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55 lines
2.6 KiB
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55 lines
2.6 KiB
HTML
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>.</p>
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<p>A <strong>subsequence</strong> of <code>nums</code> having length <code>k</code> and consisting of <strong>indices</strong> <code>i<sub>0</sub> < i<sub>1</sub> < ... < i<sub>k-1</sub></code> is <strong>balanced</strong> if the following holds:</p>
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<ul>
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<li><code>nums[i<sub>j</sub>] - nums[i<sub>j-1</sub>] >= i<sub>j</sub> - i<sub>j-1</sub></code>, for every <code>j</code> in the range <code>[1, k - 1]</code>.</li>
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</ul>
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<p>A <strong>subsequence</strong> of <code>nums</code> having length <code>1</code> is considered balanced.</p>
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<p>Return <em>an integer denoting the <strong>maximum</strong> possible <strong>sum of elements</strong> in a <strong>balanced</strong> subsequence of </em><code>nums</code>.</p>
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<p>A <strong>subsequence</strong> of an array is a new <strong>non-empty</strong> array that is formed from the original array by deleting some (<strong>possibly none</strong>) of the elements without disturbing the relative positions of the remaining elements.</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 = [3,3,5,6]
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<strong>Output:</strong> 14
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<strong>Explanation:</strong> In this example, the subsequence [3,5,6] consisting of indices 0, 2, and 3 can be selected.
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nums[2] - nums[0] >= 2 - 0.
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nums[3] - nums[2] >= 3 - 2.
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Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums.
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The subsequence consisting of indices 1, 2, and 3 is also valid.
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It can be shown that it is not possible to get a balanced subsequence with a sum greater than 14.</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,-1,-3,8]
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<strong>Output:</strong> 13
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<strong>Explanation:</strong> In this example, the subsequence [5,8] consisting of indices 0 and 3 can be selected.
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nums[3] - nums[0] >= 3 - 0.
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Hence, it is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums.
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It can be shown that it is not possible to get a balanced subsequence with a sum greater than 13.
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</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,-1]
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<strong>Output:</strong> -1
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<strong>Explanation:</strong> In this example, the subsequence [-1] can be selected.
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It is a balanced subsequence, and its sum is the maximum among the balanced subsequences of nums.
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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 <= 10<sup>5</sup></code></li>
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<li><code>-10<sup>9</sup> <= nums[i] <= 10<sup>9</sup></code></li>
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</ul>
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