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Leetcode 685 – Redundant Connection II

sudipp

In this problem, a rooted tree is a directed graph such that, there is exactly one node (the root) for which all other nodes are descendants of this node, plus every node has exactly one parent, except for the root node which has no parents.

The given input is a directed graph that started as a rooted tree with N nodes (with distinct values 1, 2, …, N), with one additional directed edge added. The added edge has two different vertices chosen from 1 to N, and was not an edge that already existed.

The resulting graph is given as a 2D-array of edges. Each element of edges is a pair [u, v]that represents a directed edge connecting nodes u and v, where u is a parent of child v.

Return an edge that can be removed so that the resulting graph is a rooted tree of N nodes. If there are multiple answers, return the answer that occurs last in the given 2D-array.

Example 1:

Input: [[1,2], [1,3], [2,3]] Output: [2,3] Explanation: The given directed graph will be like this:
1
/ \
v v
2–>3

Example 2:

Input: [[1,2], [2,3], [3,4], [4,1], [1,5]] Output: [4,1] Explanation: The given directed graph will be like this:
5 <- 1 -> 2
^ |
| v
4 <- 3

Note:
The size of the input 2D-array will be between 3 and 1000.Every integer represented in the 2D-array will be between 1 and N, where N is the size of the input array. 

public class Solution {
     public int[] FindRedundantDirectedConnection(int[][] edges) {

/*
    Step 1. Build In and Out Degree map, detect if any any vertex with Multiple parents.
    Step 2. If we don't find vertex 'A' with multiple parents
            2.1) Start at 'root' and detect any cycle with DFS, return the edge causing the cycle
    Step 3. If we find vertex 'A' with multiple parents
            3.1) if out degree at vertex 'A' is > 0, i.e there is a edge going out of the 'A' vertex
                3.1.1) Start at 'A' and detect any cycle with DFS, return the edge causing the cycle
            3.2) if there is NO outgoing edge from vertex 'A'
                3.2.1) Return the LAST edge that is ending at 'A' (i.e 'A' last parent)  
    */

    var vertexInDegree = new List<int>[edges.Length + 1];
    var vertexOutDegree = new List<int>[edges.Length + 1];

    for (int i = 0; i < edges.Length + 1; i++) vertexInDegree[i] = new List<int>();
    for (int i = 0; i < edges.Length + 1; i++) vertexOutDegree[i] = new List<int>();

    bool[] visited = new bool[edges.Length + 1]; // as vertex # starts with 1

    int vertexWithMultipleParents = -1;

    foreach (var arr in edges)
    {
        vertexInDegree[arr[1]].Add(arr[0]);
        vertexOutDegree[arr[0]].Add(arr[1]);

        if (vertexInDegree[arr[1]].Count > 1)
            vertexWithMultipleParents = arr[1];
    }

    if (vertexWithMultipleParents != -1)
    {
        //detect if there is out edges from Vertex with multiple parents
        //if yes, defect this edge cause a cycle, if yes, remove the first edge 
        //else remove the end edge 

        //start from vertex with multiple parents ***********
        int root = vertexWithMultipleParents;
        if (vertexOutDegree[root].Count >0) //if there is a out edge
        {
            Stack<KeyValuePair<int, int>> stack = new Stack<KeyValuePair<int, int>>();
            stack.Push(new KeyValuePair<int, int>(root, -1));

            while (stack.Any())
            {
                var node = stack.Pop();
                if (!visited[node.Key])
                {
                    visited[node.Key] = true;

                    foreach (int c in vertexOutDegree[node.Key])
                        stack.Push(new KeyValuePair<int, int>(c, node.Key));
                }
                else
                {
                    //cycle detected
                    return new int[] { node.Value, node.Key };
                }
            }
            return new int[] { vertexInDegree[root][1], root };
        }
        else //doesnt have any out degree, return the last one 
        {
            return new int[] { vertexInDegree[root][1], root };
        }
    }
    else
    {
        //if multple parent vertex NOT found,            
        //then search for cycle, if found, then remove the edge causing the cycle

