You are given a 0-indexed sorted array of integers nums.
You can perform the following operation any number of times:
\n\ni and j, where i < j, such that nums[i] < nums[j].i and j from nums. The remaining elements retain their original order, and the array is re-indexed.Return an integer that denotes the minimum length of nums after performing the operation any number of times (including zero).
Note that nums is sorted in non-decreasing order.
\n
Example 1:
\n\n\nInput: nums = [1,3,4,9]\nOutput: 0\nExplanation: Initially, nums = [1, 3, 4, 9].\nIn the first operation, we can choose index 0 and 1 because nums[0] < nums[1] <=> 1 < 3.\nRemove indices 0 and 1, and nums becomes [4, 9].\nFor the next operation, we can choose index 0 and 1 because nums[0] < nums[1] <=> 4 < 9.\nRemove indices 0 and 1, and nums becomes an empty array [].\nHence, the minimum length achievable is 0.\n\n
Example 2:
\n\n\nInput: nums = [2,3,6,9]\nOutput: 0\nExplanation: Initially, nums = [2, 3, 6, 9]. \nIn the first operation, we can choose index 0 and 2 because nums[0] < nums[2] <=> 2 < 6. \nRemove indices 0 and 2, and nums becomes [3, 9]. \nFor the next operation, we can choose index 0 and 1 because nums[0] < nums[1] <=> 3 < 9. \nRemove indices 0 and 1, and nums becomes an empty array []. \nHence, the minimum length achievable is 0.\n\n\n
Example 3:
\n\n\nInput: nums = [1,1,2]\nOutput: 1\nExplanation: Initially, nums = [1, 1, 2].\nIn an operation, we can choose index 0 and 2 because nums[0] < nums[2] <=> 1 < 2. \nRemove indices 0 and 2, and nums becomes [1]. \nIt is no longer possible to perform an operation on the array. \nHence, the minimum achievable length is 1. \n\n\n
\n
Constraints:
\n\n1 <= nums.length <= 1051 <= nums[i] <= 109nums is sorted in non-decreasing order.k operations, it is optimal to use the smallest k values and the largest k values in nums.",
"What is the best way to make pairs from the smallest k values and the largest k values so it is possible to remove all the pairs?",
"If we consider the smallest k values and the largest k values as two separate sorted 0-indexed arrays, a and b, It is optimal to pair a[i] and b[i]. So, a k is valid if a[i] < b[i] for all i in the range [0, k - 1].",
"The greatest possible valid k can be found using binary search.",
"The answer is nums.length - 2 * k."
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