Find longest increasing sequence (LIS)

#include <iostream>
#include <stack>

typedef unsigned int uint;

void FindLIS(const uint arr[], uint length)
{
	uint* lis = new uint[length];
	uint* pre = new uint[length];

	lis[0] = 0;
	int max_length = 0;

	for (int i = 1; i < length; ++i)
	{
		// find largest j that lis[arr[k]] < arr[i]
		int k = 0;
		for (int j = 0; j <= max_length; j++)
		{
			if (arr[lis[j]] < arr[i])
				k = j;
		}

		pre[i] = lis[k];

		if (k == max_length || arr[i] < arr[lis[k + 1]])
		{
			lis[k + 1] = i;
			max_length = std::max(max_length, k + 1);
		}
	}

	std::stack<int> stk;
	int elem_idx = lis[max_length];
	for (int i = 1; i <= max_length; ++i)
	{
		int elem = arr[elem_idx];
		stk.push(elem);
		elem_idx = pre[elem_idx];		
	}

	while (!stk.empty())
	{
		std::cout << stk.top() << " ";
		stk.pop();
	}
};

int main()
{
	const uint arr[] = {100000, 0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15};
	uint arr_length = sizeof(arr) / sizeof(arr[0]);

	FindLIS(arr, arr_length);

	return 0;
}