Question

374. 猜数字大小

English Version

题目描述

猜数字游戏的规则如下：

• 每轮游戏，我都会从 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，你猜测的数字比我选出的数字是大了还是小了。

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 3 种可能的情况（-1，1 或 0）：

• -1：我选出的数字比你猜的数字小 pick < num
• 1：我选出的数字比你猜的数字大 pick > num
• 0：我选出的数字和你猜的数字一样。恭喜！你猜对了！pick == num

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

示例 4：

输入：n = 2, pick = 2
输出：2

 

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。

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


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

/**
 * 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;
  }
}

/**
 * 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;
  }
};

/**
 * 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
 * func guess(num int) int;
 */

func guessNumber(n int) int {
  left, right := 1, n
  for left < right {
    mid := (left + right) >> 1
    if guess(mid) <= 0 {
      right = mid
    } else {
      left = mid + 1
    }
  }
  return left
}

/**
 * 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;
}

/**
 * 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;
        }
      }
    }
  }
}

/**
 * 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;
  }
}

方法二

# 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))

/**
 * 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
}