Number Guessing Game in Python using Binary Search

Last Updated : 27 Jan, 2023

In the number guessing game, the user selects a number within a defined range and then the program guesses the number. If the number guessed is wrong then the user tells the program that is the actual number is greater than the guessed number or not. Similarly, the program again guesses the number until the actual number is not guessed.
Approach: The idea is to use binary search, where in each step the half portion of the search space is reduced. Below is the illustration of the approach:

Initialize the start and end range of the number guessing.
Guess the number as middle of the search space. That is
Number = \frac{startRange + endRange}{2}
If the number guessed is correct, then terminate the program.
Otherwise, Ask the user that guessed number is less than the guessed number or not. If yes then reduce the search space accordingly.

Below is the implementation of the above approach:

Python

# Python implementation for the 
# number guessing using 
# Binary Search

# Global Arguments for playing game
args = ["N", "N", "Y"]
index = -1

# Temporary function for taking
# input from the local arguments list
def input():
    global index, args;
    index += 1
    return args[index]

# Function to guess the number in 
# a defined range of the number
def guessNumber(startRange, endRange):
    if startRange > endRange:
        return True
    
    # Middle of the range
    mid = (startRange + endRange)//2
    
    # Asking user about the 
    # actual number
    print("Is the number is ",
        mid, "?", end = " ")
    user = input()
    print(user)
    
    # Condition to check if the 
    # guessed number is actual number
    if user == "Y" or user == "y":
        print("Voila ! Successfully Guessed Number.")
        return False
        
    # Condition to check if the 
    # guessed number is not correct
    elif user == "N" or user == "n":
        print("Actual number is greater than",\
                        mid, "?", end = " ")
        user = input()
        print(user)
        if user == "Y" or user == "y":
            return guessNumber(mid+1, endRange)
        elif user == "N" or user == "n":
            return guessNumber(startRange, mid-1)
        else:
            print("Invalid Input. Print 'Y'/'N'")
            return guessNumber(startRange, endRange)
    
    # Condition to check if the user
    # input was invalid 
    else:
        print("Invalid Input. Print 'Y'/'N' ")
        return guessNumber(startRange, endRange)

# Driver Code
if __name__ == "__main__":
    print("Number Guessing game in python")
    startRange = 1
    endRange = 10
    print("Guess a number in range (1 to 10)")
    
    out = guessNumber(startRange, endRange)
    
    if out:
        print("Bad Choices")

Inputs:

N
N
Y

Outputs:

Number Guessing game in python
Guess a number in range (1 to 10)
Is the number is  5 ? N
Actual number is greater than 5 ? N
Is the number is  2 ? Y
Voila ! Successfully Guessed Number.

The time complexity of this algorithm is O(log n) as we divide the range in half with each iteration of the guessNumber function.

The space complexity of this algorithm is O(1) as we only use a constant number of variables that do not increase with the size of the input.