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

#php #leetcode #algorithms #programming

Difficulty: Easy

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:

Simulate as described

Solution:

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
{
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// 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

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