# 374 Guess Number Higher or Lower

## 374. [Guess Number Higher or Lower](https://leetcode.com/problems/guess-number-higher-or-lower/description/)

## 1. Question

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'll tell you whether the number is higher or lower.

You call a pre-defined API`guess(int num)`which returns 3 possible results (`-1`,`1`, or`0`):

```
-1 : My number is lower
 1 : My number is higher
 0 : Congrats! You got it!
```

**Example:**

```
n = 10, I pick 6.

Return 6.
```

## 2. Implementation

**(1) Binary Search**

```java
/* The guess API is defined in the parent class GuessGame.
   @param num, your guess
   @return -1 if my number is lower, 1 if my number is higher, otherwise return 0
      int guess(int num); */

public class Solution extends GuessGame {
    public int guessNumber(int n) {
        int start = 1, end = n, mid = 0;

        while (start <= end) {
            mid = start + (end - start) / 2;
            if (guess(mid) == -1) {
                end = mid - 1;
            }
            else if (guess(mid) == 1) {
                start = mid + 1;
            }
            else {
                return mid;
            }
        }
        return -1;
    }
}
```

## 3. Time & Space Complexity

时间复杂度O(logn), 空间复杂度O(1)