3536. Maximum Product of Two Digits

3536. Maximum Product of Two Digits

Difficulty: Easy

Topics: Mid Level, Math, Sorting, Weekly Contest 448

You are given a positive integer n.

Return the maximum product of any two digits in n.

Note: You may use the same digit twice if it appears more than once in n.

Example 1:

• Input: n = 31
• Output: 3
• Explanation:
  • The digits of n are [3, 1].
  • The possible products of any two digits are: 3 * 1 = 3.
  • The maximum product is 3.

Example 2:

• Input: n = 22
• Output: 4
• Explanation:
  • The digits of n are [2, 2].
  • The possible products of any two digits are: 2 * 2 = 4.
  • The maximum product is 4.

Example 3:

• Input: n = 124
• Output: 8
• Explanation:
  • The digits of n are [1, 2, 4].
  • The possible products of any two digits are: 1 * 2 = 2, 1 * 4 = 4, 2 * 4 = 8.
  • The maximum product is 8.

Example 4:

• Input: n = 99
• Output: 81

Example 5:

• Input: n = 101
• Output: 1

Example 6:

• Input: n = 1000000000
• Output: 0

Example 7:

• Input: n = 987
• Output: 72

Example 8:

• Input: n = 555
• Output: 25

Constraints:

• 10 <= n <= 10⁹

Hint:

1. Use brute force

Solution:

We convert the integer to a string, split it into an array of digits, and then use a nested loop to compute the product of every pair of digits (ensuring we don't pair a digit with itself unless it appears twice). We track and return the maximum product found.

Approach

• Convert the integer n to a string and then to an array of digits.
• Initialize a variable maxProduct to 0.
• Use two nested loops:
  • Outer loop i from 0 to len(digits)-1.
  • Inner loop j from i+1 to len(digits)-1 (to avoid duplicate pairs).
• Compute product = digits[i] * digits[j].
• Update maxProduct if product is larger.
• Return maxProduct after loops.

Let's implement this solution in PHP: 3536. Maximum Product of Two Digits

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

// Test cases
echo maxProduct(31) .  "\n";                // Output: 3
echo maxProduct(22) .  "\n";                // Output: 4
echo maxProduct(124) .  "\n";               // Output: 8
echo maxProduct(99) .  "\n";                // Output: 81
echo maxProduct(101) .  "\n";               // Output: 1
echo maxProduct(1000000000) .  "\n";        // Output: 0
echo maxProduct(987) .  "\n";               // Output: 72
echo maxProduct(555) .  "\n";               // Output: 25
?>

Explanation:

• Digit extraction: Convert n to string and split to get each digit as an integer.
• Pair iteration: The nested loops consider every unordered pair of distinct indices, which covers all combinations of two digits (including duplicates if they exist at different positions).
• Product calculation: Multiply the two digits and compare with the current maximum.
• Edge cases: The constraints ensure n has at least two digits, so the loops will always run.
• No need to sort: Brute force is sufficient since at most 10 digits → at most 45 pairs.

Complexity Analysis

• Time Complexity: O(d²), where d is the number of digits in n. Since d ≤ 10 (because n ≤ 10⁹), this is effectively constant time.
• Space Complexity: O(d) for storing the digit array, which is also constant.

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