longest nondecreasing subsequence in O(nlgn)

Question

I have the following algorithm which works well

I tried explaining it here for myself http://nemo.la/?p=943 and it is explained here http://www.geeksforgeeks.org/lon

Answer 1

Your code nearly works except a problem in your binary_search() function, this function should return the index of the first element that's greater than the target element(x) since you want the longest non-decreasing sequence. Modify it to this, it'll be OK.

If you use c++, std::lower_bound() and std::upper_bound() will help you get rid of this confusing problem. By the way, the if statement"if (height[s[k]] >= height[i])" is superfluous.

int binary_search(int first, int last, int x) {

    while(last > first)
    {
        int mid = first + (last - first) / 2;
        if(height[s[mid]] > x)
            last = mid;
        else
            first = mid + 1;
    }

    return first; /* or last */
}