        //first edge's as start
        int root = edges[0][0];

        Stack<KeyValuePair<int, int>> stack = new Stack<KeyValuePair<int, int>>();
        stack.Push(new KeyValuePair<int, int>(root, -1));

        while (stack.Any())
        {
            var node = stack.Pop();
            if (!visited[node.Key])
            {
                visited[node.Key] = true;

                foreach (int c in vertexOutDegree[node.Key])
                    stack.Push(new KeyValuePair<int, int>(c, node.Key));
            }
            else
            {
                //cycle detected
                return new int[] { node.Value, node.Key};
            }
        }
        return null;
    }   
}
}

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  301. ما در این مقاله میخواهیم در ارتباط با اهمیت استعدادیابی کودکان صحبت کنیم و بگوییم که چرا استعدادیابی
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    پدر و مادری در طول زندگی نگرانی
    از آینده فرزندان و مسیری است که کودک در زندگی طی می کند.

    بدون شک موفقیت در زندگی حاصل مجموعه ای از عوامل
    درهم پیچیده است که تفکیک آنها به راحتی امکان پذیر نیست.
    اما اگر به زندگی افراد موفق نگاهی بیندازیم در می یابیم
    همه آنها یک نقطه مشترک دارند و آن پیش رفتن در مسیری است که در آن استعداد و علاقه دارند.

    برای کلاس … نیاز به راهنمایی دارید؟ اطلاعات خود را
    از طریق دکمه نارنجی رنگ پایین صفحه
    ثبت کنید. با شما تماس می‌گیریم.

    مردم غالبا برای رسیدن به موفقیت و رضایتمندی راه های مختلفی را امتحان کرده و با آزمون و خطای فراوان
    سعی در کشف مسیر زندگی خود دارند.

    اما وظیفه والدین به عنوان نزدیک
    ترین افراد به کودک در این زمینه چیست؟در این مقاله سعی کرده ایم به این پرسش پاسخ دهیم.

    اگر جزو افرادی هستید که از رشته تحصیلی، شغل و به
    طور کلی مسیر زندگیتان راضی هستید
    به شما تبریک می گوییم. اما درصد کمی از افراد در رشته دانشگاهی و
    شغلی مشغول می شوند که در آن استعداد و به آن
    علاقه دارند. بخشی از این امر ناشی از مشکلات فرهنگی ، اجتماعی و اقتصادی جامعه است اما بخشی نیز
    از عدم وجود خودشناسی و راهنمای خوب نشات می گیرد.

    واقعیت این است که افراد کمی این شانس را دارند
    که از سالهای اولیه کودکی و بدون از این شاخه
    به آن شاخه پریدن و صرف وقت و هزینه بسیار در مسیر درست زندگی خود قرار
    بگیرند. در اغلب موارد والدین
    خواسته یا ناخواسته کودک را در مسیری
    پیش میبرند که خواسته و
    آرزوهای خود را کامیاب کنند.
    در این مطلب قصد داریم تنها تلنگر کوچکی برای والدین
    آگاه باشیم تا از خود بپرسند نقش من
    در یافتن مسیر آینده فرزندم چیست و چگونه
    می توانم فرزند شاد، موفق و رضایتمندی داشته
    باشم؟

    چرا استعدادیابی کودکان مهم است؟
    تعاریف استعداد، علاقه، هوش و خلاقیت
    قبل از هر چیز بهتر است بدانید استعداد، علاقه، هوش و خلاقیت مفاهیمی متفاوت هستند و آشنایی با این
    مفاهیم باعث می شود شما مسیر درست تری را در انتخاب
    های زندگی پیش بگیرید. البته تعاریف مختلفی
    برای هرکدام از این موارد وجود دارد اما برای آشنایی اولیه بیایید تعریفی کوتاه
    از هر کدام از آنها داشته باشیم:

