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Even Splits Codechef Solution

We Are Discuss About CODECHEF SOLUTION

Even Splits Codechef Solution

Even Splits Codechef Solution

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Problem

You are given a binary string S of length N. You can perform the following operation on it:

  • Pick any non-empty even-length¬†subsequence¬†of the string.
  • Suppose the subsequence has length¬†2k. Then, move the first¬†k¬†characters to the beginning of¬†S¬†and the other¬†k¬†to the end of¬†S¬†(without changing their order).

For example, suppose S = 01100101110. Here are some moves you can make (the chosen subsequence is marked in red):

  • 0\textcolor{red}{1}10\textcolor{red}{0}101110 \to \textcolor{red}{1}010101110\textcolor{red}{0}
  • 01\textcolor{red}{10}01\textcolor{red}{0}1\textcolor{red}{1}10 \to \textcolor{red}{10}0101110\textcolor{red}{01}
  • 011\textcolor{red}{00101110} \to \textcolor{red}{0010}011\textcolor{red}{1110}

What is the lexicographically smallest string that can be obtained after performing this operation several (possibly, zero) times?

Note: A binary string A is said to be lexicographically smaller than another binary string B of the same length if there exists an index i such that:

  • A_1 = B_1, A_2 = B_2, \ldots, A_{i-1} = B_{i-1}
  • A_i = 0¬†and¬†B_i = 1.

Input Format

  • The first line of input will contain a single integer¬†T, denoting the number of test cases. The description of the test cases follows.
  • Each test case consists of two lines of input.
    • The first line of each test case contains a single integer¬†N, the length of string¬†S.
    • The second line contains a binary string of length¬†N.

Output Format

For each testcase, output a single line containing the lexicographically shortest binary string that can be obtained by performing the given operation several times.

Constraints

  • 1 \leq T \leq 10^5
  • 1 \leq N \leq 2\cdot 10^5
  • S¬†is a binary string, i.e, contains only the characters¬†0¬†and¬†1.
  • The sum of¬†N¬†across all test cases won’t exceed¬†2\cdot 10^5.

Sample 1:

Input

Output

4
2
10
4
1001
5
11111
7
0010100
10
0011
11111
0000011

Explanation:

Test case¬†1:¬†There’s only one move possible, and it gives back the original string when made. So,¬†S¬†cannot be changed, and the answer is¬†10.

Test case 2: Make the following moves:

  • 1\textcolor{red}{0}0\textcolor{red}{1} \to \textcolor{red}{0}10\textcolor{red}{1}
  • \textcolor{red}{01}01 \to \textcolor{red}{0}01\textcolor{red}{1}

This is the lexicographically smallest string.

Test case¬†3:¬†Performing any move doesn’t change the string.

Test case 4: Make the move \textcolor{red}{001}0\textcolor{red}{1}00 \to \textcolor{red}{00}000\textcolor{red}{11}.

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Here Discuss About Even Splits Codechef Solution

SOLUTION

Even Splits Codechef Solution

SOLUTION

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