3461. Check If Digits Are Equal in String After Operations I

[mah-shamim]

Topics: Math, String, Simulation, Combinatorics, Number Theory, Weekly Contest 438

You are given a string s consisting of digits. Perform the following operation repeatedly until the string has exactly two digits:

• For each pair of consecutive digits in s, starting from the first digit, calculate a new digit as the sum of the two digits modulo 10.
• Replace s with the sequence of newly calculated digits, maintaining the order in which they are computed.

Return true if the final two digits in s are the same; otherwise, return false.

Example 1:

• Input: s = "3902"
• Output: true
• Explanation:
  • Initially, s = "3902"
  • First operation:
    • (s[0] + s[1]) % 10 = (3 + 9) % 10 = 2
    • (s[1] + s[2]) % 10 = (9 + 0) % 10 = 9
    • (s[2] + s[3]) % 10 = (0 + 2) % 10 = 2
    • s becomes "292"
  • Second operation:
    • (s[0] + s[1]) % 10 = (2 + 9) % 10 = 1
    • (s[1] + s[2]) % 10 = (9 + 2) % 10 = 1
    • s becomes "11"
  • Since the digits in "11" are the same, the output is true.

Example 2:

• Input: s = "34789"
• Output: false
• Explanation:
  • Initially, s = "34789".
  • After the first operation, s = "7157".
  • After the second operation, s = "862".
  • After the third operation, s = "48".
  • Since '4' != '8', the output is false.

Constraints:

• 3 <= s.length <= 100
• s consists of only digits.

Hint:

1. Simulate the operations as described.

[mah-shamim]

We need to repeatedly perform operations on a string of digits until only two digits remain. Each operation involves calculating a new digit from each pair of consecutive digits by taking their sum modulo 10, and then replacing the string with these new digits in order. The goal is to determine if the final two digits are the same.

Approach

1. Simulation: The problem can be solved by simulating the operations as described. We repeatedly process the string until its length is reduced to exactly two digits.
2. Operation Details: For each operation, we iterate through the current string, compute the new digits for each consecutive pair, and form a new string from these computed digits.
3. Termination Check: Once the string length becomes two, we check if both digits are identical. If they are, return true; otherwise, return false.

Let's implement this solution in PHP: 3461. Check If Digits Are Equal in String After Operations I

<?php
/**
 * @param String $s
 * @return Boolean
 */
function hasSameDigits($s) {
    while (strlen($s) > 2) {
        $new_s = '';
        for ($i = 0; $i < strlen($s) - 1; $i++) {
            $sum = (intval($s[$i]) + intval($s[$i + 1])) % 10;
            $new_s .= strval($sum);
        }
        $s = $new_s;
    }
    return $s[0] == $s[1];
}

// Test cases
// Example 1
$s1 = "3902";
echo hasSameDigits($s1) ? "true\n" : "false\n";  // Output: true

// Example 2
$s2 = "34789";
echo hasSameDigits($s2) ? "true\n" : "false\n";  // Output: false
?>

Explanation:

1. Initialization: Start with the given string s.
2. Loop Until Two Digits: Continue processing the string until its length is reduced to two.
3. Compute New Digits: For each pair of consecutive digits in the current string, compute their sum modulo 10 and append the result to a new string.
4. Update String: Replace the current string with the newly formed string after processing all consecutive pairs.
5. Check Final Digits: Once the loop exits, check if the two remaining digits are the same and return the result.

[basharul-siddike]

Thanks for solving the problem of "Check If Digits Are Equal in String After Operations I"

[mah-shamim]

Thanks