leetcode-problemset/leetcode-cn/originData/minimum-cost-path-with-alternating-directions-ii.json

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        "question": {
            "questionId": "3927",
            "questionFrontendId": "3603",
            "categoryTitle": "Algorithms",
            "boundTopicId": 3714003,
            "title": "Minimum Cost Path with Alternating Directions II",
            "titleSlug": "minimum-cost-path-with-alternating-directions-ii",
            "content": "<p>You are given two integers <code>m</code> and <code>n</code> representing the number of rows and columns of a grid, respectively.</p>\n\n<p>The cost to enter cell <code>(i, j)</code> is defined as <code>(i + 1) * (j + 1)</code>.</p>\n\n<p>You are also given a 2D integer array <code>waitCost</code> where <code>waitCost[i][j]</code> defines the cost to <strong>wait</strong> on that cell.</p>\n\n<p>The path will always begin by entering cell <code>(0, 0)</code> on move 1 and paying the entrance cost.</p>\n\n<p>At each step, you follow an alternating pattern:</p>\n\n<ul>\n\t<li>On <strong>odd-numbered</strong> seconds, you must move <strong>right</strong> or <strong>down</strong> to an <strong>adjacent</strong> cell, paying its entry cost.</li>\n\t<li>On <strong>even-numbered</strong> seconds, you must <strong>wait</strong> in place for <strong>exactly</strong> one second and pay <code>waitCost[i][j]</code> during that second.</li>\n</ul>\n\n<p>Return the <strong>minimum</strong> total cost required to reach <code>(m - 1, n - 1)</code>.</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 = 1, n = 2, waitCost = [[1,2]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The optimal path is:</p>\n\n<ul>\n\t<li>Start at cell <code>(0, 0)</code> at second 1 with entry cost <code>(0 + 1) * (0 + 1) = 1</code>.</li>\n\t<li><strong>Second 1</strong>: Move right to cell <code>(0, 1)</code> with entry cost <code>(0 + 1) * (1 + 1) = 2</code>.</li>\n</ul>\n\n<p>Thus, the total cost is <code>1 + 2 = 3</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, waitCost = [[3,5],[2,4]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">9</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The optimal path is:</p>\n\n<ul>\n\t<li>Start at cell <code>(0, 0)</code> at second 1 with entry cost <code>(0 + 1) * (0 + 1) = 1</code>.</li>\n\t<li><strong>Second 1</strong>: Move down to cell <code>(1, 0)</code> with entry cost <code>(1 + 1) * (0 + 1) = 2</code>.</li>\n\t<li><strong>Second 2</strong>: Wait at cell <code>(1, 0)</code>, paying <code>waitCost[1][0] = 2</code>.</li>\n\t<li><strong>Second 3</strong>: Move right to cell <code>(1, 1)</code> with entry cost <code>(1 + 1) * (1 + 1) = 4</code>.</li>\n</ul>\n\n<p>Thus, the total cost is <code>1 + 2 + 2 + 4 = 9</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">m = 2, n = 3, waitCost = [[6,1,4],[3,2,5]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">16</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The optimal path is:</p>\n\n<ul>\n\t<li>Start at cell <code>(0, 0)</code> at second 1 with entry cost <code>(0 + 1) * (0 + 1) = 1</code>.</li>\n\t<li><strong>Second 1</strong>: Move right to cell <code>(0, 1)</code> with entry cost <code>(0 + 1) * (1 + 1) = 2</code>.</li>\n\t<li><strong>Second 2</strong>: Wait at cell <code>(0, 1)</code>, paying <code>waitCost[0][1] = 1</code>.</li>\n\t<li><strong>Second 3</strong>: Move down to cell <code>(1, 1)</code> with entry cost <code>(1 + 1) * (1 + 1) = 4</code>.</li>\n\t<li><strong>Second 4</strong>: Wait at cell <code>(1, 1)</code>, paying <code>waitCost[1][1] = 2</code>.</li>\n\t<li><strong>Second 5</strong>: Move right to cell <code>(1, 2)</code> with entry cost <code>(1 + 1) * (2 + 1) = 6</code>.</li>\n</ul>\n\n<p>Thus, the total cost is <code>1 + 2 + 1 + 4 + 2 + 6 = 16</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>2 &lt;= m * n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>waitCost.length == m</code></li>\n\t<li><code>waitCost[0].length == n</code></li>\n\t<li><code>0 &lt;= waitCost[i][j] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "交替方向的最小路径代价 II",
