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92 lines
3.9 KiB
HTML
92 lines
3.9 KiB
HTML
<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>
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<p>The cost to enter cell <code>(i, j)</code> is defined as <code>(i + 1) * (j + 1)</code>.</p>
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<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>
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<p>The path will always begin by entering cell <code>(0, 0)</code> on move 1 and paying the entrance cost.</p>
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<p>At each step, you follow an alternating pattern:</p>
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<ul>
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<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>
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<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>
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</ul>
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<p>Return the <strong>minimum</strong> total cost required to reach <code>(m - 1, n - 1)</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">m = 1, n = 2, waitCost = [[1,2]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">3</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The optimal path is:</p>
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<ul>
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<li>Start at cell <code>(0, 0)</code> at second 1 with entry cost <code>(0 + 1) * (0 + 1) = 1</code>.</li>
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<li><strong>Second 1</strong>: Move right to cell <code>(0, 1)</code> with entry cost <code>(0 + 1) * (1 + 1) = 2</code>.</li>
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</ul>
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<p>Thus, the total cost is <code>1 + 2 = 3</code>.</p>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">m = 2, n = 2, waitCost = [[3,5],[2,4]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">9</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The optimal path is:</p>
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<ul>
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<li>Start at cell <code>(0, 0)</code> at second 1 with entry cost <code>(0 + 1) * (0 + 1) = 1</code>.</li>
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<li><strong>Second 1</strong>: Move down to cell <code>(1, 0)</code> with entry cost <code>(1 + 1) * (0 + 1) = 2</code>.</li>
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<li><strong>Second 2</strong>: Wait at cell <code>(1, 0)</code>, paying <code>waitCost[1][0] = 2</code>.</li>
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<li><strong>Second 3</strong>: Move right to cell <code>(1, 1)</code> with entry cost <code>(1 + 1) * (1 + 1) = 4</code>.</li>
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</ul>
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<p>Thus, the total cost is <code>1 + 2 + 2 + 4 = 9</code>.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">m = 2, n = 3, waitCost = [[6,1,4],[3,2,5]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">16</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The optimal path is:</p>
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<ul>
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<li>Start at cell <code>(0, 0)</code> at second 1 with entry cost <code>(0 + 1) * (0 + 1) = 1</code>.</li>
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<li><strong>Second 1</strong>: Move right to cell <code>(0, 1)</code> with entry cost <code>(0 + 1) * (1 + 1) = 2</code>.</li>
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<li><strong>Second 2</strong>: Wait at cell <code>(0, 1)</code>, paying <code>waitCost[0][1] = 1</code>.</li>
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<li><strong>Second 3</strong>: Move down to cell <code>(1, 1)</code> with entry cost <code>(1 + 1) * (1 + 1) = 4</code>.</li>
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<li><strong>Second 4</strong>: Wait at cell <code>(1, 1)</code>, paying <code>waitCost[1][1] = 2</code>.</li>
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<li><strong>Second 5</strong>: Move right to cell <code>(1, 2)</code> with entry cost <code>(1 + 1) * (2 + 1) = 6</code>.</li>
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</ul>
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<p>Thus, the total cost is <code>1 + 2 + 1 + 4 + 2 + 6 = 16</code>.</p>
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</div>
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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>1 <= m, n <= 10<sup>5</sup></code></li>
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<li><code>2 <= m * n <= 10<sup>5</sup></code></li>
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<li><code>waitCost.length == m</code></li>
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<li><code>waitCost[0].length == n</code></li>
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<li><code>0 <= waitCost[i][j] <= 10<sup>5</sup></code></li>
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</ul>
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