在列表中查找循环引用的最有效方法

时间:2017-09-29 08:25:48

标签: c# algorithm circular-reference cycle-detection

给出以下重定向列表

[
    {
        "old": "a",
        "target": "b"
    },
    {
        "old": "b",
        "target": "c"
    },
    {
        "old": "c",
        "target": "d"
    },
    {
        "old": "d",
        "target": "a"
    },
    {
        "old": "o",
        "target": "n"
    },
    {
        "old": "n",
        "target": "b"
    },
    {
        "old": "j",
        "target": "x"
    },
    {
        "old": "whatever",
        "target": "something"
    }
]

在这里,我们可以看到第一项" a"应重定向到" b"。 如果我们按照列表,我们可以看到以下模式:

a -> b
b -> c
c -> d
d -> a

所以我们最终会得到一个循环引用,因为" a"最终会指向" d"和" d"指向" a"。

查找循环引用的最有效方法是什么?

我在C#

中提出了以下算法
var items = JsonConvert.DeserializeObject<IEnumerable<Item>>(json)
    .GroupBy(x => x.Old)
    .Select(x => x.First())
    .ToDictionary(x => x.Old, x => x.Target);
var circulars = new Dictionary<string, string>();
foreach (var item in items)
{
    var target = item.Value;
    while (items.ContainsKey(target))
    {
        target = items[target];

        if (target.Equals(item.Key))
        {
            circulars.Add(target, item.Value);
            break;
        }
    }
}

这将给我一个包含4个项目的列表:

[
    {
        "old": "a",
        "target": "b"
    },
    {
        "old": "b",
        "target": "c"
    },
    {
        "old": "c",
        "target": "d"
    },
    {
        "old": "d",
        "target": "a"
    }
]

但我只想告诉用户类似的事情

&#34;嘿,你不能这样做,这将是一个循环参考,因为&#34; a&#34;指向&#34; b&#34;指向&#34; c&#34;指向&#34; d&#34;它指向&#34; a&#34;

那么,你们有什么建议吗? 我确定存在一些其他(更好的)算法来执行此操作......:)

1 个答案:

答案 0 :(得分:2)

虽然通用的图形循环查找算法可行,但由于“Old is unique,target is not”约束,您的情况有点特殊。它实际上意味着每个节点只能有一个后继节点,因此它最多只能是一个周期的一部分。此外,当DFS-Traversing节点时,不会有任何fork,因此迭代DFS实现变得非常容易。

给定任意起始节点,此函数可以找到可从起始节点到达的循环:

/// <summary>
/// Returns a node that is part of a cycle or null if no cycle is found
/// </summary>
static string FindCycleHelper(string start, Dictionary<string, string> successors, HashSet<string> stackVisited)
{
    string current = start;
    while (current != null)
    {
        if (stackVisited.Contains(current))
        {
            // this node is part of a cycle
            return current;
        }

        stackVisited.Add(current);

        successors.TryGetValue(current, out current);
    }

    return null;
}

为了保持效率,当达到已经检查过的节点时,可以将其扩展为提前返回(使用previouslyVisited):

/// <summary>
/// Returns a node that is part of a cycle or null if no cycle is found
/// </summary>
static string FindCycleHelper(string start, Dictionary<string, string> successors, HashSet<string> stackVisited, HashSet<string> previouslyVisited)
{
    string current = start;
    while (current != null)
    {
        if (previouslyVisited.Contains(current))
        {
            return null;
        }
        if (stackVisited.Contains(current))
        {
            // this node is part of a cycle
            return current;
        }

        stackVisited.Add(current);

        successors.TryGetValue(current, out current);
    }

    return null;
}

以下函数用于维护已访问集的一致性

static string FindCycle(string start, Dictionary<string, string> successors, HashSet<string> globalVisited)
{
    HashSet<string> stackVisited = new HashSet<string>();

    var result = FindCycleHelper(start, successors, stackVisited, globalVisited);

    // update collection of previously processed nodes
    globalVisited.UnionWith(stackVisited);

    return result;
}

为每个old节点调用它以检查周期。检测到循环起始节点时,可以单独创建循环信息:

// static testdata - can be obtained from JSON for real code
IEnumerable<Item> items = new Item[]
{
    new Item{ Old = "a", Target = "b" },
    new Item{ Old = "b", Target = "c" },
    new Item{ Old = "c", Target = "d" },
    new Item{ Old = "d", Target = "a" },
    new Item{ Old = "j", Target = "x" },
    new Item{ Old = "w", Target = "s" },
};
var successors = items.ToDictionary(x => x.Old, x => x.Target);

var visited = new HashSet<string>();

List<List<string>> cycles = new List<List<string>>();

foreach (var item in items)
{
    string cycleStart = FindCycle(item.Old, successors, visited);

    if (cycleStart != null)
    {
        // cycle found, get detail information about involved nodes
        List<string> cycle = GetCycleMembers(cycleStart, successors);
        cycles.Add(cycle);
    }
}

以您想要的任何方式输出您找到的周期。例如

foreach (var cycle in cycles)
{
    Console.WriteLine("Cycle:");
    Console.WriteLine(string.Join(" # ", cycle));
    Console.WriteLine();
}

GetCycleMembers的实现非常简单 - 它取决于正确的起始节点:

/// <summary>
/// Returns the list of nodes that are involved in a cycle
/// </summary>
/// <param name="cycleStart">This is required to belong to a cycle, otherwise an exception will be thrown</param>
/// <param name="successors"></param>
/// <returns></returns>
private static List<string> GetCycleMembers(string cycleStart, Dictionary<string, string> successors)
{
    var visited = new HashSet<string>();
    var members = new List<string>();
    var current = cycleStart;
    while (!visited.Contains(current))
    {
        members.Add(current);
        visited.Add(current);
        current = successors[current];
    }
    return members;
}