# [Solution] Flipping Failure solution codechef

Table of Contents

## [Solution] Flipping Failure solution codechef

Flipping Failure solution codechef – Chef has a binary string S with him and he wants to modify it using the following two types of operations –

• Type 1 : Choose any two indices i and j such that 1 \leq i, j \leq |S| and swap S_i and S_j. This operation costs 1 rupee and can be performed any number of times.
• Type 2 : Choose any prefix of length i, where 1 \leq i \leq |S|, and reverse this prefix of the binary string. This operation is free of cost and can be performed at most once.

Chef wants to obtain the lexicographically smallest string. Can you help him find the minimum cost to obtain the lexicographically smallest string?

Note:

• |S| denotes the length of the string S.
• A string A is lexicographically smaller than string B, if A_i \lt B_i, where i is the first index where A and B differ.

## [Solution] Flipping Failure solution codechef

• The first line of input will contain a single integer T, denoting the number of test cases.
• Each test case consists of a single line of input denoting S, the original string.

### Output Format

For each test case, output the minimum cost to obtain the lexicographically minimal string.

### Constraints

• 1 \leq T \leq 5\cdot 10^4
• 1 \leq |S| \leq 10^5
• The sum of |S| over all test cases won’t exceed 5\cdot 10^5.

### Sample 1:

Input

Output

3
1010
101
100100

1
0
1


## [Solution] Flipping Failure solution codechef Explanation:

Test case 1: You can perform an operation of Type 1 by choosing i = 2 and j = 3. So from 1\textcolor{violet}{0}\textcolor{olive}{1}0, you get 1100, and it has cost you 1 rupee so far. Then, you perform an operation of Type 2, by choosing i = 4. So you reverse the entire string, and so from \textcolor{red}{1100}, you get 0011. This operation is free of cost. This is the lexicographically smallest string that you can achieve, and it cost us 1 rupee to get there. So the answer is 1.

Test case 2: You can perform an operation of Type 2, by choosing i = 2. So you reverse the prefix of length 2, and so from \textcolor{red}{10}1, you get 011. This operation is free of cost. This is the lexicographically smallest string that you can achieve, and it cost us 0 rupees to get there. So the answer is 0.

Test case 3: You can perform an operation of Type 1 by choosing i = 4 and j = 6. So from 100\textcolor{violet}{1}0\textcolor{olive}{0}, you get 100001, and it has cost you 1 rupee so far. Then, you perform an operation of Type 2, by choosing i = 5. So you reverse the prefix of length 5, and so from \textcolor{red}{10000}1, you get 000011. This operation is free of cost. This is the lexicographically smallest string that you can achieve, and it cost us 1 rupee to get there. So the answer is 1.