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leetcode-cn/problem (Chinese)/统计异或值为给定值的路径数目 [count-paths-with-the-given-xor-value].html Normal file
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<p>给你一个大小为 <code>m x n</code>&nbsp;的二维整数数组&nbsp;<code>grid</code>&nbsp;和一个整数&nbsp;<code>k</code>&nbsp;。</p>
<p>你的任务是统计满足以下 <strong>条件</strong> 且从左上格子&nbsp;<code>(0, 0)</code>&nbsp;出发到达右下格子&nbsp;<code>(m - 1, n - 1)</code>&nbsp;的路径数目：</p>
<ul>
<li>每一步你可以向右或者向下走，也就是如果格子存在的话，可以从格子&nbsp;<code>(i, j)</code>&nbsp;走到格子&nbsp;<code>(i, j + 1)</code>&nbsp;或者格子&nbsp;<code>(i + 1, j)</code>&nbsp;。</li>
<li>路径上经过的所有数字&nbsp;<code>XOR</code>&nbsp;异或值必须 <strong>等于</strong>&nbsp;<code>k</code>&nbsp;。</li>
</ul>
<p>请你返回满足上述条件的路径总数。</p>
<p>由于答案可能很大，请你将答案对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong> 后返回。</p>
<p>&nbsp;</p>
<p><strong class="example">示例 1：</strong></p>
<div class="example-block">
<p><span class="example-io"><b>输入：</b>grid = [[2, 1, 5], [7, 10, 0], [12, 6, 4]], k = 11</span></p>
<p><span class="example-io"><b>输出：</b>3</span></p>
<p><b>解释：</b></p>
<p>3 条路径分别为：</p>
<ul>
<li><code>(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2)</code></li>
<li><code>(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2)</code></li>
<li><code>(0, 0) → (0, 1) → (1, 1) → (2, 1) → (2, 2)</code></li>
</ul>
</div>
<p><strong class="example">示例 2：</strong></p>
<div class="example-block">
<p><span class="example-io"><b>输入：</b>grid = [[1, 3, 3, 3], [0, 3, 3, 2], [3, 0, 1, 1]], k = 2</span></p>
<p><span class="example-io"><b>输出：</b>5</span></p>
<p><b>解释：</b></p>
<p>5 条路径分别为：</p>
<ul>
<li><code>(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (2, 3)</code></li>
<li><code>(0, 0) → (1, 0) → (1, 1) → (2, 1) → (2, 2) → (2, 3)</code></li>
<li><code>(0, 0) → (1, 0) → (1, 1) → (1, 2) → (1, 3) → (2, 3)</code></li>
<li><code>(0, 0) → (0, 1) → (1, 1) → (1, 2) → (2, 2) → (2, 3)</code></li>
<li><code>(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (2, 3)</code></li>
</ul>
</div>
<p><strong class="example">示例 3：</strong></p>
<div class="example-block">
<p><span class="example-io"><b>输入：</b>grid = [[1, 1, 1, 2], [3, 0, 3, 2], [3, 0, 2, 2]], k = 10</span></p>
<p><span class="example-io"><b>输出：</b>0</span></p>
</div>
<p>&nbsp;</p>
<p><strong>提示：</strong></p>
<ul>
<li><code>1 &lt;= m == grid.length &lt;= 300</code></li>
<li><code>1 &lt;= n == grid[r].length &lt;= 300</code></li>
<li><code>0 &lt;= grid[r][c] &lt; 16</code></li>
<li><code>0 &lt;= k &lt; 16</code></li>
</ul>