Guess the Number Higher or Lower

Problem Statement

We are playing a guessing game. The system picks a number between 1 and n. Your task is to guess the number.

You are given an API called guess which returns
-1 if your guess is higher than the picked number
1 if your guess is lower than the picked number
0 if your guess is correct

Find the picked number.

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Example

Input
n = 10
picked number = 6

Output
6

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Approach Using Binary Search

The idea is to reduce the search space by half in each step.

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Steps

1 Start with the range from 1 to n
2 Find the middle value
3 Call guess with the middle value
4 If result is 0 return the number
5 If result is -1 search in the left half
6 If result is 1 search in the right half
7 Repeat until the number is found

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Code

```python id="guess1"

The guess API is already defined

def guess(num):

def guessNumber(n):
left = 1
right = n

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

    if result == 0:
        return mid
    elif result == -1:
        right = mid - 1
    else:
        left = mid + 1

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## Explanation

The algorithm uses binary search to efficiently find the number. At each step, it checks the middle value and narrows down the search range based on the response.

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## Expected Output

Input
n = 10

Output
6

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## Conclusion

This problem is a simple example of binary search. It helps in understanding how to reduce search space and improve efficiency.

Practice this problem to strengthen your understanding of searching techniques.