3.子数组的最大和

/*
see 
http://www.cppblog.com/jake1036/archive/2013/04/10/144726.html
http://en.wikipedia.org/wiki/Maximum_subarray_problem
f(i): max subsequence value ending at i
f(i) = max(f(i-1)+a[i],a[i])
max f(i) (i=0,...n-1)

N=8
-4 , 3 ,12 , -7 , 20 , -1 , -14 , 4

3 ,12 , -7 , 20 ---> 28
*/

int dp_forward()
{// time o(n)
    // base case
    f[0] = a[0];
    int maxi = f[0];
    for (int i=1;i<N;i++)
    {
        f[i]= max(f[i-1]+a[i],a[i]);
        if (maxi<f[i])
        {
            maxi = f[i];
        }
    }
    return maxi;
}

int dp_forward2()
{
    // base case
    int f = a[0];
    int maxi = a[0];
    for (int i=1;i<N;i++)
    {
        //f= max(f+a[i],a[i]);
        if (f<0)
        {
            f = a[i];
        }
        else
        {
            f += a[i];
        }

        if (maxi<f)
        {
            maxi = f;
        }
    }
    return maxi;
}