I Might Be Wrong

2000ms

262144K

Description:

You are given a binary string $$$S$$$ of length $$$n$$$ indexed from $$$1$$$ to $$$n$$$. You can perform the following operation any number of times (possibly zero):

Choose two integers $$$l$$$ and $$$r$$$ ($$$1 \le l \le r \le n$$$). Let $$$cnt_0$$$ be the number of times 0 occurs in $$$S[l \ldots r]$$$ and $$$cnt_1$$$ be the number of times 1 occurs in $$$S[l \ldots r]$$$. You can pay $$$|cnt_0 - cnt_1| + 1$$$ coins and sort the $$$S[l \ldots r]$$$. (by $$$S[l \ldots r]$$$ we mean the substring of $$$S$$$ starting at position $$$l$$$ and ending at position $$$r$$$)
For example if $$$S = $$$ 11001, we can perform the operation on $$$S[2 \ldots 4]$$$, paying $$$|2 - 1| + 1 = 2$$$ coins, and obtain $$$S = $$$ 10011 as a new string.

Find the minimum total number of coins required to sort $$$S$$$ in increasing order.

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the size of $$$S$$$.

The second line of each test case contains a binary string $$$S$$$ of $$$n$$$ characters $$$S_1S_2 \ldots S_n$$$. ($$$S_i = $$$ 0 or $$$S_i = $$$ 1 for each $$$1 \le i \le n$$$)

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

For each test case, output the minimum total number of coins required to sort $$$S$$$ in increasing order.

Sample Input:

7
1
1
2
10
3
101
4
1000
5
11010
6
110000
20
01000010001010011000

Sample Output:

Note:

In the first test case, $$$S$$$ is already sorted.

In the second test case, it's enough to apply the operation with $$$l = 1, r = 2$$$.

In the third test case, it's enough to apply the operation with $$$l = 1, r = 2$$$.

Informação

Provedor Codeforces

Código CF1693F