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Setting n random elements of a multi-dimensional array to a value

In a two-dimensional array of integers (eg int[3,3] ), consisting of all 0 values, I'd like to set n random elements of the array to the value 1 as efficiently as possible. The problem that I am running into is that the first elements in the array are more likely to have a value of 1 than other elements later in the array.

Here is my code. In the example below I am attempting to set exactly 3 randomly-selected elements of the 3x3 array to 1.

int sum = 0;

private void MakeMatrix()
{
    for (int i = 0; i < 3; i++)
    {
        for (int k = 0; k < 3; k++)
        {
            int n = _r.Next(2);

            if (n != 1 && sum < 3)
            {
                matrix[i, k] = 1;
                sum++;
            }
            else
            {
                matrix[i, k] = 0;
            }
        }
    }
}

You might try something like the following. First initialize your matrix to all 0 values, then run the code below. It will set three random values in the matrix to 1.

int count = 0;
while (count < 3)
{
    int x = r.Next(0, 3);
    int y = r.Next(0, 3);

    if (matrix[x, y] != 1)
    {
        matrix[x, y] = 1;
        count++;
    }
}
    static int sum = 0;
    private static readonly int[,] matrix = new int[3,3];
    private static readonly Random _r = new Random();
    private static void MakeMatrix()
    {
        //by default all the element in the matrix will be zero, so setting to zero is not a issue
        // now we need to fill 3 random places with numbers between 1-3 i guess ?

        //an array of int[3] to remember which places are already used for random num
        int[] used = new int[3];
        int pos;
        for (int i = 0; i < 3; i++)
        {
            pos = _r.Next(0, 8);
            var x = Array.IndexOf(used, pos);
            while (x != -1)
            {
                pos = _r.Next(0, 8);
            }
            used[i] = pos;
            matrix[pos/3, pos%3] = _r.Next(1, 3);

        }

    }

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