## Description

https://leetcode.com/problems/guess-number-higher-or-lower/

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 3 possible results:

`-1`

: The number I picked is lower than your guess (i.e.`pick < num`

).`1`

: The number I picked is higher than your guess (i.e.`pick > num`

).`0`

: The number I picked is equal to your guess (i.e.`pick == num`

).

Return *the number that I picked*.

**Example 1:**

Input:n = 10, pick = 6Output:6

**Example 2:**

Input:n = 1, pick = 1Output:1

**Example 3:**

Input:n = 2, pick = 1Output:1

**Example 4:**

Input:n = 2, pick = 2Output:2

**Constraints:**

`1 <= n <= 2`

^{31}- 1`1 <= pick <= n`

## Explanation

Do a binary search to find the pick.

## Python Solution

```
# 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:
start = 1
end = n
while start + 1 < end:
mid = start + (end - start) // 2
if guess(mid) == 0:
return mid
elif guess(mid) == -1:
end = mid
else:
start = mid
if guess(end) == 0:
return end
if guess(start) == 0:
return start
```

- Time Complexity: O(log(N)).
- Space Complexity: O(1).