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100 lines
3.1 KiB
HTML
100 lines
3.1 KiB
HTML
<p>You are given an integer array <code>nums</code> and two integers, <code>k</code> and <code>limit</code>. Your task is to find a non-empty <strong><span data-keyword="subsequence-array">subsequence</span></strong> of <code>nums</code> that:</p>
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<ul>
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<li>Has an <strong>alternating sum</strong> equal to <code>k</code>.</li>
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<li><strong>Maximizes</strong> the product of all its numbers <em>without the product exceeding</em> <code>limit</code>.</li>
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</ul>
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<p>Return the <em>product</em> of the numbers in such a subsequence. If no subsequence satisfies the requirements, return -1.</p>
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<p>The <strong>alternating sum</strong> of a <strong>0-indexed</strong> array is defined as the <strong>sum</strong> of the elements at <strong>even</strong> indices <strong>minus</strong> the <strong>sum</strong> of the elements at <strong>odd</strong> indices.</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 = [1,2,3], k = 2, limit = 10</span></p>
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<p><strong>Output:</strong> <span class="example-io">6</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The subsequences with an alternating sum of 2 are:</p>
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<ul>
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<li><code>[1, 2, 3]</code>
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<ul>
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<li>Alternating Sum: <code>1 - 2 + 3 = 2</code></li>
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<li>Product: <code>1 * 2 * 3 = 6</code></li>
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</ul>
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</li>
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<li><code>[2]</code>
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<ul>
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<li>Alternating Sum: 2</li>
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<li>Product: 2</li>
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</ul>
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</li>
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</ul>
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<p>The maximum product within the limit is 6.</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 = [0,2,3], k = -5, limit = 12</span></p>
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<p><strong>Output:</strong> <span class="example-io">-1</span></p>
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<p><strong>Explanation:</strong></p>
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<p>A subsequence with an alternating sum of exactly -5 does not exist.</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 = [2,2,3,3], k = 0, limit = 9</span></p>
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<p><strong>Output:</strong> <span class="example-io">9</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The subsequences with an alternating sum of 0 are:</p>
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<ul>
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<li><code>[2, 2]</code>
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<ul>
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<li>Alternating Sum: <code>2 - 2 = 0</code></li>
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<li>Product: <code>2 * 2 = 4</code></li>
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</ul>
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</li>
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<li><code>[3, 3]</code>
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<ul>
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<li>Alternating Sum: <code>3 - 3 = 0</code></li>
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<li>Product: <code>3 * 3 = 9</code></li>
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</ul>
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</li>
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<li><code>[2, 2, 3, 3]</code>
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<ul>
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<li>Alternating Sum: <code>2 - 2 + 3 - 3 = 0</code></li>
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<li>Product: <code>2 * 2 * 3 * 3 = 36</code></li>
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</ul>
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</li>
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</ul>
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<p>The subsequence <code>[2, 2, 3, 3]</code> has the greatest product with an alternating sum equal to <code>k</code>, but <code>36 > 9</code>. The next greatest product is 9, which is within the limit.</p>
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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 <= nums.length <= 150</code></li>
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<li><code>0 <= nums[i] <= 12</code></li>
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<li><code>-10<sup>5</sup> <= k <= 10<sup>5</sup></code></li>
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<li><code>1 <= limit <= 5000</code></li>
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</ul>
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