// O(KN) running median computation (can be improved to O(log K * N)
// with a min-heap and max-heap.
inline void runmed(vector<double> &x, vector<double> &m) {
double n = x.size();
long k = (long)min( ( n - 1 ) / 2, ceil(0.1*n) ); // Automatically estimate K for runs.
m.resize(x.size());
long k2 = k / 2;
vector<double> x2(k);
// Advance along vector.
for(long i = 0; i < (long)x.size(); i++) {
long start = max(0L, i - k2);
long end = min((long)x.size(), i + k2 + 1);
x2.resize(end - start);
// Copy run into another vector (becaused _median modifies
// original order).
int j = 0;
while(start < end) { x2[j] = x[start]; j++; start++; }
// Compute median using that vector.
m[i] = _median(x2.begin(), x2.end());
}
}
boundary_t<Itr> _partition(Itr begin, Itr end)
{
Itr median = _median(begin, --end);
std::swap(*begin, *median);
Itr pivot = begin++, next = begin;
while (next != end)
{
if (*next < *pivot) std::swap(*(begin++), *(next++));
else if (*next > *pivot) std::swap(*next, *(end--));
else ++next;
}
std::swap(*pivot, *(--begin));
return {begin, end};
}
// This version of median will change the order of elements.
inline double median_unsafe(vector<double> &data) {
if(data.size() == 0) { std::cerr << "no data for median()" << std::endl; exit(1); }
return _median(data.begin(), data.end());
}