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45 lines
2.0 KiB
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45 lines
2.0 KiB
HTML
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.</p>
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<p>You can perform the following operation as many times as you want:</p>
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<ul>
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<li>Pick an index <code>i</code> that you haven’t picked before, and pick a prime <code>p</code> <strong>strictly less than</strong> <code>nums[i]</code>, then subtract <code>p</code> from <code>nums[i]</code>.</li>
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</ul>
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<p>Return <em>true if you can make <code>nums</code> a strictly increasing array using the above operation and false otherwise.</em></p>
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<p>A <strong>strictly increasing array</strong> is an array whose each element is strictly greater than its preceding element.</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 = [4,9,6,10]
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<strong>Output:</strong> true
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<strong>Explanation:</strong> In the first operation: Pick i = 0 and p = 3, and then subtract 3 from nums[0], so that nums becomes [1,9,6,10].
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In the second operation: i = 1, p = 7, subtract 7 from nums[1], so nums becomes equal to [1,2,6,10].
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After the second operation, nums is sorted in strictly increasing order, so the answer is true.</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 = [6,8,11,12]
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<strong>Output:</strong> true
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<strong>Explanation: </strong>Initially nums is sorted in strictly increasing order, so we don't need to make any operations.</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [5,8,3]
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<strong>Output:</strong> false
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<strong>Explanation:</strong> It can be proven that there is no way to perform operations to make nums sorted in strictly increasing order, so the answer is false.</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 <= 1000</code></li>
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<li><code>1 <= nums[i] <= 1000</code></li>
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<li><code><font face="monospace">nums.length == n</font></code></li>
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</ul>
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