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64 lines
3.0 KiB
HTML
64 lines
3.0 KiB
HTML
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<p>We are playing the Guessing Game. The game will work as follows:</p>
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<ol>
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<li>I pick a number between <code>1</code> and <code>n</code>.</li>
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<li>You guess a number.</li>
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<li>If you guess the right number, <strong>you win the game</strong>.</li>
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<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>
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<li>Every time you guess a wrong number <code>x</code>, you will pay <code>x</code> dollars. If you run out of money, <strong>you lose the game</strong>.</li>
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</ol>
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<p>Given a particular <code>n</code>, return <em>the minimum amount of money you need to <strong>guarantee a win regardless of what number I pick</strong></em>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/09/10/graph.png" style="width: 505px; height: 388px;" />
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<pre>
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<strong>Input:</strong> n = 10
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<strong>Output:</strong> 16
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<strong>Explanation:</strong> The winning strategy is as follows:
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- The range is [1,10]. Guess 7.
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- If this is my number, your total is $0. Otherwise, you pay $7.
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- If my number is higher, the range is [8,10]. Guess 9.
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- If this is my number, your total is $7. Otherwise, you pay $9.
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- If my number is higher, it must be 10. Guess 10. Your total is $7 + $9 = $16.
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- If my number is lower, it must be 8. Guess 8. Your total is $7 + $9 = $16.
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- If my number is lower, the range is [1,6]. Guess 3.
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- If this is my number, your total is $7. Otherwise, you pay $3.
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- If my number is higher, the range is [4,6]. Guess 5.
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- If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $5.
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- If my number is higher, it must be 6. Guess 6. Your total is $7 + $3 + $5 = $15.
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- If my number is lower, it must be 4. Guess 4. Your total is $7 + $3 + $5 = $15.
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- If my number is lower, the range is [1,2]. Guess 1.
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- If this is my number, your total is $7 + $3 = $10. Otherwise, you pay $1.
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- If my number is higher, it must be 2. Guess 2. Your total is $7 + $3 + $1 = $11.
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The worst case in all these scenarios is that you pay $16. Hence, you only need $16 to guarantee a win.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> n = 1
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<strong>Output:</strong> 0
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<strong>Explanation:</strong> There is only one possible number, so you can guess 1 and not have to pay anything.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> n = 2
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> There are two possible numbers, 1 and 2.
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- Guess 1.
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- If this is my number, your total is $0. Otherwise, you pay $1.
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- If my number is higher, it must be 2. Guess 2. Your total is $1.
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The worst case is that you pay $1.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= n <= 200</code></li>
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</ul>
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