leetcode-problemset/leetcode-cn/originData/trionic-array-ii.json

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        "question": {
            "questionId": "3956",
            "questionFrontendId": "3640",
            "categoryTitle": "Algorithms",
            "boundTopicId": 3740138,
            "title": "Trionic Array II",
            "titleSlug": "trionic-array-ii",
            "content": "<p data-end=\"191\" data-start=\"0\">You are given an integer array <code data-end=\"61\" data-start=\"55\">nums</code> of length <code data-end=\"75\" data-start=\"72\">n</code>.</p>\n\n<p data-end=\"191\" data-start=\"0\">A <strong data-end=\"99\" data-is-only-node=\"\" data-start=\"79\">trionic subarray</strong> is a contiguous subarray <code data-end=\"136\" data-start=\"125\">nums[l...r]</code> (with <code data-end=\"158\" data-start=\"143\">0 &lt;= l &lt; r &lt; n</code>) for which there exist indices <code>l &lt; p &lt; q &lt; r</code> such that:</p>\n\n<ul>\n\t<li data-end=\"267\" data-start=\"230\"><code data-end=\"241\" data-start=\"230\">nums[l...p]</code> is <strong>strictly</strong> increasing,</li>\n\t<li data-end=\"307\" data-start=\"270\"><code data-end=\"281\" data-start=\"270\">nums[p...q]</code> is <strong>strictly</strong> decreasing,</li>\n\t<li data-end=\"347\" data-start=\"310\"><code data-end=\"321\" data-start=\"310\">nums[q...r]</code> is <strong>strictly</strong> increasing.</li>\n</ul>\n\n<p data-end=\"609\" data-is-last-node=\"\" data-is-only-node=\"\" data-start=\"349\">Return the <strong>maximum</strong> sum of any trionic subarray in <code data-end=\"417\" data-start=\"411\">nums</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [0,-2,-1,-3,0,2,-1]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">-4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p data-end=\"129\" data-start=\"72\">Pick <code data-end=\"99\" data-start=\"92\">l = 1</code>, <code data-end=\"108\" data-start=\"101\">p = 2</code>, <code data-end=\"117\" data-start=\"110\">q = 3</code>, <code data-end=\"126\" data-start=\"119\">r = 5</code>:</p>\n\n<ul>\n\t<li data-end=\"203\" data-start=\"132\"><code data-end=\"166\" data-start=\"132\">nums[l...p] = nums[1...2] = [-2, -1]</code> is strictly increasing (<code data-end=\"200\" data-start=\"191\">-2 &lt; -1</code>).</li>\n\t<li data-end=\"277\" data-start=\"206\"><code data-end=\"240\" data-start=\"206\">nums[p...q] = nums[2...3] = [-1, -3]</code> is strictly decreasing (<code data-end=\"274\" data-start=\"265\">-1 &gt; -3</code>)</li>\n\t<li data-end=\"396\" data-start=\"280\"><code data-end=\"316\" data-start=\"280\">nums[q...r] = nums[3...5] = [-3, 0, 2]</code> is strictly increasing (<code data-end=\"353\" data-start=\"341\">-3 &lt; 0 &lt; 2</code>).</li>\n\t<li data-end=\"396\" data-start=\"280\">Sum = <code>(-2) + (-1) + (-3) + 0 + 2 = -4</code>.</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,4,2,7]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">14</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p data-end=\"519\" data-start=\"462\">Pick <code data-end=\"489\" data-start=\"482\">l = 0</code>, <code data-end=\"498\" data-start=\"491\">p = 1</code>, <code data-end=\"507\" data-start=\"500\">q = 2</code>, <code data-end=\"516\" data-start=\"509\">r = 3</code>:</p>\n\n<ul>\n\t<li data-end=\"589\" data-start=\"522\"><code data-end=\"554\" data-start=\"522\">nums[l...p] = nums[0...1] = [1, 4]</code> is strictly increasing (<code data-end=\"586\" data-start=\"579\">1 &lt; 4</code>).</li>\n\t<li data-end=\"659\" data-start=\"592\"><code data-end=\"624\" data-start=\"592\">nums[p...q] = nums[1...2] = [4, 2]</code> is strictly decreasing (<code data-end=\"656\" data-start=\"649\">4 &gt; 2</code>).</li>\n\t<li data-end=\"754\" data-is-last-node=\"\" data-start=\"662\"><code data-end=\"694\" data-start=\"662\">nums[q...r] = nums[2...3] = [2, 7]</code> is strictly increasing (<code data-end=\"726\" data-start=\"719\">2 &lt; 7</code>).</li>\n\t<li data-end=\"754\" data-is-last-node=\"\" data-start=\"662\">Sum = <code>1 + 4 + 2 + 7 = 14</code>.</li>\n</ul>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li data-end=\"883\" data-start=\"851\"><code data-end=\"881\" data-start=\"851\">4 &lt;= n = nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li data-end=\"914\" data-start=\"886\"><code data-end=\"912\" data-start=\"886\">-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li data-end=\"978\" data-is-last-node=\"\" data-start=\"917\">It is guaranteed that at least one trionic subarray exists.</li>\n</ul>\n",
            "translatedTitle": "三段式数组 II",
