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):

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

Example:
n = 10, I pick 6.

Return 6.

O(log n) binary search solution

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/* 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) {
        if (n < 1) return -1;
        int low = 1, high = n;
        while (low < high) {
            int mid = low + (high - low) / 2; // prevent overflow
            int res = guess(mid);
            if (res == 0) {
                return mid;
            } else if (res == -1) {
                high = mid - 1;
            } else {
                low = mid + 1;
            }
        }
        return low;
    }
}