leetcode-problemset/leetcode-cn/originData/maximum-fruits-harvested-after-at-most-k-steps.json

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            "questionId": "2229",
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            "categoryTitle": "Algorithms",
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            "title": "Maximum Fruits Harvested After at Most K Steps",
            "titleSlug": "maximum-fruits-harvested-after-at-most-k-steps",
            "content": "<p>Fruits are available at some positions on an infinite x-axis. You are given a 2D integer array <code>fruits</code> where <code>fruits[i] = [position<sub>i</sub>, amount<sub>i</sub>]</code> depicts <code>amount<sub>i</sub></code> fruits at the position <code>position<sub>i</sub></code>. <code>fruits</code> is already <strong>sorted</strong> by <code>position<sub>i</sub></code> in <strong>ascending order</strong>, and each <code>position<sub>i</sub></code> is <strong>unique</strong>.</p>\n\n<p>You are also given an integer <code>startPos</code> and an integer <code>k</code>. Initially, you are at the position <code>startPos</code>. From any position, you can either walk to the <strong>left or right</strong>. It takes <strong>one step</strong> to move <strong>one unit</strong> on the x-axis, and you can walk <strong>at most</strong> <code>k</code> steps in total. For every position you reach, you harvest all the fruits at that position, and the fruits will disappear from that position.</p>\n\n<p>Return <em>the <strong>maximum total number</strong> of fruits you can harvest</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/11/21/1.png\" style=\"width: 472px; height: 115px;\" />\n<pre>\n<strong>Input:</strong> fruits = [[2,8],[6,3],[8,6]], startPos = 5, k = 4\n<strong>Output:</strong> 9\n<strong>Explanation:</strong> \nThe optimal way is to:\n- Move right to position 6 and harvest 3 fruits\n- Move right to position 8 and harvest 6 fruits\nYou moved 3 steps and harvested 3 + 6 = 9 fruits in total.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/11/21/2.png\" style=\"width: 512px; height: 129px;\" />\n<pre>\n<strong>Input:</strong> fruits = [[0,9],[4,1],[5,7],[6,2],[7,4],[10,9]], startPos = 5, k = 4\n<strong>Output:</strong> 14\n<strong>Explanation:</strong> \nYou can move at most k = 4 steps, so you cannot reach position 0 nor 10.\nThe optimal way is to:\n- Harvest the 7 fruits at the starting position 5\n- Move left to position 4 and harvest 1 fruit\n- Move right to position 6 and harvest 2 fruits\n- Move right to position 7 and harvest 4 fruits\nYou moved 1 + 3 = 4 steps and harvested 7 + 1 + 2 + 4 = 14 fruits in total.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/11/21/3.png\" style=\"width: 476px; height: 100px;\" />\n<pre>\n<strong>Input:</strong> fruits = [[0,3],[6,4],[8,5]], startPos = 3, k = 2\n<strong>Output:</strong> 0\n<strong>Explanation:</strong>\nYou can move at most k = 2 steps and cannot reach any position with fruits.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= fruits.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>fruits[i].length == 2</code></li>\n\t<li><code>0 &lt;= startPos, position<sub>i</sub> &lt;= 2 * 10<sup>5</sup></code></li>\n\t<li><code>position<sub>i-1</sub> &lt; position<sub>i</sub></code> for any <code>i &gt; 0</code>&nbsp;(<strong>0-indexed</strong>)</li>\n\t<li><code>1 &lt;= amount<sub>i</sub> &lt;= 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= 2 * 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "摘水果",
