<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 {
    // Bucket sort function for each place value digit.
    void bucketSort(vector<int>& arr, int placeValue) {
        vector<vector<int>> buckets(20, vector<int>());
        // Store the respective number based on its digit.
        for (auto n : arr) {
            int digit = n / placeValue;
            digit = digit % 10;
            buckets[digit + 10].push_back(n);
        }

        // Overwrite 'arr' in sorted order of current place digits.
        arr.clear();
        for(auto v: buckets) arr.insert(arr.end(), v.begin(), v.end());
    }
    
    // Radix sort function.
    void radixSort(vector<int>& arr) {
        // Find the absolute maximum element to find max number of digits.
        int maxElement = arr[0];
        for (int& val : arr) {
            maxElement = max(abs(val), maxElement);
        }
        int maxDigits = 0;
        while (maxElement > 0) {
            maxDigits += 1;
            maxElement /= 10;
        }

        // Radix sort, least significant digit place to most significant.
        int placeValue = 1;
        for (int digit = 0; digit < maxDigits; ++digit) {
            bucketSort(arr, placeValue);
            placeValue *= 10;
        }
    }

public:
    vector<int> sortArray(vector<int>& nums) {
        radixSort(nums);
        return nums;
    }
};
108766