https://shio-chan-dev.github.io/jeanblog/tags/1d-dp/Recent content in 1D DP on Jeanphilo BlogHugo -- 0.161.1en-usSun, 03 May 2026 14:33:39 +0800https://shio-chan-dev.github.io/jeanblog/alg/leetcode/hot100/198-house-robber/Sun, 03 May 2026 14:33:39 +0800https://shio-chan-dev.github.io/jeanblog/alg/leetcode/hot100/198-house-robber/<h2 id="problem">Problem</h2> <h3 id="input-and-output">Input and Output</h3> <ul> <li>Input: an integer array <code>nums</code></li> <li><code>nums[i]</code> is the money in the <code>i</code>-th house</li> <li>Adjacent houses cannot both be robbed</li> <li>Output: return the maximum amount of money that can be robbed</li> <li>Constraints: <code>1 &lt;= nums.length &lt;= 100</code>, <code>0 &lt;= nums[i] &lt;= 400</code></li> </ul> <h3 id="examples">Examples</h3> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;"><code class="language-text" data-lang="text"><span style="display:flex;"><span>Input: nums = [1,2,3,1] </span></span><span style="display:flex;"><span>Output: 4 </span></span><span style="display:flex;"><span>Explanation: rob indices 0 and 2, for 1 + 3 = 4 </span></span></code></pre></div><div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;"><code class="language-text" data-lang="text"><span style="display:flex;"><span>Input: nums = [2,7,9,3,1] </span></span><span style="display:flex;"><span>Output: 12 </span></span><span style="display:flex;"><span>Explanation: rob indices 0, 2, and 4, for 2 + 9 + 1 = 12 </span></span></code></pre></div><p>This article uses Python only and derives 1D DP from the conflict between two choices.</p>https://shio-chan-dev.github.io/jeanblog/alg/leetcode/70-climbing-stairs/Sun, 03 May 2026 14:33:39 +0800https://shio-chan-dev.github.io/jeanblog/alg/leetcode/70-climbing-stairs/<h2 id="problem">Problem</h2> <h3 id="input-and-output">Input and Output</h3> <ul> <li>Input: an integer <code>n</code></li> <li>Meaning: climb to the top of the <code>n</code>-step staircase</li> <li>Each move can climb <code>1</code> or <code>2</code> steps</li> <li>Output: return the number of distinct ways to reach the top</li> <li>Constraints: <code>1 &lt;= n &lt;= 45</code></li> </ul> <h3 id="examples">Examples</h3> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;"><code class="language-text" data-lang="text"><span style="display:flex;"><span>Input: n = 2 </span></span><span style="display:flex;"><span>Output: 2 </span></span><span style="display:flex;"><span>Explanation: 1+1, 2 </span></span></code></pre></div><div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;"><code class="language-text" data-lang="text"><span style="display:flex;"><span>Input: n = 3 </span></span><span style="display:flex;"><span>Output: 3 </span></span><span style="display:flex;"><span>Explanation: 1+1+1, 1+2, 2+1 </span></span></code></pre></div><p>This article uses Python only and derives the final solution step by step from the meaning of <code>dp[i]</code>.</p>https://shio-chan-dev.github.io/jeanblog/alg/leetcode/746-min-cost-climbing-stairs/Sun, 03 May 2026 14:33:39 +0800https://shio-chan-dev.github.io/jeanblog/alg/leetcode/746-min-cost-climbing-stairs/<h2 id="problem">Problem</h2> <h3 id="input-and-output">Input and Output</h3> <ul> <li>Input: an integer array <code>cost</code></li> <li><code>cost[i]</code> is the cost of stepping on stair <code>i</code></li> <li>Each move can climb <code>1</code> or <code>2</code> steps</li> <li>You may start from index <code>0</code> or index <code>1</code></li> <li>Output: return the minimum cost to reach the top</li> <li>Constraints: <code>2 &lt;= cost.length &lt;= 1000</code>, <code>0 &lt;= cost[i] &lt;= 999</code></li> </ul> <h3 id="examples">Examples</h3> <div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;"><code class="language-text" data-lang="text"><span style="display:flex;"><span>Input: cost = [10,15,20] </span></span><span style="display:flex;"><span>Output: 15 </span></span><span style="display:flex;"><span>Explanation: start from index 1, pay 15, then reach the top directly </span></span></code></pre></div><div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;"><code class="language-text" data-lang="text"><span style="display:flex;"><span>Input: cost = [1,100,1,1,1,100,1,1,100,1] </span></span><span style="display:flex;"><span>Output: 6 </span></span></code></pre></div><h2 id="start-from-the-top-position-of-101520">Start from the Top Position of [10,15,20]</h2> <p>Look at the small example:</p>