You are given an array nums of n positive integers and an integer k.
Initially, you start with a score of 1. You have to maximize your score by applying the following operation at most k times:
nums[l, ..., r] that you haven't chosen previously.x of nums[l, ..., r] with the highest prime score. If multiple such elements exist, choose the one with the smallest index.x.Here, nums[l, ..., r] denotes the subarray of nums starting at index l and ending at the index r, both ends being inclusive.
The prime score of an integer x is equal to the number of distinct prime factors of x. For example, the prime score of 300 is 3 since 300 = 2 * 2 * 3 * 5 * 5.
Return the maximum possible score after applying at most k operations.
Since the answer may be large, return it modulo 109 + 7.
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Example 1:
\n\n\nInput: nums = [8,3,9,3,8], k = 2\nOutput: 81\nExplanation: To get a score of 81, we can apply the following operations:\n- Choose subarray nums[2, ..., 2]. nums[2] is the only element in this subarray. Hence, we multiply the score by nums[2]. The score becomes 1 * 9 = 9.\n- Choose subarray nums[2, ..., 3]. Both nums[2] and nums[3] have a prime score of 1, but nums[2] has the smaller index. Hence, we multiply the score by nums[2]. The score becomes 9 * 9 = 81.\nIt can be proven that 81 is the highest score one can obtain.\n\n
Example 2:
\n\n\nInput: nums = [19,12,14,6,10,18], k = 3\nOutput: 4788\nExplanation: To get a score of 4788, we can apply the following operations: \n- Choose subarray nums[0, ..., 0]. nums[0] is the only element in this subarray. Hence, we multiply the score by nums[0]. The score becomes 1 * 19 = 19.\n- Choose subarray nums[5, ..., 5]. nums[5] is the only element in this subarray. Hence, we multiply the score by nums[5]. The score becomes 19 * 18 = 342.\n- Choose subarray nums[2, ..., 3]. Both nums[2] and nums[3] have a prime score of 2, but nums[2] has the smaller index. Hence, we multipy the score by nums[2]. The score becomes 342 * 14 = 4788.\nIt can be proven that 4788 is the highest score one can obtain.\n\n\n
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Constraints:
\n\n1 <= nums.length == n <= 1051 <= nums[i] <= 1051 <= k <= min(n * (n + 1) / 2, 109)nums[i]'s prime score s[i] by factoring in O(sqrt(nums[i])) time.nums[i], find the nearest index left[i] on the left (if any) such that s[left[i]] >= s[i]. if none is found, set left[i] to -1. Similarly, find the nearest index right[i] on the right (if any) such that s[right[i]] > s[i]. If none is found, set right[i] to n.right[i] and left[i].i, if left[i] + 1 <= l <= i <= r <= right[i] - 1, then s[i] is the maximum value in the range [l, r]. For this particular i, there are ranges[i] = (i - left[i]) * (right[i] - i) ranges where index i will be chosen.nums by non-increasing prime score, each element will be chosen min(ranges[i], remainingK) times, where reaminingK denotes the number of remaining operations. Therefore, the score will be multiplied by s[i]^min(ranges[i],remainingK).A^B mod C.Compiled with clang 11 using the latest C++ 20 standard.
Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
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