374. Guess Number Higher Or Lower - Explanation

Problem Link

Description

We are playing the Guess Game. The game is as follows:

I pick a number from 1 to n. You have to guess which number I picked.

Every time you guess wrong, I will tell you whether the number I picked is higher or lower than your guess.

You call a pre-defined API int guess(int num), which returns three possible results:

  • 0: your guess is equal to the number I picked (i.e. num == pick).
  • -1: Your guess is higher than the number I picked (i.e. num > pick).
  • 1: Your guess is lower than the number I picked (i.e. num < pick).

Return the number that I picked.

Example 1:

Input: n = 5, pick = 3

Output: 3

Example 2:

Input: n = 15, pick = 10

Output: 10

Example 3:

Input: n = 1, pick = 1

Output: 1

Constraints:

  • 1 <= pick <= n <= ((2^31)-1)


# 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:
        for num in range(1, n + 1):
            if guess(num) == 0:
                return num

Time & Space Complexity

  • Time complexity: O(n)O(n)
  • Space complexity: O(1)O(1)
# 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:
        l, r = 1, n
        while True:
            m = (l + r) // 2
            res = guess(m)
            if res > 0:
                l = m + 1
            elif res < 0:
                r = m - 1
            else:
                return m

Time & Space Complexity

  • Time complexity: O(log⁡n)O(\log n)
  • Space complexity: O(1)O(1)
# 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:
        l, r = 1, n
        while True:
            m1 = l + (r - l) // 3
            m2 = r - (r - l) // 3
            if guess(m1) == 0:
                return m1
            if guess(m2) == 0:
                return m2
            if guess(m1) + guess(m2) == 0:
                l = m1 + 1
                r = m2 - 1
            elif guess(m1) == -1:
                r = m1 - 1
            else:
                l = m2 + 1

Time & Space Complexity

  • Time complexity: O(log⁡3n)O(\log_3 n)
  • Space complexity: O(1)O(1)