leetcode-problemset/leetcode-cn/originData/minimum-levels-to-gain-more-points.json

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        "question": {
            "questionId": "3355",
            "questionFrontendId": "3096",
            "categoryTitle": "Algorithms",
            "boundTopicId": 2713737,
            "title": "Minimum Levels to Gain More Points",
            "titleSlug": "minimum-levels-to-gain-more-points",
            "content": "<p>You are given a binary array <code>possible</code> of length <code>n</code>.</p>\n\n<p>Alice and Bob are playing a game that consists of <code>n</code> levels. Some of the levels in the game are <strong>impossible</strong> to clear while others can <strong>always</strong> be cleared. In particular, if <code>possible[i] == 0</code>, then the <code>i<sup>th</sup></code> level is <strong>impossible</strong> to clear for <strong>both</strong> the players. A player gains <code>1</code> point on clearing a level and loses <code>1</code> point if the player fails to clear it.</p>\n\n<p>At the start of the game, Alice will play some levels in the <strong>given order</strong> starting from the <code>0<sup>th</sup></code> level, after which Bob will play for the rest of the levels.</p>\n\n<p>Alice wants to know the <strong>minimum</strong> number of levels she should play to gain more points than Bob, if both players play optimally to <strong>maximize</strong> their points.</p>\n\n<p>Return <em>the <strong>minimum</strong> number of levels Alice should play to gain more points</em>. <em>If this is <strong>not</strong> possible, return</em> <code>-1</code>.</p>\n\n<p><strong>Note</strong> that each player must play at least <code>1</code> level.</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\">possible = [1,0,1,0]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Let&#39;s look at all the levels that Alice can play up to:</p>\n\n<ul>\n\t<li>If Alice plays only level 0 and Bob plays the rest of the levels, Alice has 1 point, while Bob has -1 + 1 - 1 = -1 point.</li>\n\t<li>If Alice plays till level 1 and Bob plays the rest of the levels, Alice has 1 - 1 = 0 points, while Bob has 1 - 1 = 0 points.</li>\n\t<li>If Alice plays till level 2 and Bob plays the rest of the levels, Alice has 1 - 1 + 1 = 1 point, while Bob has -1 point.</li>\n</ul>\n\n<p>Alice must play a minimum of 1 level to gain more points.</p>\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\">possible = [1,1,1,1,1]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Let&#39;s look at all the levels that Alice can play up to:</p>\n\n<ul>\n\t<li>If Alice plays only level 0 and Bob plays the rest of the levels, Alice has 1 point, while Bob has 4 points.</li>\n\t<li>If Alice plays till level 1 and Bob plays the rest of the levels, Alice has 2 points, while Bob has 3 points.</li>\n\t<li>If Alice plays till level 2 and Bob plays the rest of the levels, Alice has 3 points, while Bob has 2 points.</li>\n\t<li>If Alice plays till level 3 and Bob plays the rest of the levels, Alice has 4 points, while Bob has 1 point.</li>\n</ul>\n\n<p>Alice must play a minimum of 3 levels to gain more points.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">possible = [0,0]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">-1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The only possible way is for both players to play 1 level each. Alice plays level 0 and loses 1 point. Bob plays level 1 and loses 1 point. As both players have equal points, Alice can&#39;t gain more points than Bob.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n == possible.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>possible[i]</code> is either <code>0</code> or <code>1</code>.</li>\n</ul>\n",
            "translatedTitle": "得到更多分数的最少关卡数目",
            "translatedContent": "<p>给你一个长度为 <code>n</code>&nbsp;的二进制数组&nbsp;<code>possible</code>&nbsp;。</p>\n\n<p>Alice 和 Bob 正在玩一个有 <code>n</code> 个关卡的游戏，游戏中有一些关卡是 <strong>困难</strong>&nbsp;模式，其他的关卡是 <strong>简单</strong>&nbsp;模式。如果&nbsp;<code>possible[i] == 0</code>&nbsp;，那么第&nbsp;<code>i</code> 个关卡是 <strong>困难</strong>&nbsp;模式，两个玩家&nbsp;<strong>都不可能</strong> 通过。一个玩家通过一个简单模式的关卡可以获得 <code>1</code>&nbsp;分，遇到困难模式的关卡将失去 <code>1</code>&nbsp;分。</p>\n\n<p>游戏的一开始，Alice 将从第 <code>0</code>&nbsp;级开始 <strong>按顺序</strong> 完成一些关卡，然后 Bob 会完成剩下的所有关卡。</p>\n\n<p>假设两名玩家都采取最优策略，目的是&nbsp;<strong>最大化</strong>&nbsp;自己的得分，Alice 想知道自己&nbsp;<strong>最少</strong> 需要完成多少个关卡，才能获得比 Bob 更多的分数。