3754. Concatenate Non-Zero Digits and Multiply by Sum I

[mah-shamim]

Topics: Mid Level, Math, Weekly Contest 477

You are given an integer n.

Form a new integer x by concatenating all the non-zero digits of n in their original order. If there are no non-zero digits, x = 0.

Let sum be the sum of digits in x.

Return an integer representing the value of x * sum.

Example 1:

• Input: n = 10203004
• Output: 12340
• Explanation:
  • The non-zero digits are 1, 2, 3, and 4. Thus, x = 1234.
  • The sum of digits is sum = 1 + 2 + 3 + 4 = 10.
  • Therefore, the answer is x * sum = 1234 * 10 = 12340.

Example 2:

• Input: n = 1000
• Output: 1
• Explanation:
  • The non-zero digit is 1, so x = 1 and sum = 1.
  • Therefore, the answer is x * sum = 1 * 1 = 1.

Example 3:

• Input: n = 0
• Output: 0

Example 4:

• Input: n = 5
• Output: 25

Example 5:

• Input: n = 123456789
• Output: 5555555505

Example 6:

• Input: n = 101010
• Output: 333

Example 7:

• Input: n = 1000000000
• Output: 1

Constraints:

• 0 <= n <= 10⁹

Hint:

1. Simulate as described

[mah-shamim]

We implement a straightforward solution that processes the input integer n by extracting all non-zero digits, constructing a new number from them, calculating their sum, and returning their product. Our approach handles the edge case where no non-zero digits exist by returning 0.

Approach

• Digit Extraction: Convert the integer n to a string and split it into an array of individual digit characters
• Filter Non-Zero Digits: Remove all digit characters equal to '0' using array filtering
• Edge Case Handling: If no non-zero digits remain, return 0 immediately
• Construct x: Join the filtered digit characters into a string and convert to integer
• Calculate Sum: Sum the numeric values of all non-zero digits
• Compute Result: Return the product of x and sum

Let's implement this solution in PHP: 3754. Concatenate Non-Zero Digits and Multiply by Sum I

<?php
/**
 * @param Integer $n
 * @return Integer
 */
function sumAndMultiply(int $n): int
{
    $digits = str_split((string) $n);
    $nonZeroDigits = array_filter($digits, fn($d) => $d !== '0');

    if (empty($nonZeroDigits)) {
        return 0;
    }

    $x = (int) implode('', $nonZeroDigits);
    $sum = array_sum($nonZeroDigits);

    return $x * $sum;
}

// Test cases
echo sumAndMultiply(10203004) .  "\n";          // Output: 12340
echo sumAndMultiply(1000) .  "\n";              // Output: 1
echo sumAndMultiply(0) .  "\n";                 // Output: 0
echo sumAndMultiply(5) .  "\n";                 // Output: 25
echo sumAndMultiply(123456789) .  "\n";         // Output: 5555555505
echo sumAndMultiply(101010) .  "\n";            // Output: 333
echo sumAndMultiply(1000000000) .  "\n";        // Output: 1
?>

Explanation:

• String Conversion: We treat the number as a string to easily access each digit individually without complex arithmetic operations
• Zero Filtering: We filter out '0' characters since they contribute nothing to either x (they don't change the numeric value when concatenated with other digits) or the sum
• Empty Array Check: When all digits are zero, we return 0 early to avoid processing an empty array
• Number Reconstruction: Joining the filtered digits creates the number formed by all non-zero digits in their original order
• Sum Calculation: Using array_sum on the digit characters automatically converts them to integers, giving us the digit sum
• Final Multiplication: Multiplying x by sum yields the required result per the problem specification

Complexity Analysis

• Time Complexity: O(d) where d is the number of digits in n (maximum 10 digits since n ≤ 10⁹)

  • String conversion and splitting: O(d)
  • Array filtering: O(d)
  • Array summing: O(d)
  • Join and integer conversion: O(d)

• Space Complexity: O(d) for storing the digit arrays

  • The split array stores d characters
  • The filtered array stores at most d characters
  • Both are negligible as d ≤ 10

[topugit]

Thanks for solving the problem of "Concatenate Non-Zero Digits and Multiply by Sum I"

[mah-shamim]

Thanks