<p>Given an array of integers <code>nums</code>, sort the array in ascending order and return it.</p>

<p>You must solve the problem <strong>without using any built-in</strong> functions in <code>O(nlog(n))</code> time complexity and with the smallest space complexity possible.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,2,3,1]
<strong>Output:</strong> [1,2,3,5]
<strong>Explanation:</strong> After sorting the array, the positions of some numbers are not changed (for example, 2 and 3), while the positions of other numbers are changed (for example, 1 and 5).
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [5,1,1,2,0,0]
<strong>Output:</strong> [0,0,1,1,2,5]
<strong>Explanation:</strong> Note that the values of nums are not necessairly unique.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>-5 * 10<sup>4</sup> &lt;= nums[i] &lt;= 5 * 10<sup>4</sup></code></li>
</ul>

const static auto initialize = [] {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    return nullptr;
}();

class Solution {
    pair<int, int> min_max(auto begin, auto end) const {
        if (end - begin < 1)
            return {INT_MAX, INT_MIN};
        pair<int, int> output(*begin, *begin);
        for (auto it = begin + 1; it != end; ++it) {
            if (*it > output.second)
                output.second = *it;
            else if (*it < output.first)
                output.first = *it;
        }
        return output;
    }

    void radix_sort2(auto begin, auto end) const {
        if (end - begin < 2)
            return;
        vector<vector<int>> data(0x00010000);
        for (auto it = begin; it != end; ++it)
        {
            data[*it & 0x0000ffff].push_back(*it);
        }
            

        int j = 0;
        for (auto& it : data) {

            // radix_sort(it.begin(), it.end(), bitCheck >> 16, shift -16 );
            for (auto i : it)
                *(begin + j++) = i;
        }
    }

    void radix_sort(auto begin, auto end) const {
        int shift = 16;
        u_int bitCheck = 0xffff0000;
        if (end - begin < 2)
            return;
        vector<vector<int>> data(0x00010000);
        for (auto it = begin; it != end; ++it) {
            u_int place = (*it & bitCheck) >> shift;
            if (place < 0x00008000)
                place += 0x00008000;
            else
                place -= 0x00008000;
            data[place].push_back(*it);
        }

        int j = 0;
        for (auto& it : data) {

            radix_sort2(it.begin(), it.end());
            for (auto i : it)
                *(begin + j++) = i;
        }
    }

    void counting_sort(auto begin, auto end) const {
        if (end - begin < 2)
            return;

        pair<int, int> edge = min_max(begin, end);

        const int BUCKET = edge.second - edge.first + 1;

        vector<int> data(BUCKET, 0);
        for (auto it = begin; it != end;)
            ++data[*it++ - edge.first];

        int k = 0;
        for (int i = 0; i < BUCKET; ++i) {
            for (int j = 0; j < data[i]; ++j)
                *(begin + k++) = i + edge.first;
        }
    }

public:
    vector<int>& sortArray(vector<int>& nums) const {
        radix_sort(nums.begin(), nums.end());
        return nums;
    }
};
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