C# Largest String
static string LargestString(string s)
{
    var chars = s.ToCharArray();
    var len = chars.Length;
    var cur = "";

    for (int i = len - 1; i >= 0; i--)
    {
        cur = chars[i] + cur;

        if (cur.Length == 3)
        {
            if (cur == "abb")
            {
                chars[i] = 'b';
                chars[i + 1] = 'a';
                chars[i + 2] = 'a';

                if (i + 4 < len && chars[i + 4] == 'b')
                {
                    i += 4 + 1;
                }
                else if (i + 3 < len && chars[i + 3] == 'b')
                {
                    i += 3 + 1;
                }
                else if (chars[i + 2] == 'b')
                {
                    i += 2 + 1;
                }
            }

            if (chars[i + 1] == 'b')
            {
                i += 1 + 1;
            }
            else
            {
                i++;
            }
            cur = "";
        }
    }

    return new string(chars);
}

This builds the biggest valid string it can under the challenge rules by always choosing the best next character it is allowed to use.

C# Max Counters
static int[] MaxCounters(int n, int[] a)
{
    var counters = new int[n];
    var maxCounter = 0;
    var lastUpdate = 0;
    var condition = n + 1;

    foreach (var v in a)
    {
        if (v <= n)
        {
            var index = v - 1;
            if (counters[index] < lastUpdate)
            {
                counters[index] = lastUpdate;
            }
            counters[index]++;
            maxCounter = Math.Max(counters[index], maxCounter);
        }
        if (v == condition)
        {
            lastUpdate = maxCounter;
        }
    }

    // apply all max operations to avoid O(M*N) complexity
    for (int k = 0; k < counters.Length; k++)
    {
        if (counters[k] < lastUpdate)
        {
            counters[k] = lastUpdate;
        }
    }

    return counters;
}

This delays the expensive “set all counters to max” work until it is really needed, which keeps the solution fast.

C# Max Double Slice Sum
static long MaxDoubleSliceSum(int[] a)
{
    var size = a.Length;
    if (size < 3)
    {
        return 0;
    }

    var p1 = new long[size];
    var p2 = new long[size];
    p1[1] = 0;
    p2[size - 2] = 0;

    for (int i = 2; i < size - 1; i++)
    {
        p1[i] = Math.Max(0, p1[i - 1] + a[i - 1]);
        p2[size - i - 1] = Math.Max(0, p2[size - i] + a[size - i]);
    }

    var sum = p1[1] + p2[1];
    for (int i = 1; i < size - 1; i++)
    {
        sum = Math.Max(sum, p1[i] + p2[i]);
    }

    return sum;
}

This keeps the best sum ending on the left and starting on the right, then combines them around each middle position.

C# Max Product Of Three
static long MaxProductOfThree(int[] a)
{
    var sorted = (int[])a.Clone();
    Array.Sort(sorted);
    var c = sorted.Length;

    return Math.Max(
        (long)sorted[c - 1] * sorted[c - 2] * sorted[c - 3],
        (long)sorted[0] * sorted[1] * sorted[c - 1]
    );
}

This checks the useful extremes, because the best product can come from either the three largest numbers or two negatives plus one large positive.

C# Max Profit
static int MaxProfit(int[] a)
{
    var price = a[0];
    var profit = 0;

    foreach (var v in a)
    {
        price = Math.Min(price, v);
        profit = Math.Max(profit, v - price);
    }

    return profit;
}

This tracks the lowest buy price seen so far and updates the best profit as it scans the prices once.

C# Max Slice Sum
static long MaxSliceSum(int[] a)
{
    long tmp = long.MinValue;
    long max = long.MinValue;

    foreach (var v in a)
    {
        tmp = Math.Max(tmp + v, v);
        max = Math.Max(max, tmp);
    }

    return max;
}

This is a Kadane-style scan: keep the best running sum and the best overall sum while moving once through the array.

C# Min Avg Two Slice
static int MinAvgTwoSlice(int[] a)
{
    var idx = 0;
    double min = (a[0] + a[1]) / 2.0;

    for (int i = 0; i < a.Length - 1; i++)
    {
        double cur = (a[i] + a[i + 1]) / 2.0;
        if (i + 2 < a.Length)
        {
            double three = (a[i] + a[i + 1] + a[i + 2]) / 3.0;
            cur = cur < three ? cur : three;
        }
        if (cur < min)
        {
            min = cur;
            idx = i;
        }
    }

    return idx;
}

This leans on the key trick for this problem: the minimum average slice is always length 2 or 3.

C# Min Perimeter Rectangle
static long MinPerimeterRectangle(long n)
{
    long i = 1;
    long min = long.MaxValue;

    while (i * i < n)
    {
        if (n % i == 0)
        {
            min = Math.Min(min, 2 * (i + n / i));
        }
        i++;
    }

    return min;
}

This searches factor pairs up to the square root and picks the pair with the smallest perimeter.

C# Missing Integer
static int MissingInteger(int[] a)
{
    var min = 1;
    var distinct = new HashSet<int>(a).ToList();
    distinct.Sort();

    foreach (var v in distinct)
    {
        if (v > 0)
        {
            if (min != v)
            {
                break;
            }
            min++;
        }
    }

    return min;
}

This records the positive numbers that exist, then returns the smallest positive value that is still missing.

C# Nesting
static int Nesting(string s)
{
    if (string.IsNullOrEmpty(s))
    {
        return 1;
    }

    var stack = new Stack<char>();
    foreach (var v in s)
    {
        if (v == ')')
        {
            if (stack.Count == 0 || stack.Pop() != '(')
            {
                return 0;
            }
        }
        else
        {
            stack.Push(v);
        }
    }

    return stack.Count == 0 ? 1 : 0;
}

This treats the string like a balance counter: open parentheses add one, closing ones remove one.