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48 lines
3.3 KiB
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48 lines
3.3 KiB
HTML
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<p>You are given a <strong>0-indexed</strong> array of integers <code>nums</code> of length <code>n</code>, and two <strong>positive</strong> integers <code>k</code> and <code>dist</code>.</p>
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<p>The <strong>cost</strong> of an array is the value of its <strong>first</strong> element. For example, the cost of <code>[1,2,3]</code> is <code>1</code> while the cost of <code>[3,4,1]</code> is <code>3</code>.</p>
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<p>You need to divide <code>nums</code> into <code>k</code> <strong>disjoint contiguous </strong><span data-keyword="subarray-nonempty">subarrays</span>, such that the difference between the starting index of the <strong>second</strong> subarray and the starting index of the <code>kth</code> subarray should be <strong>less than or equal to</strong> <code>dist</code>. In other words, if you divide <code>nums</code> into the subarrays <code>nums[0..(i<sub>1</sub> - 1)], nums[i<sub>1</sub>..(i<sub>2</sub> - 1)], ..., nums[i<sub>k-1</sub>..(n - 1)]</code>, then <code>i<sub>k-1</sub> - i<sub>1</sub> <= dist</code>.</p>
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<p>Return <em>the <strong>minimum</strong> possible sum of the cost of these</em> <em>subarrays</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 = [1,3,2,6,4,2], k = 3, dist = 3
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<strong>Output:</strong> 5
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<strong>Explanation:</strong> The best possible way to divide nums into 3 subarrays is: [1,3], [2,6,4], and [2]. This choice is valid because i<sub>k-1</sub> - i<sub>1</sub> is 5 - 2 = 3 which is equal to dist. The total cost is nums[0] + nums[2] + nums[5] which is 1 + 2 + 2 = 5.
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It can be shown that there is no possible way to divide nums into 3 subarrays at a cost lower than 5.
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</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 = [10,1,2,2,2,1], k = 4, dist = 3
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<strong>Output:</strong> 15
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<strong>Explanation:</strong> The best possible way to divide nums into 4 subarrays is: [10], [1], [2], and [2,2,1]. This choice is valid because i<sub>k-1</sub> - i<sub>1</sub> is 3 - 1 = 2 which is less than dist. The total cost is nums[0] + nums[1] + nums[2] + nums[3] which is 10 + 1 + 2 + 2 = 15.
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The division [10], [1], [2,2,2], and [1] is not valid, because the difference between i<sub>k-1</sub> and i<sub>1</sub> is 5 - 1 = 4, which is greater than dist.
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It can be shown that there is no possible way to divide nums into 4 subarrays at a cost lower than 15.
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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 = [10,8,18,9], k = 3, dist = 1
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<strong>Output:</strong> 36
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<strong>Explanation:</strong> The best possible way to divide nums into 4 subarrays is: [10], [8], and [18,9]. This choice is valid because i<sub>k-1</sub> - i<sub>1</sub> is 2 - 1 = 1 which is equal to dist.The total cost is nums[0] + nums[1] + nums[2] which is 10 + 8 + 18 = 36.
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The division [10], [8,18], and [9] is not valid, because the difference between i<sub>k-1</sub> and i<sub>1</sub> is 3 - 1 = 2, which is greater than dist.
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It can be shown that there is no possible way to divide nums into 3 subarrays at a cost lower than 36.
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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>3 <= n <= 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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<li><code>3 <= k <= n</code></li>
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<li><code>k - 2 <= dist <= n - 2</code></li>
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</ul>
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