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74 lines
2.6 KiB
HTML
74 lines
2.6 KiB
HTML
<p>You are given an integer array <code>nums</code> of length <code>n</code>.</p>
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<p>You start at index 0, and your goal is to reach index <code>n - 1</code>.</p>
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<p>From any index <code>i</code>, you may perform one of the following operations:</p>
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<ul>
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<li><strong>Adjacent Step</strong>: Jump to index <code>i + 1</code> or <code>i - 1</code>, if the index is within bounds.</li>
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<li><strong>Prime Teleportation</strong>: If <code>nums[i]</code> is a <span data-keyword="prime-number">prime number</span> <code>p</code>, you may instantly jump to any index <code>j != i</code> such that <code>nums[j] % p == 0</code>.</li>
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</ul>
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<p>Return the <strong>minimum</strong> number of jumps required to reach index <code>n - 1</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">nums = [1,2,4,6]</span></p>
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<p><strong>Output:</strong> <span class="example-io">2</span></p>
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<p><strong>Explanation:</strong></p>
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<p>One optimal sequence of jumps is:</p>
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<ul>
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<li>Start at index <code>i = 0</code>. Take an adjacent step to index 1.</li>
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<li>At index <code>i = 1</code>, <code>nums[1] = 2</code> is a prime number. Therefore, we teleport to index <code>i = 3</code> as <code>nums[3] = 6</code> is divisible by 2.</li>
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</ul>
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<p>Thus, the answer is 2.</p>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">nums = [2,3,4,7,9]</span></p>
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<p><strong>Output:</strong> <span class="example-io">2</span></p>
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<p><strong>Explanation:</strong></p>
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<p>One optimal sequence of jumps is:</p>
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<ul>
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<li>Start at index <code>i = 0</code>. Take an adjacent step to index <code>i = 1</code>.</li>
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<li>At index <code>i = 1</code>, <code>nums[1] = 3</code> is a prime number. Therefore, we teleport to index <code>i = 4</code> since <code>nums[4] = 9</code> is divisible by 3.</li>
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</ul>
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<p>Thus, the answer is 2.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">nums = [4,6,5,8]</span></p>
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<p><strong>Output:</strong> <span class="example-io">3</span></p>
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<p><strong>Explanation:</strong></p>
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<ul>
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<li>Since no teleportation is possible, we move through <code>0 → 1 → 2 → 3</code>. Thus, the answer is 3.</li>
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</ul>
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</div>
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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 <= n == nums.length <= 10<sup>5</sup></code></li>
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<li><code>1 <= nums[i] <= 10<sup>6</sup></code></li>
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</ul>
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