<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:
    def minIncrementForUnique(self, nums: List[int]) -> int:
        # We want to maky every element in the array unique, a great way to test uniqueness is either
        # Hashset or sorting array. In this case, we need the position i of the array to increment, so
        # we can't use a hashset data structure. So we can sort the array to determine if a particular element
        # i is unique by seeing if it is equal to i - 1.
        # If nums[i] > nums[i - 1], then each element is unique, no moves are needed.
        # If nums[i] == nums[i - 1] then increment nums[i] by 1 to make the element unique.
        # If nums[i] < nums[i - 1], then nums[i - 1] must have been incremented previously, since the array
        # was in sorted ascending order. 
        # E.g. [1, 1, 2, 2, 3, 7] --> [1, 2, 2, 2, 3, 7] --> [1, 2, 3, 2, 3, 7] -->
        # Now we see 2 (nums[3]) is < 3 (nums[2]) 
        # So we should instead of incrementing by 1, we do min_moves = nums[i - 1] - nums[i] + 1
        # and then change nums[i] = nums[i - 1] + 1
        # So we can do this for == as well so we just need to check if nums[i] <= nums[i - 1]

        nums.sort()
        min_moves = 0
        print(nums)
        for i in range(1, len(nums)):
            if nums[i] <= nums[i - 1]:
                min_moves += nums[i - 1] - nums[i] + 1
                nums[i] = nums[i - 1] + 1 
        
        return min_moves
30900