F. Ironical Solution 1

Codeforces

IDCF10240F

Time1000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

Diego wants to message his friend Ketzia, for this he will first grab a word and encode it as numbers and then apply some encryption to the numbers and send it to her. Ironically, after coming up with this solution he realized that this system has to send word by word, only works for words were every letter is in alphabetical order and also there are many chat services that are free and will encrypt messages securely so there was no need to invent this encryption system. In order to encrypt Diego will first grab a word of $N$ characters and convert every character into its numerical ASCII (for example 'A' -> 65, '0' -> 48, 'a' -> 97). After that he will have exactly $N$ positive numbers. Given those $N$ numbers, he will generate all possible $2^N$ subsets and then for each subset get the sum of all the numbers in the subset, he will then sort the sums and send them to Ketzia. She will decrypt the message by doing the inverse of the encryption steps. For this particular problem, he will do the encryption of the message. An integer $N$ $(1 <= N <= 20)$, the amount of characters that the word that Diego is sending to Ketzia has. The word will have its characters sorted in non-decreasing order by ASCII value. A single word of length $N$ containing only lower and upper case letters and numbers. $2^N$ numbers sorted in non-decreasing order in the same line, the encrypted word. ## Input An integer $N$ $(1 <= N <= 20)$, the amount of characters that the word that Diego is sending to Ketzia has. The word will have its characters sorted in non-decreasing order by ASCII value.A single word of length $N$ containing only lower and upper case letters and numbers. ## Output $2^N$ numbers sorted in non-decreasing order in the same line, the encrypted word. [samples]

**Definitions** Let $ N \in \mathbb{Z} $ with $ 1 \leq N \leq 20 $. Let $ w = c_1 c_2 \dots c_N $ be a string of length $ N $, where each $ c_i $ is a character with ASCII value $ a_i = \text{ord}(c_i) $, and $ a_1 \leq a_2 \leq \dots \leq a_N $. Let $ A = (a_1, a_2, \dots, a_N) $ be the sequence of ASCII values. **Constraints** - $ 1 \leq N \leq 20 $ - $ a_i \in \mathbb{Z}^+ $ for all $ i \in \{1, \dots, N\} $ - $ a_1 \leq a_2 \leq \dots \leq a_N $ **Objective** Compute the multiset of subset sums: $$ S = \left\{ \sum_{i \in I} a_i \,\middle|\, I \subseteq \{1, 2, \dots, N\} \right\} $$ Output the elements of $ S $ sorted in non-decreasing order.

API Response (JSON)

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    "name": "F. Ironical Solution 1",
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      "time_limit": 1000,
      "memory_limit": 262144
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