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@ -3025,9 +3025,6 @@ dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
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<li>当 <span class="arithmatex">\(j\)</span> 等于 <span class="arithmatex">\(1\)</span> ,即上一轮跳了 <span class="arithmatex">\(1\)</span> 阶时,这一轮只能选择跳 <span class="arithmatex">\(2\)</span> 阶;</li>
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<li>当 <span class="arithmatex">\(j\)</span> 等于 <span class="arithmatex">\(1\)</span> ,即上一轮跳了 <span class="arithmatex">\(1\)</span> 阶时,这一轮只能选择跳 <span class="arithmatex">\(2\)</span> 阶;</li>
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<li>当 <span class="arithmatex">\(j\)</span> 等于 <span class="arithmatex">\(2\)</span> ,即上一轮跳了 <span class="arithmatex">\(2\)</span> 阶时,这一轮可选择跳 <span class="arithmatex">\(1\)</span> 阶或跳 <span class="arithmatex">\(2\)</span> 阶;</li>
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<li>当 <span class="arithmatex">\(j\)</span> 等于 <span class="arithmatex">\(2\)</span> ,即上一轮跳了 <span class="arithmatex">\(2\)</span> 阶时,这一轮可选择跳 <span class="arithmatex">\(1\)</span> 阶或跳 <span class="arithmatex">\(2\)</span> 阶;</li>
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</ul>
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</ul>
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<p><img alt="考虑约束下的递推关系" src="../intro_to_dynamic_programming.assets/climbing_stairs_constraint_state_transfer.png" /></p>
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<p align="center"> Fig. 考虑约束下的递推关系 </p>
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<p>在该定义下,<span class="arithmatex">\(dp[i, j]\)</span> 表示状态 <span class="arithmatex">\([i, j]\)</span> 对应的方案数。由此,我们便能推导出以下的状态转移方程:</p>
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<p>在该定义下,<span class="arithmatex">\(dp[i, j]\)</span> 表示状态 <span class="arithmatex">\([i, j]\)</span> 对应的方案数。由此,我们便能推导出以下的状态转移方程:</p>
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<div class="arithmatex">\[
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<div class="arithmatex">\[
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\begin{cases}
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\begin{cases}
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@ -3035,6 +3032,9 @@ dp[i, 1] = dp[i-1, 2] \\
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dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
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dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
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\end{cases}
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\end{cases}
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\]</div>
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\]</div>
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<p><img alt="考虑约束下的递推关系" src="../intro_to_dynamic_programming.assets/climbing_stairs_constraint_state_transfer.png" /></p>
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<p align="center"> Fig. 考虑约束下的递推关系 </p>
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<p>最终,返回 <span class="arithmatex">\(dp[n, 1] + dp[n, 2]\)</span> 即可,两者之和代表爬到第 <span class="arithmatex">\(n\)</span> 阶的方案总数。</p>
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<p>最终,返回 <span class="arithmatex">\(dp[n, 1] + dp[n, 2]\)</span> 即可,两者之和代表爬到第 <span class="arithmatex">\(n\)</span> 阶的方案总数。</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="8:11"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Java</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Python</label><label for="__tabbed_8_4">Go</label><label for="__tabbed_8_5">JavaScript</label><label for="__tabbed_8_6">TypeScript</label><label for="__tabbed_8_7">C</label><label for="__tabbed_8_8">C#</label><label for="__tabbed_8_9">Swift</label><label for="__tabbed_8_10">Zig</label><label for="__tabbed_8_11">Dart</label></div>
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