            "translatedContent": "<p data-end=\"191\" data-start=\"0\">给你一个长度为 <code data-end=\"75\" data-start=\"72\">n</code> 的整数数组 <code data-end=\"61\" data-start=\"55\">nums</code>。</p>\n\n<p data-end=\"191\" data-start=\"0\"><strong data-end=\"99\" data-is-only-node=\"\" data-start=\"79\">三段式子数组</strong> 是一个连续子数组 <code data-end=\"136\" data-start=\"125\">nums[l...r]</code>（满足 <code data-end=\"158\" data-start=\"143\">0 &lt;= l &lt; r &lt; n</code>），并且存在下标&nbsp;<code>l &lt; p &lt; q &lt; r</code>，使得：</p>\n\n<ul>\n\t<li data-end=\"267\" data-start=\"230\"><code data-end=\"241\" data-start=\"230\">nums[l...p]</code> <strong>严格</strong> 递增，</li>\n\t<li data-end=\"307\" data-start=\"270\"><code data-end=\"281\" data-start=\"270\">nums[p...q]</code> <strong>严格</strong> 递减，</li>\n\t<li data-end=\"347\" data-start=\"310\"><code data-end=\"321\" data-start=\"310\">nums[q...r]</code> <strong>严格</strong> 递增。</li>\n</ul>\n\n<p data-end=\"609\" data-is-last-node=\"\" data-is-only-node=\"\" data-start=\"349\">请你从数组 <code data-end=\"417\" data-start=\"411\">nums</code>&nbsp;的所有三段式子数组中找出和最大的那个，并返回其&nbsp;<strong>最大&nbsp;</strong>和。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">nums = [0,-2,-1,-3,0,2,-1]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">-4</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p data-end=\"129\" data-start=\"72\">选择 <code data-end=\"99\" data-start=\"92\">l = 1</code>, <code data-end=\"108\" data-start=\"101\">p = 2</code>, <code data-end=\"117\" data-start=\"110\">q = 3</code>, <code data-end=\"126\" data-start=\"119\">r = 5</code>：</p>\n\n<ul>\n\t<li data-end=\"203\" data-start=\"132\"><code data-end=\"166\" data-start=\"132\">nums[l...p] = nums[1...2] = [-2, -1]</code> 严格递增&nbsp;(<code data-end=\"200\" data-start=\"191\">-2 &lt; -1</code>)。</li>\n\t<li data-end=\"277\" data-start=\"206\"><code data-end=\"240\" data-start=\"206\">nums[p...q] = nums[2...3] = [-1, -3]</code> 严格递减&nbsp;(<code data-end=\"274\" data-start=\"265\">-1 &gt; -3</code>)。</li>\n\t<li data-end=\"396\" data-start=\"280\"><code data-end=\"316\" data-start=\"280\">nums[q...r] = nums[3...5] = [-3, 0, 2]</code> 严格递增&nbsp;(<code data-end=\"353\" data-start=\"341\">-3 &lt; 0 &lt; 2</code>)。</li>\n\t<li data-end=\"396\" data-start=\"280\">和 = <code>(-2) + (-1) + (-3) + 0 + 2 = -4</code>。</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">示例 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">nums = [1,4,2,7]</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">14</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p data-end=\"519\" data-start=\"462\">选择 <code data-end=\"489\" data-start=\"482\">l = 0</code>, <code data-end=\"498\" data-start=\"491\">p = 1</code>, <code data-end=\"507\" data-start=\"500\">q = 2</code>, <code data-end=\"516\" data-start=\"509\">r = 3</code>：</p>\n\n<ul>\n\t<li data-end=\"589\" data-start=\"522\"><code data-end=\"554\" data-start=\"522\">nums[l...p] = nums[0...1] = [1, 4]</code> 严格递增&nbsp;(<code data-end=\"586\" data-start=\"579\">1 &lt; 4</code>)。</li>\n\t<li data-end=\"659\" data-start=\"592\"><code data-end=\"624\" data-start=\"592\">nums[p...q] = nums[1...2] = [4, 2]</code> 严格递减&nbsp;(<code data-end=\"656\" data-start=\"649\">4 &gt; 2</code>)。</li>\n\t<li data-end=\"754\" data-is-last-node=\"\" data-start=\"662\"><code data-end=\"694\" data-start=\"662\">nums[q...r] = nums[2...3] = [2, 7]</code> 严格递增&nbsp;(<code data-end=\"726\" data-start=\"719\">2 &lt; 7</code>)。</li>\n\t<li data-end=\"754\" data-is-last-node=\"\" data-start=\"662\">和 = <code>1 + 4 + 2 + 7 = 14</code>。</li>\n</ul>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li data-end=\"883\" data-start=\"851\"><code data-end=\"881\" data-start=\"851\">4 &lt;= n = nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li data-end=\"914\" data-start=\"886\"><code data-end=\"912\" data-start=\"886\">-10<sup>9</sup> &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li data-end=\"978\" data-is-last-node=\"\" data-start=\"917\">保证至少存在一个三段式子数组。</li>\n</ul>\n",
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                "Use dynamic programming",
                "Let four arrays <code>dp0...dp3</code> where <code>dpk[i]</code> is the max sum of a subarray ending at <code>i</code> after finishing <code>k</code> of the four phases (start -> inc -> dec -> inc)",
                "Process each <code>i>0</code>",
                "If <code>nums[i]>nums[i‑1]</code>, set <code>dp1[i]=max(dp1[i‑1]+nums[i], dp0[i‑1]+nums[i])</code>, <code>dp3[i]=max(dp3[i‑1]+nums[i], dp2[i‑1]+nums[i])</code>",
                "If <code>nums[i]<nums[i‑1]</code>, set <code>dp2[i]=max(dp2[i‑1]+nums[i], dp1[i‑1]+nums[i])</code>",
                "Always carry over <code>dp0[i]=dp0[i‑1]+nums[i]</code> when <code>nums[i]>nums[i‑1]</code>",
                "Return the maximum value in <code>dp3</code>"
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target=\\\"_blank\\\">\\u300c\\u4ed3\\u9889\\u7f16\\u7a0b\\u8bed\\u8a00\\u5f00\\u53d1\\u6307\\u5357\\u300d<\\/a><\\/p>\"]}",
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