You are given a 0-indexed array of positive integers nums and a positive integer limit.
In one operation, you can choose any two indices i and j and swap nums[i] and nums[j] if |nums[i] - nums[j]| <= limit.
Return the lexicographically smallest array that can be obtained by performing the operation any number of times.
\n\nAn array a is lexicographically smaller than an array b if in the first position where a and b differ, array a has an element that is less than the corresponding element in b. For example, the array [2,10,3] is lexicographically smaller than the array [10,2,3] because they differ at index 0 and 2 < 10.
\n
Example 1:
\n\n\nInput: nums = [1,5,3,9,8], limit = 2\nOutput: [1,3,5,8,9]\nExplanation: Apply the operation 2 times:\n- Swap nums[1] with nums[2]. The array becomes [1,3,5,9,8]\n- Swap nums[3] with nums[4]. The array becomes [1,3,5,8,9]\nWe cannot obtain a lexicographically smaller array by applying any more operations.\nNote that it may be possible to get the same result by doing different operations.\n\n\n
Example 2:
\n\n\nInput: nums = [1,7,6,18,2,1], limit = 3\nOutput: [1,6,7,18,1,2]\nExplanation: Apply the operation 3 times:\n- Swap nums[1] with nums[2]. The array becomes [1,6,7,18,2,1]\n- Swap nums[0] with nums[4]. The array becomes [2,6,7,18,1,1]\n- Swap nums[0] with nums[5]. The array becomes [1,6,7,18,1,2]\nWe cannot obtain a lexicographically smaller array by applying any more operations.\n\n\n
Example 3:
\n\n\nInput: nums = [1,7,28,19,10], limit = 3\nOutput: [1,7,28,19,10]\nExplanation: [1,7,28,19,10] is the lexicographically smallest array we can obtain because we cannot apply the operation on any two indices.\n\n\n
\n
Constraints:
\n\n1 <= nums.length <= 1051 <= nums[i] <= 1091 <= limit <= 109给你一个下标从 0 开始的 正整数 数组 nums 和一个 正整数 limit 。
在一次操作中，你可以选择任意两个下标 i 和 j，如果 满足 |nums[i] - nums[j]| <= limit ，则交换 nums[i] 和 nums[j] 。
返回执行任意次操作后能得到的 字典序最小的数组 。
\n\n如果在数组 a 和数组 b 第一个不同的位置上，数组 a 中的对应元素比数组 b 中的对应元素的字典序更小，则认为数组 a 就比数组 b 字典序更小。例如，数组 [2,10,3] 比数组 [10,2,3] 字典序更小，下标 0 处是两个数组第一个不同的位置，且 2 < 10 。
\n\n
示例 1：
\n\n\n输入：nums = [1,5,3,9,8], limit = 2\n输出：[1,3,5,8,9]\n解释：执行 2 次操作：\n- 交换 nums[1] 和 nums[2] 。数组变为 [1,3,5,9,8] 。\n- 交换 nums[3] 和 nums[4] 。数组变为 [1,3,5,8,9] 。\n即便执行更多次操作，也无法得到字典序更小的数组。\n注意，执行不同的操作也可能会得到相同的结果。\n\n\n
示例 2：
\n\n\n输入：nums = [1,7,6,18,2,1], limit = 3\n输出：[1,6,7,18,1,2]\n解释：执行 3 次操作：\n- 交换 nums[1] 和 nums[2] 。数组变为 [1,6,7,18,2,1] 。\n- 交换 nums[0] 和 nums[4] 。数组变为 [2,6,7,18,1,1] 。\n- 交换 nums[0] 和 nums[5] 。数组变为 [1,6,7,18,1,2] 。\n即便执行更多次操作，也无法得到字典序更小的数组。\n\n\n
示例 3：
\n\n\n输入：nums = [1,7,28,19,10], limit = 3\n输出：[1,7,28,19,10]\n解释：[1,7,28,19,10] 是字典序最小的数组，因为不管怎么选择下标都无法执行操作。\n\n\n
\n\n
提示：
\n\n1 <= nums.length <= 1051 <= nums[i] <= 1091 <= limit <= 109nums are nodes and the pairs satisfying the condition have an edge between them.",
"Instead of constructing all edges, we only care about the connected components.",
"Can we use DSU?",
"Sort nums. Now we just need to consider if the consecutive elements have an edge to check if they belong to the same connected component. Hence, all connected components become a list of position-consecutive elements after sorting.",
"For each index of nums from 0 to nums.length - 1 we can change it to the current minimum value we have in its connected component and remove that value from the connected component."
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