    این مطلب را هم از دست ندهید:

    از کجا بدانید فرزندتان استعداد نقاشی دارد؟

    بهترین سن برای استعدادیابی چه زمانی است؟

    استعداد موسیقی در کودکان

    چگونه استعداد خود را کشف کنیم؟

    تست هالند؛ استعدادیابی و هدایت شغلی

    استعداد: یعنی یادگیری یک مهارت با صرف انرژی
    و زمان کمتر. به عبارت دیگر اگر شما مثلا
    نقاشی را در 3 جلسه یاد میگیرید در حالیکه متوسط افراد
    در 7 جلسه آن را یاد می گیرند می توان گفت شما استعداد نقاشی دارید.

    علاقه: علایق غالبا ترجیحات
    افراد هستند. این امور غالبا شامل مواردی
    است که پرداختن به آن شما را به وجد می آورد اما لزوما در آن توانایی ندارید.
    مثلا ممکن است شما به موسیقی علاقه داشته باشید اما نتوانید یک موزیسین فوق العاده شوید.

    هوش: هوش توانایی کلی وجامع فرد است برای اینکه به طور
    هدفمند عمل کند، به طورمنطقی بیندیشد و به طور موثر
    با محیطش به مبادله بپردازد.

    خلاقیت: به کار گرفتن توانایی های
    ذهنی برای خلق یک فکر، ایده و یا اثر جدید را خلاقیت می گویند.

    حالا که با هر یک ازین موارد آشنا شدید بهتر در
    می یابید که همه موارد فوق در رسیدن به موفقیت ما نقش دارند.

    در واقع برای حصول به بهترین نتیجه هر
    یک از این موارد باید در حالت بهینه برای یک فرد
    قرار بگیرند.

    خیلی از ما اشخاصی در زندگی می شناسیم که هوش
    زیادی دارند. اما شغل و جایگاه اجتماعی
    مناسبی ندارند. حتی این هوش را در مسیر نادرست به کار می گیرند.
    و یا فرد در مسیری پیش می رود که به آن علاقه داشته اما در آن استعداد کافی ندارد.

    بنابراین با کندی بسیار مسیر را طی کرده.

    تازه بعد از همه اینها به فردی متوسط و نه عالی در آن زمینه تبدیل خواهد شد.

    اینها تنها مثال هایی برای درک
    اهمیت همراهی همه این عوامل است.

    چرا استعدادیابی کودکان مهم است؟

    جلوگیری از اتلاف وقت
    استعدادیابی باعث می‌شود افراد وقت خود را در زندگی تلف نکنند و از همان ابتدا سراغ کاری بروند که
    در آن بهتر هستند. عدم شناخت صحیح استعدادها و علایق
    باعث می شود کودک در زندگی مسیرهایی پیش بگیرد که در آن راضی و خوشحال نیست.

    این امر در همه انتخاب های مهم زندگی از جمله انتخاب رشته دبیرستان و دانشگاه و انتخاب شغل نمود زیادی دارد.

    جلوگیری از اتلاف انرژی
    وقتی کودک در کاری استعداد دارید آن را با صرف انرژی کمتری انجام می دهد.
    مثلا اگر در موسیقی استعداد دارد آن را بسیار
    سریعتر از متوسط افراد یاد میگیرد.
    این امر هم باعث افزایش انگیزه کودک می شود و هم موجب می شود او برای امور دیگر زندگی انرژی بیشتری داشته باشد.

    جلوگیری از اتلاف سرمایه
    وقتی شما استعداد کودک خود را نمی شناسید ممکن است زمان و پول
    زیادی صرف کلاس های مختلف برای یادگیری مهارت هایی کنید که کودک در آن احساس خوبی ندارد.
    شناخت استعدادها موجب می شود کودک تنها مهارت
    هایی را یاد بگیرید که موجب موفقیتش می
    شود.

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