leetcode-problemset/leetcode-cn/originData/minimum-cost-for-cutting-cake-ii.json

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        "question": {
            "questionId": "3500",
            "questionFrontendId": "3219",
            "categoryTitle": "Algorithms",
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            "title": "Minimum Cost for Cutting Cake II",
            "titleSlug": "minimum-cost-for-cutting-cake-ii",
            "content": "<p>There is an <code>m x n</code> cake that needs to be cut into <code>1 x 1</code> pieces.</p>\n\n<p>You are given integers <code>m</code>, <code>n</code>, and two arrays:</p>\n\n<ul>\n\t<li><code>horizontalCut</code> of size <code>m - 1</code>, where <code>horizontalCut[i]</code> represents the cost to cut along the horizontal line <code>i</code>.</li>\n\t<li><code>verticalCut</code> of size <code>n - 1</code>, where <code>verticalCut[j]</code> represents the cost to cut along the vertical line <code>j</code>.</li>\n</ul>\n\n<p>In one operation, you can choose any piece of cake that is not yet a <code>1 x 1</code> square and perform one of the following cuts:</p>\n\n<ol>\n\t<li>Cut along a horizontal line <code>i</code> at a cost of <code>horizontalCut[i]</code>.</li>\n\t<li>Cut along a vertical line <code>j</code> at a cost of <code>verticalCut[j]</code>.</li>\n</ol>\n\n<p>After the cut, the piece of cake is divided into two distinct pieces.</p>\n\n<p>The cost of a cut depends only on the initial cost of the line and does not change.</p>\n\n<p>Return the <strong>minimum</strong> total cost to cut the entire cake into <code>1 x 1</code> pieces.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">m = 3, n = 2, horizontalCut = [1,3], verticalCut = [5]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">13</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/06/04/ezgifcom-animated-gif-maker-1.gif\" style=\"width: 280px; height: 320px;\" /></p>\n\n<ul>\n\t<li>Perform a cut on the vertical line 0 with cost 5, current total cost is 5.</li>\n\t<li>Perform a cut on the horizontal line 0 on <code>3 x 1</code> subgrid with cost 1.</li>\n\t<li>Perform a cut on the horizontal line 0 on <code>3 x 1</code> subgrid with cost 1.</li>\n\t<li>Perform a cut on the horizontal line 1 on <code>2 x 1</code> subgrid with cost 3.</li>\n\t<li>Perform a cut on the horizontal line 1 on <code>2 x 1</code> subgrid with cost 3.</li>\n</ul>\n\n<p>The total cost is <code>5 + 1 + 1 + 3 + 3 = 13</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">m = 2, n = 2, horizontalCut = [7], verticalCut = [4]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">15</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>Perform a cut on the horizontal line 0 with cost 7.</li>\n\t<li>Perform a cut on the vertical line 0 on <code>1 x 2</code> subgrid with cost 4.</li>\n\t<li>Perform a cut on the vertical line 0 on <code>1 x 2</code> subgrid with cost 4.</li>\n</ul>\n\n<p>The total cost is <code>7 + 4 + 4 = 15</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>horizontalCut.length == m - 1</code></li>\n\t<li><code>verticalCut.length == n - 1</code></li>\n\t<li><code>1 &lt;= horizontalCut[i], verticalCut[i] &lt;= 10<sup>3</sup></code></li>\n</ul>\n",
            "translatedTitle": "切蛋糕的最小总开销 II",
            "translatedContent": "<p>有一个&nbsp;<code>m x n</code>&nbsp;大小的矩形蛋糕，需要切成&nbsp;<code>1 x 1</code>&nbsp;的小块。</p>\n\n<p>给你整数&nbsp;<code>m</code>&nbsp;，<code>n</code>&nbsp;和两个数组：</p>\n\n<ul>\n\t<li><code>horizontalCut</code> 的大小为&nbsp;<code>m - 1</code>&nbsp;，其中&nbsp;<code>horizontalCut[i]</code>&nbsp;表示沿着水平线 <code>i</code>&nbsp;切蛋糕的开销。</li>\n\t<li><code>verticalCut</code> 的大小为&nbsp;<code>n - 1</code>&nbsp;，其中&nbsp;<code>verticalCut[j]</code>&nbsp;表示沿着垂直线&nbsp;<code>j</code>&nbsp;切蛋糕的开销。</li>\n</ul>\n\n<p>一次操作中，你可以选择任意不是&nbsp;<code>1 x 1</code>&nbsp;大小的矩形蛋糕并执行以下操作之一：</p>\n\n<ol>\n\t<li>沿着水平线&nbsp;<code>i</code>&nbsp;切开蛋糕，开销为&nbsp;<code>horizontalCut[i]</code>&nbsp;。</li>\n\t<li>沿着垂直线&nbsp;<code>j</code>&nbsp;切开蛋糕，开销为&nbsp;<code>verticalCut[j]</code>&nbsp;。</li>\n</ol>\n\n<p>每次操作后，这块蛋糕都被切成两个独立的小蛋糕。</p>\n\n<p>每次操作的开销都为最开始对应切割线的开销，并且不会改变。</p>\n\n<p>请你返回将蛋糕全部切成&nbsp;<code>1 x 1</code>&nbsp;的蛋糕块的&nbsp;<strong>最小</strong>&nbsp;总开销。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>m = 3, n = 2, horizontalCut = [1,3], verticalCut = [5]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>13</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/06/04/ezgifcom-animated-gif-maker-1.gif\" style=\"width: 280px; height: 320px;\" /></p>\n\n<ul>\n\t<li>沿着垂直线 0 切开蛋糕，开销为 5 。</li>\n\t<li>沿着水平线 0 切开&nbsp;<code>3 x 1</code>&nbsp;的蛋糕块，开销为 1 。</li>\n\t<li>沿着水平线 0 切开 <code>3 x 1</code>&nbsp;的蛋糕块，开销为 1 。</li>\n\t<li>沿着水平线 1 切开 <code>2 x 1</code>&nbsp;的蛋糕块，开销为 3 。</li>\n\t<li>沿着水平线 1 切开 <code>2 x 1</code>&nbsp;的蛋糕块，开销为 3 。</li>\n</ul>\n\n<p>总开销为&nbsp;<code>5 + 1 + 1 + 3 + 3 = 13</code>&nbsp;。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>m = 2, n = 2, horizontalCut = [7], verticalCut = [4]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>15</span></p>\n\n<p><strong>解释：</strong></p>\n\n<ul>\n\t<li>沿着水平线 0 切开蛋糕，开销为 7 。</li>\n\t<li>沿着垂直线 0 切开&nbsp;<code>1 x 2</code>&nbsp;的蛋糕块，开销为 4 。</li>\n\t<li>沿着垂直线 0 切开&nbsp;<code>1 x 2</code>&nbsp;的蛋糕块，开销为 4 。</li>\n</ul>\n\n<p>总开销为&nbsp;<code>7 + 4 + 4 = 15</code>&nbsp;。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>horizontalCut.length == m - 1</code></li>\n\t<li><code>verticalCut.length == n - 1</code></li>\n\t<li><code>1 &lt;= horizontalCut[i], verticalCut[i] &lt;= 10<sup>3</sup></code></li>\n</ul>\n",
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