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"categoryTitle": "Algorithms",
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"title": "Minimum Operations to Write the Letter Y on a Grid",
"titleSlug": "minimum-operations-to-write-the-letter-y-on-a-grid",
"content": "<p>You are given a <strong>0-indexed</strong> <code>n x n</code> grid where <code>n</code> is odd, and <code>grid[r][c]</code> is <code>0</code>, <code>1</code>, or <code>2</code>.</p>\n\n<p>We say that a cell belongs to the Letter <strong>Y</strong> if it belongs to one of the following:</p>\n\n<ul>\n\t<li>The diagonal starting at the top-left cell and ending at the center cell of the grid.</li>\n\t<li>The diagonal starting at the top-right cell and ending at the center cell of the grid.</li>\n\t<li>The vertical line starting at the center cell and ending at the bottom border of the grid.</li>\n</ul>\n\n<p>The Letter <strong>Y</strong> is written on the grid if and only if:</p>\n\n<ul>\n\t<li>All values at cells belonging to the Y are equal.</li>\n\t<li>All values at cells not belonging to the Y are equal.</li>\n\t<li>The values at cells belonging to the Y are different from the values at cells not belonging to the Y.</li>\n</ul>\n\n<p>Return <em>the <strong>minimum</strong> number of operations needed to write the letter Y on the grid given that in one operation you can change the value at any cell to</em> <code>0</code><em>,</em> <code>1</code><em>,</em> <em>or</em> <code>2</code><em>.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/22/y2.png\" style=\"width: 461px; height: 121px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,2,2],[1,1,0],[0,1,0]]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> We can write Y on the grid by applying the changes highlighted in blue in the image above. After the operations, all cells that belong to Y, denoted in bold, have the same value of 1 while those that do not belong to Y are equal to 0.\nIt can be shown that 3 is the minimum number of operations needed to write Y on the grid.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/22/y3.png\" style=\"width: 701px; height: 201px;\" />\n<pre>\n<strong>Input:</strong> grid = [[0,1,0,1,0],[2,1,0,1,2],[2,2,2,0,1],[2,2,2,2,2],[2,1,2,2,2]]\n<strong>Output:</strong> 12\n<strong>Explanation:</strong> We can write Y on the grid by applying the changes highlighted in blue in the image above. After the operations, all cells that belong to Y, denoted in bold, have the same value of 0 while those that do not belong to Y are equal to 2. \nIt can be shown that 12 is the minimum number of operations needed to write Y on the grid.</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= n &lt;= 49 </code></li>\n\t<li><code>n == grid.length == grid[i].length</code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 2</code></li>\n\t<li><code>n</code> is odd.</li>\n</ul>\n",
"translatedTitle": "在矩阵上写出字母 Y 所需的最少操作次数",
"translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始、大小为 <code>n x n</code> 的矩阵 <code>grid</code> ,其中 <code>n</code> 为奇数,且 <code>grid[r][c]</code> 的值为 <code>0</code> 、<code>1</code> 或 <code>2</code> 。</p>\n\n<p>如果一个单元格属于以下三条线中的任一一条,我们就认为它是字母 <strong>Y</strong> 的一部分:</p>\n\n<ul>\n\t<li>从左上角单元格开始到矩阵中心单元格结束的对角线。</li>\n\t<li>从右上角单元格开始到矩阵中心单元格结束的对角线。</li>\n\t<li>从中心单元格开始到矩阵底部边界结束的垂直线。</li>\n</ul>\n\n<p>当且仅当满足以下全部条件时,可以判定矩阵上写有字母 <strong>Y </strong></p>\n\n<ul>\n\t<li>属于 Y 的所有单元格的值相等。</li>\n\t<li>不属于 Y 的所有单元格的值相等。</li>\n\t<li>属于 Y 的单元格的值与不属于Y的单元格的值不同。</li>\n</ul>\n\n<p>每次操作你可以将任意单元格的值改变为 <code>0</code> 、<code>1</code> 或 <code>2</code> 。返回在矩阵上写出字母 Y 所需的 <strong>最少 </strong>操作次数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/22/y2.png\" style=\"width: 461px; height: 121px;\" />\n<pre>\n<strong>输入:</strong>grid = [[1,2,2],[1,1,0],[0,1,0]]\n<strong>输出:</strong>3\n<strong>解释:</strong>将在矩阵上写出字母 Y 需要执行的操作用蓝色高亮显示。操作后,所有属于 Y 的单元格(加粗显示)的值都为 1 ,而不属于 Y 的单元格的值都为 0 。\n可以证明写出 Y 至少需要进行 3 次操作。\n</pre>\n\n<p><strong class=\"example\">示例 2</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/22/y3.png\" style=\"width: 701px; height: 201px;\" />\n<pre>\n<strong>输入:</strong>grid = [[0,1,0,1,0],[2,1,0,1,2],[2,2,2,0,1],[2,2,2,2,2],[2,1,2,2,2]]\n<strong>输出:</strong>12\n<strong>解释:</strong>将在矩阵上写出字母 Y 需要执行的操作用蓝色高亮显示。操作后,所有属于 Y 的单元格(加粗显示)的值都为 0 ,而不属于 Y 的单元格的值都为 2 。\n可以证明写出 Y 至少需要进行 12 次操作。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= n &lt;= 49</code></li>\n\t<li><code>n == grid.length == grid[i].length</code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 2</code></li>\n\t<li><code>n</code> 为奇数。</li>\n</ul>\n",
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