/**
 * Sort algorithm for nearly-sorted data.
 *
 * Runtime:
 * - Worst case O(n^2) [smallrange / descending]
 * - random case O(nlogn)
 * Space: same as runtime
 */
#include <vector> // can do with malloc only if needed but this spares more ram. Also can do with a stack data type..
#include <cstdint> // uint32_t

// TODO: outliersort(...) function with parametrizable "what is an outlier?" and "init" functions!
//       why? Because when I renamed outnsi to outlier I realized the only rule is to keep the begin
//       of the array sorted but otherwise we better put into the outlier data that would make us
//       less likely to be able to fill-in more data points (think of real outliers like [1 9000 2 3 4 ...8999]

// TODO: simple to make this work with custom comparator and type..
void nsort(uint32_t *arr, int n) {
	// Temp space - worst case O(n) size
	std::vector<uint32_t> outlier;

	// Split [i: read, j: write]
	uint32_t max = (n > 0) ? arr[0] : 0;
	uint32_t i = 1;
	uint32_t j = 1;

	while(i < n) {
		if(arr[i] < max) {
			outlier.push_back(arr[i++]);
		} else if(i > j) {
			arr[j++] = arr[i++];
		}
	}

	if(outlier.size() > 1) {
		// Recursion
		nsort(&outlier[0], outlier.size());

		// Merge-from-right [j: sorted right-index, i: write index]
		uint32_t k = outlier.size() - 1;
		--j;
		--i;
		while(i >= 0) {
			if(outlier[k] > arr[j]) {
				arr[i--] = outlier[k--];
			} else {
				arr[i--] = arr[j--];
			}
		}
	}
}