CTRL+A, CTRL+C, CTRL+V

(http://leetcode.com/2011/01/ctrla-ctrlc-ctrlv.html)

Imagine you have a special keyboard with the following keys:

A

Ctrl + A

Ctrl + C

Ctrl + V

where CTRL+A, CTRL+C, CTRL+V each acts as one function key for "Select All", "Copy", and "Paste" operations respectively.

If you can only press the keyboard for N times (with the above four keys), please write a program to produce maximum numbers of A. If possible, please also print out the sequence of keys.

That is to say, the input parameter is N (No. of keys that you can press), the output is M (No. of As that you can produce).

The Code:

int findMaxK(int n)
{
    int power = 2;
    double max = 0.0;
    int maxK = 0;
    while (n > 0)
    {
        n -= 2;
        double t = (double)n/power;
        double r = pow(t, (double)power);
        if (r > max)
        {
            maxK = power;
            max = r;
        }
        power++;
    }
    return maxK;
}

unsigned int f(int n)
{
    if (n <= 7)
        return n;
    int k = findMaxK(n);

    int sum = n - 2*(k-1);
    unsigned int mul = 1;
    while (k > 0)
    {
        int avg = sum/k;
        mul *= avg;
        k--;
        sum -= avg;
    }
    assert(sum == 0);

    return mul;
}