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chapter_dynamic_programming/dp_solution_pipeline/index.html
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@@ -4087,7 +4087,7 @@ dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="暴力搜索递归树" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dfs.png" /></a></p>
<p align="center"> 图 14-14 &nbsp; 暴力搜索递归树 </p>
<p>每个状态都有向下和向右两种选择，从左上角走到右下角总共需要 <span class="arithmatex">\(m + n - 2\)</span> 步，所以最差时间复杂度为 <span class="arithmatex">\(O(2^{m + n})\)</span> ，其中 <span class="arithmatex">\(n\)</span> 和 <span class="arithmatex">\(m\)</span> 分别为网格的行数和列数。请注意，这种计算方式未考虑临近网格边界的情况，当到达网络边界时只剩下一种选择，因此实际的路径数量会少一些。</p>
<p>每个状态都有向下和向右两种选择，从左上角走到右下角总共需要 <span class="arithmatex">\(m + n - 2\)</span> 步，所以最差时间复杂度为 <span class="arithmatex">\(O(2^{m + n})\)</span> ，其中 <span class="arithmatex">\(n\)</span> 和 <span class="arithmatex">\(m\)</span> 分别为网格的行数和列数。请注意，这种计算方式未考虑临近网格边界的情况，当到达网格边界时只剩下一种选择，因此实际的路径数量会少一些。</p>
<h3 id="2">2. &nbsp; 方法二：记忆化搜索<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>我们引入一个和网格 <code>grid</code> 相同尺寸的记忆列表 <code>mem</code> ，用于记录各个子问题的解，并将重叠子问题进行剪枝：</p>
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