,graph,visited,longestPath)
        }
        dp[k] = max(dp[k],1+dp[u])
    }
}

然后最长的路径就是值 dp[mainModule]。但是当在有周期的大型项目上运行这个时，我每次都会得到不同的答案。这个算法有错误吗？

解决方法

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