Guess Number Higher or Lower

Hi everyone!
Today I solved a fun problem based on a guessing game, and it turns out to be a perfect example of binary search.

Problem
We need to guess a number between 1 and n.
We are given an API:

• -1 → guess is too high
• 1 → guess is too low
• 0 → correct guess Our task is to find the correct number.

My Approach
At first, I thought of guessing numbers one by one (linear search), but that would be slow.
Then I realized:

Since the range is sorted (1 to n), we can use binary search.

Logic

• Start with range low = 1 and high = n
• Find middle value
• Use guess(mid):
  • If correct → return mid
  • If too high → search left half
  • If too low → search right half

Code (Python)

The guess API is already defined for you.

class Solution:
def guessNumber(self, n: int) -> int:
low = 1
high = n

    while low <= high:
        mid = (low + high) // 2
        res = guess(mid)

        if res == 0:
            return mid
        elif res == -1:
            high = mid - 1
        else:
            low = mid + 1

    return -1

Time & Space Complexity

• Time: O(log n)
• Space: O(1)

Key Insight

Binary search reduces the search space by half each time, making it very efficient.

What I Learned

• Binary search can be applied even without arrays
• Always look for sorted patterns
• This is a classic interview problem

Thanks for reading!
Feel free to share your thoughts or alternative approaches.