            "translatedContent": "<p>在一个无限的 x 坐标轴上，有许多水果分布在其中某些位置。给你一个二维整数数组 <code>fruits</code> ，其中 <code>fruits[i] = [position<sub>i</sub>, amount<sub>i</sub>]</code> 表示共有 <code>amount<sub>i</sub></code> 个水果放置在 <code>position<sub>i</sub></code> 上。<code>fruits</code> 已经按 <code>position<sub>i</sub></code> <strong>升序排列</strong> ，每个 <code>position<sub>i</sub></code> <strong>互不相同</strong> 。</p>\n\n<p>另给你两个整数 <code>startPos</code> 和 <code>k</code> 。最初，你位于 <code>startPos</code> 。从任何位置，你可以选择 <strong>向左或者向右</strong> 走。在 x 轴上每移动 <strong>一个单位</strong> ，就记作 <strong>一步</strong> 。你总共可以走 <strong>最多</strong> <code>k</code> 步。你每达到一个位置，都会摘掉全部的水果，水果也将从该位置消失（不会再生）。</p>\n\n<p>返回你可以摘到水果的 <strong>最大总数</strong> 。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/11/21/1.png\" style=\"width: 472px; height: 115px;\">\n<pre><strong>输入：</strong>fruits = [[2,8],[6,3],[8,6]], startPos = 5, k = 4\n<strong>输出：</strong>9\n<strong>解释：</strong>\n最佳路线为：\n- 向右移动到位置 6 ，摘到 3 个水果\n- 向右移动到位置 8 ，摘到 6 个水果\n移动 3 步，共摘到 3 + 6 = 9 个水果\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/11/21/2.png\" style=\"width: 512px; height: 129px;\">\n<pre><strong>输入：</strong>fruits = [[0,9],[4,1],[5,7],[6,2],[7,4],[10,9]], startPos = 5, k = 4\n<strong>输出：</strong>14\n<strong>解释：</strong>\n可以移动最多 k = 4 步，所以无法到达位置 0 和位置 10 。\n最佳路线为：\n- 在初始位置 5 ，摘到 7 个水果\n- 向左移动到位置 4 ，摘到 1 个水果\n- 向右移动到位置 6 ，摘到 2 个水果\n- 向右移动到位置 7 ，摘到 4 个水果\n移动 1 + 3 = 4 步，共摘到 7 + 1 + 2 + 4 = 14 个水果\n</pre>\n\n<p><strong>示例 3：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/11/21/3.png\" style=\"width: 476px; height: 100px;\">\n<pre><strong>输入：</strong>fruits = [[0,3],[6,4],[8,5]], startPos = 3, k = 2\n<strong>输出：</strong>0\n<strong>解释：</strong>\n最多可以移动 k = 2 步，无法到达任一有水果的地方\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= fruits.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>fruits[i].length == 2</code></li>\n\t<li><code>0 &lt;= startPos, position<sub>i</sub> &lt;= 2 * 10<sup>5</sup></code></li>\n\t<li>对于任意 <code>i &gt; 0</code> ，<code>position<sub>i-1</sub> &lt; position<sub>i</sub></code> 均成立（下标从 <strong>0</strong> 开始计数）</li>\n\t<li><code>1 &lt;= amount<sub>i</sub> &lt;= 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= 2 * 10<sup>5</sup></code></li>\n</ul>\n",
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                "Does an optimal path have very few patterns? For example, could a path that goes left, turns and goes right, then turns again and goes left be any better than a path that simply goes left, turns, and goes right?",
                "The optimal path turns at most once. That is, the optimal path is one of these: to go left only; to go right only; to go left, turn and go right; or to go right, turn and go left.",
                "Moving x steps left then k-x steps right gives you a range of positions that you can reach.",
                "Use prefix sums to get the sum of all fruits for each possible range.",
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1.17<\\/code><\\/p>\\r\\n\\r\\n<p>\\u652f\\u6301 <a href=\\\"https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap \\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 <a href=\\\"http:\\/\\/www.grantjenks.com\\/docs\\/sortedcontainers\\/\\\" target=\\\"_blank\\\">sortedcontainers<\\/a> \\u5e93\\u3002<\\/p>\"],\"scala\":[\"Scala\",\"<p>\\u7248\\u672c\\uff1a<code>Scala 2.13<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"<p>\\u7248\\u672c\\uff1a<code>Kotlin 1.3.10<\\/code><\\/p>\"],\"rust\":[\"Rust\",\"<p>\\u7248\\u672c\\uff1a<code>rust 1.58.1<\\/code><\\/p>\\r\\n\\r\\n<p>\\u652f\\u6301 crates.io \\u7684 <a href=\\\"https:\\/\\/crates.io\\/crates\\/rand\\\" target=\\\"_blank\\\">rand<\\/a><\\/p>\"],\"php\":[\"PHP\",\"<p><code>PHP 8.1<\\/code>.<\\/p>\\r\\n\\r\\n<p>With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"<p>TypeScript 4.5.4<\\/p>\\r\\n\\r\\n<p>Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2020<\\/p>\"],\"racket\":[\"Racket\",\"<p><a href=\\\"https:\\/\\/docs.racket-lang.org\\/guide\\/performance.html#%28tech._c%29\\\" target=\\\"_blank\\\">Racket CS<\\/a> v8.3<\\/p>\\r\\n\\r\\n<p>\\u4f7f\\u7528 #lang racket<\\/p>\\r\\n\\r\\n<p>\\u5df2\\u9884\\u5148 (require data\\/gvector data\\/queue data\\/order data\\/heap). \\u82e5\\u9700\\u4f7f\\u7528\\u5176\\u5b83\\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u53ef\\u81ea\\u884c require\\u3002<\\/p>\"],\"erlang\":[\"Erlang\",\"Erlang\\/OTP 24.2\"],\"elixir\":[\"Elixir\",\"Elixir 1.13.0 with Erlang\\/OTP 24.2\"]}",
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