{ "data": { "question": { "questionId": "375", "questionFrontendId": "375", "categoryTitle": "Algorithms", "boundTopicId": 1601, "title": "Guess Number Higher or Lower II", "titleSlug": "guess-number-higher-or-lower-ii", "content": "
We are playing the Guessing Game. The game will work as follows:
\n\n1
and n
.x
, you will pay x
dollars. If you run out of money, you lose the game.Given a particular n
, return the minimum amount of money you need to guarantee a win regardless of what number I pick.
\n
Example 1:
\n\n\nInput: n = 10\nOutput: 16\nExplanation: The winning strategy is as follows:\n- The range is [1,10]. Guess 7.\n - If this is my number, your total is $0. Otherwise, you pay $7.\n - If my number is higher, the range is [8,10]. Guess 9.\n - If this is my number, your total is $7. Otherwise, you pay $9.\n - If my number is higher, it must be 10. Guess 10. Your total is $7 + $9 = $16.\n - If my number is lower, it must be 8. Guess 8. Your total is $7 + $9 = $16.\n - If my number is lower, the range is [1,6]. Guess 3.\n - If this is my number, your total is $7. Otherwise, you pay $3.\n - If my number is higher, the range is [4,6]. Guess 5.\n - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $5.\n - If my number is higher, it must be 6. Guess 6. Your total is $7 + $3 + $5 = $15.\n - If my number is lower, it must be 4. Guess 4. Your total is $7 + $3 + $5 = $15.\n - If my number is lower, the range is [1,2]. Guess 1.\n - If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $1.\n - 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\n\n
Example 2:
\n\n\nInput: n = 1\nOutput: 0\nExplanation: There is only one possible number, so you can guess 1 and not have to pay anything.\n\n\n
Example 3:
\n\n\nInput: n = 2\nOutput: 1\nExplanation: There are two possible numbers, 1 and 2.\n- Guess 1.\n - If this is my number, your total is $0. Otherwise, you pay $1.\n - If my number is higher, it must be 2. Guess 2. Your total is $1.\nThe worst case is that you pay $1.\n\n\n
\n
Constraints:
\n\n1 <= n <= 200
我们正在玩一个猜数游戏,游戏规则如下:
\n\n1
到 n
之间选择一个数字。x
并且猜错了的时候,你需要支付金额为 x
的现金。如果你花光了钱,就会 输掉游戏 。给你一个特定的数字 n
,返回能够 确保你获胜 的最小现金数,不管我选择那个数字 。
\n\n
示例 1:
\n\n\n输入:n = 10\n输出:16\n解释:制胜策略如下:\n- 数字范围是 [1,10] 。你先猜测数字为 7 。\n - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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\n\n
示例 2:
\n\n\n输入:n = 1\n输出:0\n解释: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\n\n
示例 3:
\n\n\n输入:n = 2\n输出:1\n解释:有两个可能的数字 1 和 2 。\n- 你可以先猜 1 。\n - 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 - 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\n\n
\n\n
提示:
\n\n1 <= n <= 200
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use-after-free<\\/code>\\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n
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Python 2.7.12<\\/code><\\/p>\\r\\n\\r\\n
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Python 3.10<\\/code><\\/p>\\r\\n\\r\\n
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