<p>You are given an integer array <code>nums</code>. In one move, you can pick an index <code>i</code> where <code>0 &lt;= i &lt; nums.length</code> and increment <code>nums[i]</code> by <code>1</code>.</p>

<p>Return <em>the minimum number of moves to make every value in </em><code>nums</code><em> <strong>unique</strong></em>.</p>

<p>The test cases are generated so that the answer fits in a 32-bit integer.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,2]
<strong>Output:</strong> 1
<strong>Explanation:</strong> After 1 move, the array could be [1, 2, 3].
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,2,1,2,1,7]
<strong>Output:</strong> 6
<strong>Explanation:</strong> After 6 moves, the array could be [3, 4, 1, 2, 5, 7].
It can be shown that it is impossible for the array to have all unique values with 5 or less moves.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
</ul>


class Solution {
public:
	int minIncrementForUnique(vector<int>& nums) {
		std::vector<std::pair<int, int>> counts;
		std::ranges::sort(nums, std::greater());

		int cnt{ 0 };
		for (int i = 0; i < nums.size() - 1; i++) {
			cnt++;
			if (nums[i] != nums[i + 1]) {
				counts.push_back({ nums[i],cnt });
				cnt = 0;
			}
		}
		if (cnt > 0) {
			counts.push_back({ nums[nums.size() - 1],cnt + 1 });
		}
		else {
			counts.push_back({ nums[nums.size() - 1],1 });
		}

		int res{ 0 };
		while (!counts.empty()) {
			auto [val, cnt] = counts.back(); counts.pop_back();
			int steps = cnt - 1;
			if (steps > 0) {
				res += steps;
				if (!counts.empty() && val + 1 == counts.back().first) {
					counts.back().second += steps;
				}
				else {
					counts.push_back({ val + 1, steps });
				}
			}
		}

		return res;
	}
};
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