Longest Increasing Subsequence problem.

Problem Statement: Given an array of integers, determine the longest increasing subsequence (not necesarily contiguous).

Solution #1: Below is the equation and the code for the problem,

Equations:
LIS[i] = MAX( LIS[j] ) + 1; where 0 <= j < i and A[i] > A[j]

#define MAX(a, b) ((a)>(b))?(a):(b)

int LIS[1000];

int lis(int* A, int len)
{
    int i, j;
    int max;

    LIS[0] = 1;

    for(i=1; i < len; i++)
    {
        max = 0;
        for(j=0; j < i; j++)
        {
            if(A[i] > A[j])
                max = MAX(max, LIS[j]);
        }

        printf("max: %d\n", max);

        LIS[i] = max + 1;
    }

    return LIS[len-1];
}

int main()
{
    int A[] = {4, 3, 9, 4 ,1 ,6};

    printf("LIS: %d\n", lis(A, 6));
    return 0;
}