A15791. Binary String Sorting
编程题
普及/提高-
知识点
题目描述
You are given a binary string $s$ consisting of only characters 0 and/or 1.
You can perform several operations on this string (possibly zero). There are two types of operations:
- choose two consecutive elements and swap them. In order to perform this operation, you pay $10^{12}$ coins;
- choose any element from the string and remove it. In order to perform this operation, you pay $10^{12}+1$ coins.
Your task is to calculate the minimum number of coins required to sort the string $s$ in non-decreasing order (i. e. transform $s$ so that $s_1 \le s_2 \le \dots \le s_m$ , where $m$ is the length of the string after applying all operations). An empty string is also considered sorted in non-decreasing order.
You can perform several operations on this string (possibly zero). There are two types of operations:
- choose two consecutive elements and swap them. In order to perform this operation, you pay $10^{12}$ coins;
- choose any element from the string and remove it. In order to perform this operation, you pay $10^{12}+1$ coins.
Your task is to calculate the minimum number of coins required to sort the string $s$ in non-decreasing order (i. e. transform $s$ so that $s_1 \le s_2 \le \dots \le s_m$ , where $m$ is the length of the string after applying all operations). An empty string is also considered sorted in non-decreasing order.
输入格式
The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases.
The only line of each test case contains the string $s$ ( $1 \le |s| \le 3 \cdot 10^5$ ), consisting of only characters 0 and/or 1.
The sum of lengths of all given strings doesn't exceed $3 \cdot 10^5$ .
The only line of each test case contains the string $s$ ( $1 \le |s| \le 3 \cdot 10^5$ ), consisting of only characters 0 and/or 1.
The sum of lengths of all given strings doesn't exceed $3 \cdot 10^5$ .
输出格式
For each test case, print a single integer — the minimum number of coins required to sort the string $s$ in non-decreasing order.
输入输出样例
输入 #1
6 100 0 0101 00101101 1001101 11111
输出 #1
1000000000001 0 1000000000000 2000000000001 2000000000002 0
说明/提示
In the first example, you have to remove the $1$ -st element, so the string becomes equal to 00.
In the second example, the string is already sorted.
In the third example, you have to swap the $2$ -nd and the $3$ -rd elements, so the string becomes equal to 0011.
In the fourth example, you have to swap the $3$ -rd and the $4$ -th elements, so the string becomes equal to 00011101, and then remove the $7$ -th element, so the string becomes equal to 0001111.
In the fifth example, you have to remove the $1$ -st element, so the string becomes equal to 001101, and then remove the $5$ -th element, so the string becomes equal to 00111.
In the sixth example, the string is already sorted.
In the second example, the string is already sorted.
In the third example, you have to swap the $2$ -nd and the $3$ -rd elements, so the string becomes equal to 0011.
In the fourth example, you have to swap the $3$ -rd and the $4$ -th elements, so the string becomes equal to 00011101, and then remove the $7$ -th element, so the string becomes equal to 0001111.
In the fifth example, you have to remove the $1$ -st element, so the string becomes equal to 001101, and then remove the $5$ -th element, so the string becomes equal to 00111.
In the sixth example, the string is already sorted.