You are given a 0-indexed integer array nums containing positive integers.
Your task is to minimize the length of nums by performing the following operations any number of times (including zero):
i and j from nums, such that nums[i] > 0 and nums[j] > 0.nums[i] % nums[j] at the end of nums.i and j from nums.Return an integer denoting the minimum length of nums after performing the operation any number of times.
\n
Example 1:
\n\n\nInput: nums = [1,4,3,1]\nOutput: 1\nExplanation: One way to minimize the length of the array is as follows:\nOperation 1: Select indices 2 and 1, insert nums[2] % nums[1] at the end and it becomes [1,4,3,1,3], then delete elements at indices 2 and 1.\nnums becomes [1,1,3].\nOperation 2: Select indices 1 and 2, insert nums[1] % nums[2] at the end and it becomes [1,1,3,1], then delete elements at indices 1 and 2.\nnums becomes [1,1].\nOperation 3: Select indices 1 and 0, insert nums[1] % nums[0] at the end and it becomes [1,1,0], then delete elements at indices 1 and 0.\nnums becomes [0].\nThe length of nums cannot be reduced further. Hence, the answer is 1.\nIt can be shown that 1 is the minimum achievable length.\n\n
Example 2:
\n\n\nInput: nums = [5,5,5,10,5]\nOutput: 2\nExplanation: One way to minimize the length of the array is as follows:\nOperation 1: Select indices 0 and 3, insert nums[0] % nums[3] at the end and it becomes [5,5,5,10,5,5], then delete elements at indices 0 and 3.\nnums becomes [5,5,5,5]. \nOperation 2: Select indices 2 and 3, insert nums[2] % nums[3] at the end and it becomes [5,5,5,5,0], then delete elements at indices 2 and 3. \nnums becomes [5,5,0]. \nOperation 3: Select indices 0 and 1, insert nums[0] % nums[1] at the end and it becomes [5,5,0,0], then delete elements at indices 0 and 1.\nnums becomes [0,0].\nThe length of nums cannot be reduced further. Hence, the answer is 2.\nIt can be shown that 2 is the minimum achievable length.\n\n
Example 3:
\n\n\nInput: nums = [2,3,4]\nOutput: 1\nExplanation: One way to minimize the length of the array is as follows: \nOperation 1: Select indices 1 and 2, insert nums[1] % nums[2] at the end and it becomes [2,3,4,3], then delete elements at indices 1 and 2.\nnums becomes [2,3].\nOperation 2: Select indices 1 and 0, insert nums[1] % nums[0] at the end and it becomes [2,3,1], then delete elements at indices 1 and 0.\nnums becomes [1].\nThe length of nums cannot be reduced further. Hence, the answer is 1.\nIt can be shown that 1 is the minimum achievable length.\n\n
\n
Constraints:
\n\n1 <= nums.length <= 1051 <= nums[i] <= 109nums be x; we can consider the following cases:",
"If x occurs once: The minimum length of nums achievable in this case is 1, since every other value, y, can be paired with x, resulting in deleting x and y, and inserting x % y == x, since x < y. So, only x remains after the operations.",
"If there is a value y in nums such that y % x is not equal to 0: The minimum achievable length in this case is 1 as well, because inserting y % x creates a new minimum, since y % x < x, returning to the first case.",
"If neither of the previous cases holds, and x occurs cnt times: The minimum length of nums achievable in this case is ceil(cnt / 2)."
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