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c# - 在列表中查找循环引用的最有效方法

转载 作者:塔克拉玛干 更新时间:2023-11-03 02:59:24 25 4
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给定以下重定向列表

[
{
"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个项目“a”应该重定向到“b”。如果我们按照列表进行操作,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”,而“d”会指向“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,如下所示:

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

但我只对告诉用户类似的事情感兴趣

“嘿,你不能那样做,这将是一个循环引用,因为“a”指向“b”,“b”指向“c”,“c”指向“d”,“d”指向“a”

那么,你们有什么建议吗?我确定存在其他一些(更好的)算法来执行此操作...:)

最佳答案

虽然通用图循环查找算法会起作用,但由于“旧的是唯一的,目标不是” 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循环的一部分。另外,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,此函数可以找到从起始节点可达的环:

/// <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,可以扩展到到达一个已经检查过的节点时提前返回(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;
}

下面的函数用来维护访问集的一致性

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 节点调用它以检查循环。当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循环。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;
}

关于c# - 在列表中查找循环引用的最有效方法,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/46484725/

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