Editorial for An Animal Contest 3 P2 - Monkey Potato

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Author: sjay05

Denote S = \{a_1, a_2, \dots, a_D\} to be the set of all valid digits given in input.

Subtask 1

For this subtask, notice that we can take the smallest digit in S and output it K times.

Time Complexity: \mathcal{O}(K)

Subtask 2

Consider 4 cases:

  • S = \{0\}:

    • No valid integer can be formed with the digit 0, so -1 should be outputted.
  • \min S = 0:

    Let the second smallest digit in S be b.

    • K \le 2
      • The smallest palindrome consists of K b's.
    • K > 2
      • A K length palindrome can be constructed with the form: b00 \dots 00b.
  • \min S > 0:

    • Let the smallest digit in S be b. The K length palindrome is: bb \dots bb.

Time Complexity: \mathcal{O}(K)


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