3783. Mirror Distance of an Integer

Difficulty: Easy

Topics: Mid Level, Math, Weekly Contest 481

You are given an integer n.

Define its mirror distance as: abs(n - reverse(n)) where reverse(n) is the integer formed by reversing the digits of n.

Return an integer denoting the mirror distance of n.

abs(x) denotes the absolute value of x.

Example 1:

Input: n = 25
Output: 27
Explanation:
- reverse(25) = 52.
- Thus, the answer is abs(25 - 52) = 27.

Example 2:

Input: n = 10
Output: 9
Explanation:
- reverse(10) = 01 which is 1.
- Thus, the answer is abs(10 - 1) = 9.

Example 3:

Input: n = 7
Output: 0
Explanation:
- reverse(7) = 7.
- Thus, the answer is abs(7 - 7) = 0.

Example 4:

Input: n = 100
Output: 99

Constraints:

1 <= n <= 10⁹

Hint:

Simulate as described

Solution:

The function calculates the mirror distance of an integer by reversing its digits, then returning the absolute difference between the original number and its reverse.

Approach:

Convert the integer to its digit-reversed form without converting to a string.
Use a loop to extract digits from the original number and build the reversed number.
Return the absolute difference between the original and reversed numbers.

Let's implement this solution in PHP: 3783. Mirror Distance of an Integer

<?php
/**
 * @param Integer $n
 * @return Integer
 */
function mirrorDistance(int $n): int
{
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// Test cases
echo mirrorDistance(25) . "\n";         // Output: 27
echo mirrorDistance(10) . "\n";         // Output: 9
echo mirrorDistance(7) . "\n";          // Output: 0
echo mirrorDistance(100) . "\n";        // Output: 99
?>

Explanation:

Reverse the digits:
- Repeatedly take the last digit of n using n % 10.
- Append it to reversed by multiplying reversed by 10 and adding the digit.
- Remove the last digit from n using integer division by 10.
- Continue until n becomes 0.
Handle leading zeros:
- The reversal process automatically discards leading zeros because they don’t contribute to the integer value (e.g., 10 → 1).
Compute mirror distance:
- Use abs(original - reversed) to get the positive difference.

Complexity

Time Complexity: O(d) where d is the number of digits in n (at most 10, since n ≤ 10⁹).
Space Complexity: O(1) — only a few integer variables used.

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