            "translatedContent": "<p>给你两个整数 <code>m</code> 和 <code>n</code>，分别表示网格的行数和列数。</p>\n\n<p>进入单元格 <code>(i, j)</code> 的成本定义为 <code>(i + 1) * (j + 1)</code>。</p>\n\n<p>另外给你一个二维整数数组 <code>waitCost</code>，其中 <code>waitCost[i][j]</code> 定义了在该单元格&nbsp;<strong>等待&nbsp;</strong>的成本。</p>\n\n<p>路径始终从第 1 步进入单元格 <code>(0, 0)</code>&nbsp;并支付入场花费开始。</p>\n\n<p>每一步，你都遵循交替模式：</p>\n\n<ul>\n\t<li>在&nbsp;<strong>奇数秒&nbsp;</strong>，你必须向&nbsp;<strong>右&nbsp;</strong>或向&nbsp;<strong>下&nbsp;</strong>移动到&nbsp;<strong>相邻&nbsp;</strong>的单元格，并支付其进入成本。</li>\n\t<li>在&nbsp;<strong>偶数秒&nbsp;</strong>，你必须原地&nbsp;<strong>等待</strong><strong>恰好</strong>&nbsp;1 秒并在 1 秒期间支付 <code>waitCost[i][j]</code>。</li>\n</ul>\n\n<p>返回到达 <code>(m - 1, n - 1)</code> 所需的&nbsp;<strong>最小&nbsp;</strong>总成本。</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><strong>输入：</strong><span class=\"example-io\">m = 1, n = 2, waitCost = [[1,2]]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">3</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>最佳路径为：</p>\n\n<ul>\n\t<li>从第 1 秒开始在单元格 <code>(0, 0)</code>，进入成本为 <code>(0 + 1) * (0 + 1) = 1</code>。</li>\n\t<li><strong>第 1 秒</strong>：向右移动到单元格 <code>(0, 1)</code>，进入成本为 <code>(0 + 1) * (1 + 1) = 2</code>。</li>\n</ul>\n\n<p>因此，总成本为 <code>1 + 2 = 3</code>。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">m = 2, n = 2, waitCost = [[3,5],[2,4]]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">9</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>最佳路径为：</p>\n\n<ul>\n\t<li>从第 1 秒开始在单元格 <code>(0, 0)</code>，进入成本为 <code>(0 + 1) * (0 + 1) = 1</code>。</li>\n\t<li><strong>第 1 秒</strong>：向下移动到单元格 <code>(1, 0)</code>，进入成本为 <code>(1 + 1) * (0 + 1) = 2</code>。</li>\n\t<li><strong>第 2 秒</strong>：在单元格 <code>(1, 0)</code> 等待，支付 <code>waitCost[1][0] = 2</code>。</li>\n\t<li><strong>第 3 秒</strong>：向右移动到单元格 <code>(1, 1)</code>，进入成本为 <code>(1 + 1) * (1 + 1) = 4</code>。</li>\n</ul>\n\n<p>因此，总成本为 <code>1 + 2 + 2 + 4 = 9</code>。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">m = 2, n = 3, waitCost = [[6,1,4],[3,2,5]]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">16</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>最佳路径为：</p>\n\n<ul>\n\t<li>从第 1 秒开始在单元格 <code>(0, 0)</code>，进入成本为 <code>(0 + 1) * (0 + 1) = 1</code>。</li>\n\t<li><strong>第 1 秒</strong>：向右移动到单元格 <code>(0, 1)</code>，进入成本为 <code>(0 + 1) * (1 + 1) = 2</code>。</li>\n\t<li><strong>第 2 秒</strong>：在单元格 <code>(0, 1)</code> 等待，支付 <code>waitCost[0][1] = 1</code>。</li>\n\t<li><strong>第 3 秒</strong>：向下移动到单元格 <code>(1, 1)</code>，进入成本为 <code>(1 + 1) * (1 + 1) = 4</code>。</li>\n\t<li><strong>第 4 秒</strong>：在单元格 <code>(1, 1)</code> 等待，支付 <code>waitCost[1][1] = 2</code>。</li>\n\t<li><strong>第 5 秒</strong>：向右移动到单元格 <code>(1, 2)</code>，进入成本为 <code>(1 + 1) * (2 + 1) = 6</code>。</li>\n</ul>\n\n<p>因此，总成本为 <code>1 + 2 + 1 + 4 + 2 + 6 = 16</code>。</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>2 &lt;= m * n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>waitCost.length == m</code></li>\n\t<li><code>waitCost[0].length == n</code></li>\n\t<li><code>0 &lt;= waitCost[i][j] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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target=\\\"_blank\\\">\\u300c\\u4ed3\\u9889\\u7f16\\u7a0b\\u8bed\\u8a00\\u5f00\\u53d1\\u6307\\u5357\\u300d<\\/a><\\/p>\"]}",
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