I. Playing With Strings

Codeforces

IDCF10102I

Time2000ms

Memory64MB

Difficulty—

English · Original

Formal · Original

Dani and Mike are two kids ,They are playing games all day and when they don't find a game to play they invent a game . There is about an hour to arrive to school, because they love playing with strings Dani invented a game , Given a string and the winner is the first who form a palindrome string using all letters of this string according to the following sample rules : 1- player can rearrange letters to form a string . 2- the formed string must be palindrome and use all letters of the given string. 3- if there is more than one string chose the lexicographically smallest string . EX: string is "abacb" player can form : "abcba" and "bacab" ,but "abcba" is the lexicographically smallest. Mike asked you to write a Program to compute the palindrome string so he can beat Dani. Your program will be tested on one or more test cases. The first line of the input will be a single integer T, the number of test cases (1 ≤ T ≤ 1000). Every test case on one line contain one string ,the length of the string will not exceed 1000 lower case English letter. For each test case print a single line containing the lexicographically smallest palindrome string according to the rules above. If there is no such string print "impossible" Palindrome string is a string which reads the same backward or forward. Lexicographic order means that the strings are arranged in the way as they appear in a dictionary. ## Input Your program will be tested on one or more test cases. The first line of the input will be a single integer T, the number of test cases (1 ≤ T ≤ 1000). Every test case on one line contain one string ,the length of the string will not exceed 1000 lower case English letter. ## Output For each test case print a single line containing the lexicographically smallest palindrome string according to the rules above. If there is no such string print "impossible" [samples] ## Note Palindrome string is a string which reads the same backward or forward.Lexicographic order means that the strings are arranged in the way as they appear in a dictionary.

**Definitions** Let $ T \in \mathbb{Z} $ be the number of test cases. For each test case: - Let $ n, k \in \mathbb{Z} $ with $ 1 \leq k < n \leq 10^5 $. - Let $ X = (x_0, x_1, \dots, x_{n-1}) $ be a strictly increasing sequence of integers with $ 0 \leq x_i \leq 10^9 $, representing hole positions. **Constraints** 1. $ 1 \leq T \leq \text{unknown bound} $ (implied by input format). 2. For each test case: $ 1 \leq k < n \leq 100000 $, and $ x_0 < x_1 < \dots < x_{n-1} $. **Objective** Find the minimum value $ \ell \in \mathbb{R}^+ $ such that there exists a set of $ k $ intervals (strips), each of length at most $ \ell $, that collectively cover all $ n $ holes. Equivalently: Minimize $ \ell $ such that $ X $ can be covered by $ k $ intervals $ [a_j, a_j + \ell] $, $ j = 1, \dots, k $, where each $ x_i \in \bigcup_{j=1}^k [a_j, a_j + \ell] $.

API Response (JSON)

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    "name": "I. Playing With Strings",
    "description": {
      "content": "Dani and Mike are two kids ,They are playing games all day and when they don't find a game to play they invent a game . There is about an hour to arrive to school, because they love playing with strin",
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    },
    "platform": "Codeforces",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 65536
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "CF10102I"
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      "statement_type": "Markdown",
      "content": "Dani and Mike are two kids ,They are playing games all day and when they don't find a game to play they invent a game . There is about an hour to arrive to school, because they love playing with strin...",
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