| { |
| "id": 3001, |
| "name": "apply-operations-to-maximize-score", |
| "difficulty": "Hard", |
| "link": "https://leetcode.com/problems/apply-operations-to-maximize-score/", |
| "date": "2023-08-06", |
| "task_description": "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: Choose any **non-empty** subarray `nums[l, ..., r]` that you haven't chosen previously. Choose an element `x` of `nums[l, ..., r]` with the highest **prime score**. If multiple such elements exist, choose the one with the smallest index. Multiply your score by `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`. **Example 1:** ``` **Input:** nums = [8,3,9,3,8], k = 2 **Output:** 81 **Explanation:** To get a score of 81, we can apply the following operations: - 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. - 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. It can be proven that 81 is the highest score one can obtain. ``` **Example 2:** ``` **Input:** nums = [19,12,14,6,10,18], k = 3 **Output:** 4788 **Explanation:** To get a score of 4788, we can apply the following operations: - 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. - 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. - 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. It can be proven that 4788 is the highest score one can obtain. ``` **Constraints:** `1 <= nums.length == n <= 105` `1 <= nums[i] <= 105` `1 <= k <= min(n * (n + 1) / 2, 109)`", |
| "test_case": [ |
| { |
| "label": "Example 1", |
| "input": "nums = [8,3,9,3,8], k = 2", |
| "output": "81 " |
| }, |
| { |
| "label": "Example 2", |
| "input": "nums = [19,12,14,6,10,18], k = 3", |
| "output": "4788 " |
| } |
| ], |
| "constraints": [ |
| "Choose any non-empty subarray nums[l, ..., r] that you haven't chosen previously.", |
| "Choose an element x of nums[l, ..., r] with the highest prime score. If multiple such elements exist, choose the one with the smallest index.", |
| "Multiply your score by x.", |
| "1 <= nums.length == n <= 105", |
| "1 <= nums[i] <= 105", |
| "1 <= k <= min(n * (n + 1) / 2, 109)" |
| ], |
| "python_template": "class Solution(object):\n def maximumScore(self, nums, k):\n \"\"\"\n :type nums: List[int]\n :type k: int\n :rtype: int\n \"\"\"\n ", |
| "java_template": "class Solution {\n public int maximumScore(List<Integer> nums, int k) {\n \n }\n}", |
| "metadata": { |
| "func_name": "maximumScore" |
| } |
| } |
