{ "data": { "question": { "questionId": "1669", "questionFrontendId": "1547", "boundTopicId": null, "title": "Minimum Cost to Cut a Stick", "titleSlug": "minimum-cost-to-cut-a-stick", "content": "

Given a wooden stick of length n units. The stick is labelled from 0 to n. For example, a stick of length 6 is labelled as follows:

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Given an integer array cuts where cuts[i] denotes a position you should perform a cut at.

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You should perform the cuts in order, you can change the order of the cuts as you wish.

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The cost of one cut is the length of the stick to be cut, the total cost is the sum of costs of all cuts. When you cut a stick, it will be split into two smaller sticks (i.e. the sum of their lengths is the length of the stick before the cut). Please refer to the first example for a better explanation.

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Return the minimum total cost of the cuts.

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Example 1:

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\nInput: n = 7, cuts = [1,3,4,5]\nOutput: 16\nExplanation: Using cuts order = [1, 3, 4, 5] as in the input leads to the following scenario:\n\"\"\nThe first cut is done to a rod of length 7 so the cost is 7. The second cut is done to a rod of length 6 (i.e. the second part of the first cut), the third is done to a rod of length 4 and the last cut is to a rod of length 3. The total cost is 7 + 6 + 4 + 3 = 20.\nRearranging the cuts to be [3, 5, 1, 4] for example will lead to a scenario with total cost = 16 (as shown in the example photo 7 + 4 + 3 + 2 = 16).
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Example 2:

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\nInput: n = 9, cuts = [5,6,1,4,2]\nOutput: 22\nExplanation: If you try the given cuts ordering the cost will be 25.\nThere are much ordering with total cost <= 25, for example, the order [4, 6, 5, 2, 1] has total cost = 22 which is the minimum possible.\n
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Constraints:

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