Check if mirror image of a number is same if displayed in seven segment displays in Python

In seven-segment displays, only certain digits look the same when mirrored horizontally. We need to check if a number appears identical to its mirror image when displayed on such a device.

The digits that look the same when mirrored in seven-segment displays are 0, 1, and 8. Other digits like 2, 3, 4, 5, 6, 7, 9 don't have symmetric mirror images.

Understanding Seven-Segment Mirror Images

Algorithm Steps

To solve this problem, we follow these steps ?

• Convert the number to string format
• Check if all digits are mirror-symmetric (only 0, 1, 8)
• Check if the number reads the same forwards and backwards (palindrome)
• Return True only if both conditions are met

Example

Let us see the implementation to get better understanding ?

def solve(n):
    num_str = str(n)
    
    # Check if all digits are mirror-symmetric
    for i in range(len(num_str)):
        if num_str[i] not in ['0', '1', '8']:
            return False
    
    # Check if the number is a palindrome
    left = 0
    right = len(num_str) - 1
    while left < right:
        if num_str[left] != num_str[right]:
            return False
        left += 1
        right -= 1
    
    return True

# Test cases
n = 818
print(f"Input: {n}")
print(f"Output: {solve(n)}")

# Additional test cases
test_cases = [0, 1, 8, 11, 88, 101, 181, 123, 808]
print("\nAdditional test cases:")
for num in test_cases:
    result = solve(num)
    print(f"{num}: {result}")

Input: 818
Output: True

Additional test cases:
0: True
1: True
8: True
11: True
88: True
101: True
181: True
123: False
808: True

How It Works

The solution works in two phases:

1. Digit validation: We check each digit to ensure it's mirror-symmetric (0, 1, or 8)
2. Palindrome check: We use two pointers to verify the number reads the same forwards and backwards

For example, 818 passes both tests ? all digits (8, 1, 8) are mirror-symmetric, and it reads the same forwards and backwards.

Alternative Approach

We can also solve this using string slicing for the palindrome check ?

def solve_alternative(n):
    num_str = str(n)
    
    # Check if all digits are mirror-symmetric
    valid_digits = {'0', '1', '8'}
    if not all(digit in valid_digits for digit in num_str):
        return False
    
    # Check if palindrome using slicing
    return num_str == num_str[::-1]

# Test the alternative approach
n = 818
print(f"Alternative approach result: {solve_alternative(n)}")

Alternative approach result: True

Conclusion

To check if a number's mirror image is the same in seven-segment displays, verify that all digits are mirror-symmetric (0, 1, 8) and the number is a palindrome. This ensures the number appears identical when horizontally mirrored.