leetcode-problemset/leetcode/originData/apply-operations-to-maximize-score.json

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            "title": "Apply Operations to Maximize Score",
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            "content": "<p>You are given an array <code>nums</code> of <code>n</code> positive integers and an integer <code>k</code>.</p>\n\n<p>Initially, you start with a score of <code>1</code>. You have to maximize your score by applying the following operation at most <code>k</code> times:</p>\n\n<ul>\n\t<li>Choose any <strong>non-empty</strong> subarray <code>nums[l, ..., r]</code> that you haven&#39;t chosen previously.</li>\n\t<li>Choose an element <code>x</code> of <code>nums[l, ..., r]</code> with the highest <strong>prime score</strong>. If multiple such elements exist, choose the one with the smallest index.</li>\n\t<li>Multiply your score by <code>x</code>.</li>\n</ul>\n\n<p>Here, <code>nums[l, ..., r]</code> denotes the subarray of <code>nums</code> starting at index <code>l</code> and ending at the index <code>r</code>, both ends being inclusive.</p>\n\n<p>The <strong>prime score</strong> of an integer <code>x</code> is equal to the number of distinct prime factors of <code>x</code>. For example, the prime score of <code>300</code> is <code>3</code> since <code>300 = 2 * 2 * 3 * 5 * 5</code>.</p>\n\n<p>Return <em>the <strong>maximum possible score</strong> after applying at most </em><code>k</code><em> operations</em>.</p>\n\n<p>Since the answer may be large, return it modulo <code>10<sup>9 </sup>+ 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [8,3,9,3,8], k = 2\n<strong>Output:</strong> 81\n<strong>Explanation:</strong> 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.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [19,12,14,6,10,18], k = 3\n<strong>Output:</strong> 4788\n<strong>Explanation:</strong> 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</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length == n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= min(n * (n + 1) / 2, 10<sup>9</sup>)</code></li>\n</ul>\n",
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                    "lang": "C++",
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                    "code": "class Solution {\npublic:\n    int maximumScore(vector<int>& nums, int k) {\n        \n    }\n};",
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                    "code": "class Solution(object):\n    def maximumScore(self, nums, k):\n        \"\"\"\n        :type nums: List[int]\n        :type k: int\n        :rtype: int\n        \"\"\"\n        ",
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                    "code": "/**\n * @param {number[]} nums\n * @param {number} k\n * @return {number}\n */\nvar maximumScore = function(nums, k) {\n    \n};",
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                    "code": "# @param {Integer[]} nums\n# @param {Integer} k\n# @return {Integer}\ndef maximum_score(nums, k)\n    \nend",
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                    "code": "impl Solution {\n    pub fn maximum_score(nums: Vec<i32>, k: i32) -> i32 {\n        \n    }\n}",
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                    "lang": "PHP",
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                    "code": "class Solution {\n\n    /**\n     * @param Integer[] $nums\n     * @param Integer $k\n     * @return Integer\n     */\n    function maximumScore($nums, $k) {\n        \n    }\n}",
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                    "code": "(define/contract (maximum-score nums k)\n  (-> (listof exact-integer?) exact-integer? exact-integer?)\n\n  )",
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                    "lang": "Erlang",
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                    "code": "-spec maximum_score(Nums :: [integer()], K :: integer()) -> integer().\nmaximum_score(Nums, K) ->\n  .",
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                    "code": "defmodule Solution do\n  @spec maximum_score(nums :: [integer], k :: integer) :: integer\n  def maximum_score(nums, k) do\n\n  end\nend",
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            "hints": [
                "<div class=\"_1l1MA\">Calculate <code>nums[i]</code>'s prime score <code>s[i]</code> by factoring in <code>O(sqrt(nums[i]))</code> time.</div>",
                "<div class=\"_1l1MA\">For each <code>nums[i]</code>, find the nearest index <code>left[i]</code> on the left (if any) such that <code>s[left[i]] >= s[i]</code>. if none is found, set <code>left[i]</code> to <code>-1</code>. Similarly, find the nearest index <code>right[i]</code> on the right (if any) such that <code>s[right[i]] > s[i]</code>. If none is found, set <code>right[i]</code> to <code>n</code>.</div>",
                "<div class=\"_1l1MA\">Use a monotonic stack to compute <code>right[i]</code> and <code>left[i]</code>.</div>",
                "<div class=\"_1l1MA\">For each index <code>i</code>, if <code>left[i] + 1 <= l <= i <= r <= right[i] - 1</code>, then <code>s[i]</code> is the maximum value in the range <code>[l, r]</code>. For this particular <code>i</code>, there are <code>ranges[i] = (i - left[i]) * (right[i] - i)</code> ranges where index <code>i</code> will be chosen.</div>",
                "<div class=\"_1l1MA\">Loop over all elements of <code>nums</code> by non-increasing prime score, each element will be chosen <code>min(ranges[i], remainingK)</code> times, where <code>reaminingK</code> denotes the number of remaining operations. Therefore, the score will be multiplied by <code>s[i]^min(ranges[i],remainingK)</code>.</div>",
                "<div class=\"_1l1MA\">Use fast exponentiation to quickly calculate <code>A^B mod C</code>.</div>"
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