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64 lines
3.4 KiB
HTML
64 lines
3.4 KiB
HTML
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> containing <strong>positive</strong> integers.</p>
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<p>Your task is to <strong>minimize</strong> the length of <code>nums</code> by performing the following operations <strong>any</strong> number of times (including zero):</p>
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<ul>
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<li>Select <strong>two</strong> <strong>distinct</strong> indices <code>i</code> and <code>j</code> from <code>nums</code>, such that <code>nums[i] > 0</code> and <code>nums[j] > 0</code>.</li>
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<li>Insert the result of <code>nums[i] % nums[j]</code> at the end of <code>nums</code>.</li>
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<li>Delete the elements at indices <code>i</code> and <code>j</code> from <code>nums</code>.</li>
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</ul>
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<p>Return <em>an integer denoting the <strong>minimum</strong> <strong>length</strong> of </em><code>nums</code><em> after performing the operation any number of times.</em></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 = [1,4,3,1]
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> One way to minimize the length of the array is as follows:
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Operation 1: Select indices 2 and 1, insert nums[2] % nums[1] at the end and it becomes [1,4,3,1,3], then delete elements at indices 2 and 1.
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nums becomes [1,1,3].
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Operation 2: Select indices 1 and 2, insert nums[1] % nums[2] at the end and it becomes [1,1,3,1], then delete elements at indices 1 and 2.
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nums becomes [1,1].
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Operation 3: Select indices 1 and 0, insert nums[1] % nums[0] at the end and it becomes [1,1,0], then delete elements at indices 1 and 0.
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nums becomes [0].
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The length of nums cannot be reduced further. Hence, the answer is 1.
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It can be shown that 1 is the minimum achievable length. </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 = [5,5,5,10,5]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> One way to minimize the length of the array is as follows:
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Operation 1: Select indices 0 and 3, insert nums[0] % nums[3] at the end and it becomes [5,5,5,10,5,5], then delete elements at indices 0 and 3.
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nums becomes [5,5,5,5].
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Operation 2: Select indices 2 and 3, insert nums[2] % nums[3] at the end and it becomes [5,5,5,5,0], then delete elements at indices 2 and 3.
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nums becomes [5,5,0].
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Operation 3: Select indices 0 and 1, insert nums[0] % nums[1] at the end and it becomes [5,5,0,0], then delete elements at indices 0 and 1.
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nums becomes [0,0].
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The length of nums cannot be reduced further. Hence, the answer is 2.
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It can be shown that 2 is the minimum achievable length. </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 = [2,3,4]
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> One way to minimize the length of the array is as follows:
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Operation 1: Select indices 1 and 2, insert nums[1] % nums[2] at the end and it becomes [2,3,4,3], then delete elements at indices 1 and 2.
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nums becomes [2,3].
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Operation 2: Select indices 1 and 0, insert nums[1] % nums[0] at the end and it becomes [2,3,1], then delete elements at indices 1 and 0.
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nums becomes [1].
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The length of nums cannot be reduced further. Hence, the answer is 1.
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It can be shown that 1 is the minimum achievable length.</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 <= 10<sup>5</sup></code></li>
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<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>
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</ul>
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