leetcode-problemset/leetcode-cn/originData/guess-number-higher-or-lower-ii.json

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            "title": "Guess Number Higher or Lower II",
            "titleSlug": "guess-number-higher-or-lower-ii",
            "content": "<p>We are playing the Guessing Game. The game will work as follows:</p>\n\n<ol>\n\t<li>I pick a number between&nbsp;<code>1</code>&nbsp;and&nbsp;<code>n</code>.</li>\n\t<li>You guess a number.</li>\n\t<li>If you guess the right number, <strong>you win the game</strong>.</li>\n\t<li>If you guess the wrong number, then I will tell you whether the number I picked is <strong>higher or lower</strong>, and you will continue guessing.</li>\n\t<li>Every time you guess a wrong number&nbsp;<code>x</code>, you will pay&nbsp;<code>x</code>&nbsp;dollars. If you run out of money, <strong>you lose the game</strong>.</li>\n</ol>\n\n<p>Given a particular&nbsp;<code>n</code>, return&nbsp;<em>the minimum amount of money you need to&nbsp;<strong>guarantee a win regardless of what number I pick</strong></em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/09/10/graph.png\" style=\"width: 505px; height: 388px;\" />\n<pre>\n<strong>Input:</strong> n = 10\n<strong>Output:</strong> 16\n<strong>Explanation:</strong> The winning strategy is as follows:\n- The range is [1,10]. Guess 7.\n&nbsp;   - If this is my number, your total is $0. Otherwise, you pay $7.\n&nbsp;   - If my number is higher, the range is [8,10]. Guess 9.\n&nbsp;       - If this is my number, your total is $7. Otherwise, you pay $9.\n&nbsp;       - If my number is higher, it must be 10. Guess 10. Your total is $7 + $9 = $16.\n&nbsp;       - If my number is lower, it must be 8. Guess 8. Your total is $7 + $9 = $16.\n&nbsp;   - If my number is lower, the range is [1,6]. Guess 3.\n&nbsp;       - If this is my number, your total is $7. Otherwise, you pay $3.\n&nbsp;       - If my number is higher, the range is [4,6]. Guess 5.\n&nbsp;           - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $5.\n&nbsp;           - If my number is higher, it must be 6. Guess 6. Your total is $7 + $3 + $5 = $15.\n&nbsp;           - If my number is lower, it must be 4. Guess 4. Your total is $7 + $3 + $5 = $15.\n&nbsp;       - If my number is lower, the range is [1,2]. Guess 1.\n&nbsp;           - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $1.\n&nbsp;           - If my number is higher, it must be 2. Guess 2. Your total is $7 + $3 + $1 = $11.\nThe worst case in all these scenarios is that you pay $16. Hence, you only need $16 to guarantee a win.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1\n<strong>Output:</strong> 0\n<strong>Explanation:</strong>&nbsp;There is only one possible number, so you can guess 1 and not have to pay anything.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2\n<strong>Output:</strong> 1\n<strong>Explanation:</strong>&nbsp;There are two possible numbers, 1 and 2.\n- Guess 1.\n&nbsp;   - If this is my number, your total is $0. Otherwise, you pay $1.\n&nbsp;   - If my number is higher, it must be 2. Guess 2. Your total is $1.\nThe worst case is that you pay $1.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 200</code></li>\n</ul>\n",
            "translatedTitle": "猜数字大小 II",
