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374. 猜数字大小

English Version

题目描述

我们正在玩猜数字游戏。猜数字游戏的规则如下：

我会从 1 到 n 随机选择一个数字。 请你猜选出的是哪个数字。

如果你猜错了，我会告诉你，我选出的数字比你猜测的数字大了还是小了。

你可以通过调用一个预先定义好的接口 int guess(int num) 来获取猜测结果，返回值一共有三种可能的情况：

  • -1：你猜的数字比我选出的数字大 （即 num > pick）。
  • 1：你猜的数字比我选出的数字小 （即 num < pick）。
  • 0：你猜的数字与我选出的数字相等。（即 num == pick）。

返回我选出的数字。

 

示例 1：

输入：n = 10, pick = 6
输出：6

示例 2：

输入：n = 1, pick = 1
输出：1

示例 3：

输入：n = 2, pick = 1
输出：1

 

提示：

  • 1 <= n <= 231 - 1
  • 1 <= pick <= n

解法

方法一：二分查找

我们在区间 $[1,..n]$ 进行二分查找，找到第一个满足 guess(x) <= 0 的数，即为答案。

时间复杂度 $O(\log n)$。其中 $n$ 为题目给定的上限。空间复杂度 $O(1)$。

Python3

# The guess API is already defined for you.
# @param num, your guess
# @return -1 if num is higher than the picked number
#          1 if num is lower than the picked number
#          otherwise return 0
# def guess(num: int) -> int:


class Solution:
    def guessNumber(self, n: int) -> int:
        return bisect.bisect(range(1, n + 1), 0, key=lambda x: -guess(x))

Java

/**
 * Forward declaration of guess API.
 * @param  num   your guess
 * @return 	     -1 if num is lower than the guess number
 *			      1 if num is higher than the guess number
 *               otherwise return 0
 * int guess(int num);
 */

public class Solution extends GuessGame {
    public int guessNumber(int n) {
        int left = 1, right = n;
        while (left < right) {
            int mid = (left + right) >>> 1;
            if (guess(mid) <= 0) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
}

C++

/**
 * Forward declaration of guess API.
 * @param  num   your guess
 * @return 	     -1 if num is lower than the guess number
 *			      1 if num is higher than the guess number
 *               otherwise return 0
 * int guess(int num);
 */

class Solution {
public:
    int guessNumber(int n) {
        int left = 1, right = n;
        while (left < right) {
            int mid = left + ((right - left) >> 1);
            if (guess(mid) <= 0) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
};

Go

/**
 * Forward declaration of guess API.
 * @param  num   your guess
 * @return 	     -1 if num is higher than the picked number
 *			      1 if num is lower than the picked number
 *               otherwise return 0
 * func guess(num int) int;
 */

func guessNumber(n int) int {
	return sort.Search(n, func(i int) bool {
		i++
		return guess(i) <= 0
	}) + 1
}

TypeScript

/**
 * Forward declaration of guess API.
 * @param {number} num   your guess
 * @return 	            -1 if num is lower than the guess number
 *			             1 if num is higher than the guess number
 *                       otherwise return 0
 * var guess = function(num) {}
 */

function guessNumber(n: number): number {
    let l = 1;
    let r = n;
    while (l < r) {
        const mid = (l + r) >>> 1;
        if (guess(mid) <= 0) {
            r = mid;
        } else {
            l = mid + 1;
        }
    }
    return l;
}

Rust

/**
 * Forward declaration of guess API.
 * @param  num   your guess
 * @return 	     -1 if num is lower than the guess number
 *			      1 if num is higher than the guess number
 *               otherwise return 0
 * unsafe fn guess(num: i32) -> i32 {}
 */

impl Solution {
    unsafe fn guessNumber(n: i32) -> i32 {
        let mut l = 1;
        let mut r = n;
        loop {
            let mid = l + (r - l) / 2;
            match guess(mid) {
                -1 => {
                    r = mid - 1;
                }
                1 => {
                    l = mid + 1;
                }
                _ => {
                    break mid;
                }
            }
        }
    }
}

C#

/**
 * Forward declaration of guess API.
 * @param  num   your guess
 * @return 	     -1 if num is higher than the picked number
 *			      1 if num is lower than the picked number
 *               otherwise return 0
 * int guess(int num);
 */

public class Solution : GuessGame {
    public int GuessNumber(int n) {
        int left = 1, right = n;
        while (left < right) {
            int mid = left + ((right - left) >> 1);
            if (guess(mid) <= 0) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }
}