How do I calculate the time complexity of the function?

Question

int coin_row(int[] array, int index, int length)
{
    if (index >= length) //beyond last coin
    {
        return 0;
    }

    int value = array[index];
    if (index >= length - 1) //last coin
    {
        return value;
    }
    else if (index >= length - 2) //second last coin
    {
        return max(value, coin+row(array, index+1);
    }

    return max(value+coin_row(array, index+2,length), coin_row(array, index+1,length));
}

What should I do when calculating the time complexity of this recursive function?

Answer 1

It's O(n).

To see this: write a recurrence relation. Here is it T(n) = T(n+1) + O(1) and T(l) = 1 . The O(1) in the first equation comes from the max() function.

Since each step requires O(1) operations, and there are n recusive calls where n is the length. The time complexity is O(n*1) = O(n).