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50 lines
3.0 KiB
HTML
50 lines
3.0 KiB
HTML
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<p>You are given an array <code>nums</code> of <code>n</code> positive integers and an integer <code>k</code>.</p>
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<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>
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<ul>
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<li>Choose any <strong>non-empty</strong> subarray <code>nums[l, ..., r]</code> that you haven't chosen previously.</li>
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<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>
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<li>Multiply your score by <code>x</code>.</li>
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</ul>
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<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>
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<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>
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<p>Return <em>the <strong>maximum possible score</strong> after applying at most </em><code>k</code><em> operations</em>.</p>
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<p>Since the answer may be large, return it modulo <code>10<sup>9 </sup>+ 7</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [8,3,9,3,8], k = 2
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<strong>Output:</strong> 81
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<strong>Explanation:</strong> To get a score of 81, we can apply the following operations:
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- 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.
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- 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.
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It can be proven that 81 is the highest score one can obtain.</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [19,12,14,6,10,18], k = 3
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<strong>Output:</strong> 4788
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<strong>Explanation:</strong> To get a score of 4788, we can apply the following operations:
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- 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.
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- 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.
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- 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.
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It can be proven that 4788 is the highest score one can obtain.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= nums.length == n <= 10<sup>5</sup></code></li>
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<li><code>1 <= nums[i] <= 10<sup>5</sup></code></li>
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<li><code>1 <= k <= min(n * (n + 1) / 2, 10<sup>9</sup>)</code></li>
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</ul>
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