            "translatedContent": "<p>我们正在玩一个猜数游戏，游戏规则如下：</p>\n\n<ol>\n\t<li>我从&nbsp;<code>1</code><strong>&nbsp;</strong>到 <code>n</code> 之间选择一个数字。</li>\n\t<li>你来猜我选了哪个数字。</li>\n\t<li>如果你猜到正确的数字，就会 <strong>赢得游戏</strong> 。</li>\n\t<li>如果你猜错了，那么我会告诉你，我选的数字比你的 <strong>更大或者更小</strong> ，并且你需要继续猜数。</li>\n\t<li>每当你猜了数字 <code>x</code> 并且猜错了的时候，你需要支付金额为 <code>x</code> 的现金。如果你花光了钱，就会<strong> 输掉游戏</strong> 。</li>\n</ol>\n\n<p>给你一个特定的数字 <code>n</code> ，返回能够 <strong>确保你获胜</strong> 的最小现金数，<strong>不管我选择那个数字</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/2020/09/10/graph.png\" style=\"width: 505px; height: 388px;\" />\n<pre>\n<strong>输入：</strong>n = 10\n<strong>输出：</strong>16\n<strong>解释：</strong>制胜策略如下：\n- 数字范围是 [1,10] 。你先猜测数字为 7 。\n&nbsp;   - 如果这是我选中的数字，你的总费用为 $0 。否则，你需要支付 $7 。\n&nbsp;   - 如果我的数字更大，则下一步需要猜测的数字范围是 [8,10] 。你可以猜测数字为 9 。\n&nbsp;       - 如果这是我选中的数字，你的总费用为 $7 。否则，你需要支付 $9 。\n&nbsp;       - 如果我的数字更大，那么这个数字一定是 10 。你猜测数字为 10 并赢得游戏，总费用为 $7 + $9 = $16 。\n&nbsp;       - 如果我的数字更小，那么这个数字一定是 8 。你猜测数字为 8 并赢得游戏，总费用为 $7 + $9 = $16 。\n&nbsp;   - 如果我的数字更小，则下一步需要猜测的数字范围是 [1,6] 。你可以猜测数字为 3 。\n&nbsp;       - 如果这是我选中的数字，你的总费用为 $7 。否则，你需要支付 $3 。\n&nbsp;       - 如果我的数字更大，则下一步需要猜测的数字范围是 [4,6] 。你可以猜测数字为 5 。\n&nbsp;           - 如果这是我选中的数字，你的总费用为 $7 + $3 = $10 。否则，你需要支付 $5 。\n&nbsp;           - 如果我的数字更大，那么这个数字一定是 6 。你猜测数字为 6 并赢得游戏，总费用为 $7 + $3 + $5 = $15 。\n&nbsp;           - 如果我的数字更小，那么这个数字一定是 4 。你猜测数字为 4 并赢得游戏，总费用为 $7 + $3 + $5 = $15 。\n&nbsp;       - 如果我的数字更小，则下一步需要猜测的数字范围是 [1,2] 。你可以猜测数字为 1 。\n&nbsp;           - 如果这是我选中的数字，你的总费用为 $7 + $3 = $10 。否则，你需要支付 $1 。\n&nbsp;           - 如果我的数字更大，那么这个数字一定是 2 。你猜测数字为 2 并赢得游戏，总费用为 $7 + $3 + $1 = $11 。\n在最糟糕的情况下，你需要支付 $16 。因此，你只需要 $16 就可以确保自己赢得游戏。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 1\n<strong>输出：</strong>0\n<strong>解释：</strong>只有一个可能的数字，所以你可以直接猜 1 并赢得游戏，无需支付任何费用。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 2\n<strong>输出：</strong>1\n<strong>解释：</strong>有两个可能的数字 1 和 2 。\n- 你可以先猜 1 。\n&nbsp;   - 如果这是我选中的数字，你的总费用为 $0 。否则，你需要支付 $1 。\n&nbsp;   - 如果我的数字更大，那么这个数字一定是 2 。你猜测数字为 2 并赢得游戏，总费用为 $1 。\n最糟糕的情况下，你需要支付 $1 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 200</code></li>\n</ul>\n",
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href=\\\"https:\\/\\/github.com\\/datastructures-js\\/queue\\\" target=\\\"_blank\\\"> datastructures-js\\/queue<\\/a>\\u3002<\\/p>\"],\"ruby\":[\"Ruby\",\"<p>\\u4f7f\\u7528<code>Ruby 3.1<\\/code>\\u6267\\u884c<\\/p>\\r\\n\\r\\n<p>\\u4e00\\u4e9b\\u5e38\\u7528\\u7684\\u6570\\u636e\\u7ed3\\u6784\\u5df2\\u5728 Algorithms \\u6a21\\u5757\\u4e2d\\u63d0\\u4f9b\\uff1ahttps:\\/\\/www.rubydoc.info\\/github\\/kanwei\\/algorithms\\/Algorithms<\\/p>\"],\"swift\":[\"Swift\",\"<p>\\u7248\\u672c\\uff1a<code>Swift 5.5.2<\\/code><\\/p>\\r\\n\\r\\n<p>\\u6211\\u4eec\\u901a\\u5e38\\u4fdd\\u8bc1\\u66f4\\u65b0\\u5230 <a href=\\\"https:\\/\\/swift.org\\/download\\/\\\" target=\\\"_blank\\\">Apple\\u653e\\u51fa\\u7684\\u6700\\u65b0\\u7248Swift<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u53d1\\u73b0Swift\\u4e0d\\u662f\\u6700\\u65b0\\u7248\\u7684\\uff0c\\u8bf7\\u8054\\u7cfb\\u6211\\u4eec\\uff01\\u6211\\u4eec\\u5c06\\u5c3d\\u5feb\\u66f4\\u65b0\\u3002<\\/p>\"],\"golang\":[\"Go\",\"<p>\\u7248\\u672c\\uff1a<code>Go 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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