</p>\n\n<p>请你返回 Alice 获得比 Bob 更多的分数所需要完成的 <strong>最少</strong> 关卡数目，如果 <strong>无法</strong>&nbsp;达成，那么返回 <code>-1</code>&nbsp;。</p>\n\n<p><strong>注意</strong>，每个玩家都至少需要完成&nbsp;<code>1</code> 个关卡。</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><span class=\"example-io\"><b>输入：</b>possible = [1,0,1,0]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>1</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>我们来看一下 Alice 可以完成的关卡数目：</p>\n\n<ul>\n\t<li>如果 Alice 只完成关卡 0 ，Bob 完成剩下的所有关卡，那么 Alice 获得 1 分，Bob 获得 -1 + 1 - 1 = -1 分。</li>\n\t<li>如果 Alice 完成到关卡 1 ，Bob 完成剩下的所有关卡，那么 Alice 获得&nbsp;1 - 1 = 0 分，Bob 获得 1 - 1 = 0 分。</li>\n\t<li>如果 Alice 完成到关卡 2 ，Bob 完成剩下的所有关卡，那么 Alice 获得&nbsp;1 - 1 + 1 = 1 分，Bob 获得 -1 分。</li>\n</ul>\n\n<p>Alice 需要完成至少一个关卡获得更多的分数。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>possible = [1,1,1,1,1]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>3</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>我们来看一下 Alice 可以完成的关卡数目：</p>\n\n<ul>\n\t<li>如果 Alice 只完成关卡 0 ，Bob 完成剩下的所有关卡，那么 Alice 获得 1 分，Bob 获得 4 分。</li>\n\t<li>如果 Alice 完成到关卡 1 ，Bob 完成剩下的所有关卡，那么 Alice 获得&nbsp;2 分，Bob 获得 3 分。</li>\n\t<li>如果 Alice 完成到关卡 2 ，Bob 完成剩下的所有关卡，那么 Alice 获得&nbsp;3 分，Bob 获得 2&nbsp;分。</li>\n\t<li>如果 Alice 完成到关卡 3&nbsp;，Bob 完成剩下的所有关卡，那么 Alice 获得 4&nbsp;分，Bob 获得 1&nbsp;分。</li>\n</ul>\n\n<p>Alice 需要完成至少三个关卡获得更多的分数。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>possible = [0,0]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>-1</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>两名玩家只能各完成 1 个关卡，Alice 完成关卡 0 得到 -1 分，Bob 完成关卡 1 得到 -1 分。两名玩家得分相同，所以 Alice 无法得到更多分数。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n == possible.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>possible[i]</code>&nbsp;要么是&nbsp;<code>0</code>&nbsp;要么是&nbsp;<code>1</code> 。</li>\n</ul>\n",
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\\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.11<\\/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 3.3.1<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"<p>\\u7248\\u672c\\uff1a<code>Kotlin 1.9.0<\\/code><\\/p>\\r\\n\\r\\n<p>\\u6211\\u4eec\\u4f7f\\u7528\\u7684\\u662f JetBrains \\u63d0\\u4f9b\\u7684 experimental compiler\\u3002\\u5982\\u679c\\u60a8\\u8ba4\\u4e3a\\u60a8\\u9047\\u5230\\u4e86\\u7f16\\u8bd1\\u5668\\u76f8\\u5173\\u7684\\u95ee\\u9898\\uff0c\\u8bf7\\u5411\\u6211\\u4eec\\u53cd\\u9988<\\/p>\"],\"rust\":[\"Rust\",\"<p>\\u7248\\u672c\\uff1a<code>rust 1.79.0<\\/code><\\/p>\\r\\n\\r\\n<p>\\u652f\\u6301 crates.io \\u7684 <a href=\\\"https:\\/\\/crates.io\\/crates\\/rand\\\" target=\\\"_blank\\\">rand<\\/a> \\u548c <a href=\\\"https:\\/\\/crates.io\\/crates\\/regex\\\" target=\\\"_blank\\\">regex<\\/a><\\/p>\"],\"php\":[\"PHP\",\"<p><code>PHP 8.2<\\/code>.<\\/p>\\r\\n\\r\\n<p>With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"<p>TypeScript 5.1.6<\\/p>\\r\\n\\r\\n<p>Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2022<\\/p>\\r\\n\\r\\n<p><a href=\\\"https:\\/\\/lodash.com\\\" target=\\\"_blank\\\">lodash.js<\\/a> \\u5e93\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5305\\u542b\\u3002<\\/p>\\r\\n\\r\\n<p> \\u5982\\u9700\\u4f7f\\u7528\\u961f\\u5217\\/\\u4f18\\u5148\\u961f\\u5217\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 <a href=\\\"https:\\/\\/github.com\\/datastructures-js\\/priority-queue\\/blob\\/v5\\/README.md\\\" target=\\\"_blank\\\"> datastructures-js\\/priority-queue@5.4.0<\\/a>\\uff0c<a href=\\\"https:\\/\\/github.com\\/datastructures-js\\/queue\\/tree\\/v4.2.3\\\" target=\\\"_blank\\\"> datastructures-js\\/queue@4.2.3<\\/a> \\u4ee5\\u53ca <a href=\\\"https:\\/\\/github.com\\/datastructures-js\\/deque\\/tree\\/v1.0.4\\\" target=\\\"_blank\\\"> datastructures-js\\/deque@1.0.4<\\/a>\\u3002<\\/p>\"],\"racket\":[\"Racket\",\"<p><a href=\\\"https:\\/\\/docs.racket-lang.org\\/guide\\/performance.html#%28tech._c%29\\\" target=\\\"_blank\\\">Racket CS<\\/a> v8.15<\\/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 26\"],\"elixir\":[\"Elixir\",\"Elixir 1.17 with Erlang\\/OTP 26\"],\"dart\":[\"Dart\",\"<p>Dart 3.2\\u3002\\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 <a href=\\\"https:\\/\\/pub.dev\\/packages\\/collection\\/versions\\/1.18.0\\\" target=\\\"_blank\\\">collection<\\/a> \\u5305<\\/p>\\r\\n\\r\\n<p>\\u60a8\\u7684\\u4ee3\\u7801\\u5c06\\u4f1a\\u88ab\\u4e0d\\u7f16\\u8bd1\\u76f4\\u63a5\\u8fd0\\u884c<\\/p>\"],\"cangjie\":[\"Cangjie\",\"<p>\\u7248\\u672c\\uff1a0.53.11 (cjnative)<\\/p>\\r\\n\\r\\n<p>\\u7f16\\u8bd1\\u53c2\\u6570\\uff1a<code>-O2 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