<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>

class Solution {
public:
    void merge(vector<int>& nums, vector<int>& smaller, vector<int>& bigger) {
        nums.clear();
        for (auto& x : smaller)
            nums.push_back(x);
        for (auto& x : bigger)
            nums.push_back(x);
        smaller.clear();
        bigger.clear();
    }

    void radixSort(vector<int>& nums, bool positive = true) {
        int bits = sizeof(int) * 8, size = nums.size();
        vector<int> zeros, ones;
        unsigned int d;
        for (int i = 0; i < bits - 1; i++) {
            d = 1 << i;

            for (auto& num : nums) {
                if ((num & d) == 0) {
                    zeros.push_back(num);
                } else {
                    ones.push_back(num);
                }
            }
            merge(nums, zeros, ones);
        }
    }

    vector<int> sortArray(vector<int>& nums) {

        vector<int> zeros, ones, positive, negative;

        for (auto& num : nums) {
            if (num >= 0)
                positive.push_back(num);
            else
                negative.push_back(num);
        }

        radixSort(positive);
        radixSort(negative, false);
        merge(nums, negative, positive);

        return nums;
    }
};
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