mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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182 lines
18 KiB
JSON
182 lines
18 KiB
JSON
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"questionId": "1896",
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"title": "Maximum Score from Performing Multiplication Operations",
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"content": "<p>You are given two <strong>0-indexed</strong> integer arrays <code>nums</code> and <code>multipliers</code><strong> </strong>of size <code>n</code> and <code>m</code> respectively, where <code>n >= m</code>.</p>\n\n<p>You begin with a score of <code>0</code>. You want to perform <strong>exactly</strong> <code>m</code> operations. On the <code>i<sup>th</sup></code> operation (<strong>0-indexed</strong>) you will:</p>\n\n<ul>\n <li>Choose one integer <code>x</code> from <strong>either the start or the end </strong>of the array <code>nums</code>.</li>\n <li>Add <code>multipliers[i] * x</code> to your score.\n <ul>\n <li>Note that <code>multipliers[0]</code> corresponds to the first operation, <code>multipliers[1]</code> to the second operation, and so on.</li>\n </ul>\n </li>\n <li>Remove <code>x</code> from <code>nums</code>.</li>\n</ul>\n\n<p>Return <em>the <strong>maximum</strong> score after performing </em><code>m</code> <em>operations.</em></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3], multipliers = [3,2,1]\n<strong>Output:</strong> 14\n<strong>Explanation:</strong> An optimal solution is as follows:\n- Choose from the end, [1,2,<strong><u>3</u></strong>], adding 3 * 3 = 9 to the score.\n- Choose from the end, [1,<strong><u>2</u></strong>], adding 2 * 2 = 4 to the score.\n- Choose from the end, [<strong><u>1</u></strong>], adding 1 * 1 = 1 to the score.\nThe total score is 9 + 4 + 1 = 14.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [-5,-3,-3,-2,7,1], multipliers = [-10,-5,3,4,6]\n<strong>Output:</strong> 102\n<strong>Explanation: </strong>An optimal solution is as follows:\n- Choose from the start, [<u><strong>-5</strong></u>,-3,-3,-2,7,1], adding -5 * -10 = 50 to the score.\n- Choose from the start, [<strong><u>-3</u></strong>,-3,-2,7,1], adding -3 * -5 = 15 to the score.\n- Choose from the start, [<strong><u>-3</u></strong>,-2,7,1], adding -3 * 3 = -9 to the score.\n- Choose from the end, [-2,7,<strong><u>1</u></strong>], adding 1 * 4 = 4 to the score.\n- Choose from the end, [-2,<strong><u>7</u></strong>], adding 7 * 6 = 42 to the score. \nThe total score is 50 + 15 - 9 + 4 + 42 = 102.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>m == multipliers.length</code></li>\n\t<li><code>1 <= m <= 300</code></li>\n\t<li><code>m <= n <= 10<sup>5</sup></code><code> </code></li>\n\t<li><code>-1000 <= nums[i], multipliers[i] <= 1000</code></li>\n</ul>\n",
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"At first glance, the solution seems to be greedy, but if you try to greedily take the largest value from the beginning or the end, this will not be optimal.",
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"You should try all scenarios but this will be costly.",
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"Memoizing the pre-visited states while trying all the possible scenarios will reduce the complexity, and hence dp is a perfect choice here."
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