LC374. Guess Number Higher or Lower¶

Problem Description¶

LeetCode Problem 374: 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:

-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).
0: your guess is equal to the number I picked (i.e. num == pick).

Return the number that I picked.

Clarification¶

picked number is between 1 to n number
call guess to return guess results

Assumption¶

Solution¶

Approach - Binary Search¶

Essentially, the problem is to find the target in an array of 1 to n (sorted). We can use binary search to find the picked number by using the guess results from the api function.

Python

class Solution:
    def guessNumber(self, n: int) -> int:
        left, right = 1, n

        while left <= right:
            mid = (left + right) // 2

            res = guess(mid)
            if res == 0:
                return mid
            elif res == -1:
                right = mid - 1
            else:
                left = mid + 1

        return -1  # if not found

Complexity Analysis¶

Time complexity: \(O(\log n)\)
Since using binary search, the time complexity is \(O(\log n)\).
Space complexity: \(O(1)\)
Just use two index variables.