102407: [AtCoder]ABC240 Ex - Sequence of Substrings

Problem Statement

You are given a string $S = s_1 s_2 \ldots s_N$ of length $N$ consisting of $0$'s and $1$'s.

Find the maximum integer $K$ such that there is a sequence of $K$ pairs of integers $\big((L_1, R_1), (L_2, R_2), \ldots, (L_K, R_K)\big)$ that satisfy all three conditions below.

• $1 \leq L_i \leq R_i \leq N$ for each $i = 1, 2, \ldots, K$.
• $R_i \lt L_{i+1}$ for $i = 1, 2, \ldots, K-1$.
• The string $s_{L_i}s_{L_i+1} \ldots s_{R_i}$ is strictly lexicographically smaller than the string $s_{L_{i+1}}s_{L_{i+1}+1}\ldots s_{R_{i+1}}$.

Constraints

• $1 \leq N \leq 2.5 \times 10^4$
• $N$ is an integer.
• $S$ is a string of length $N$ consisting of $0$'s and $1$'s.

Input

Input is given from Standard Input in the following format:

$N$
$S$

Output

Print the answer.

Sample Input 1

7
0101010

Sample Output 1

3

For $K = 3$, one sequence satisfying the conditition is $(L_1, R_1) = (1, 1), (L_2, R_2) = (3, 5), (L_3, R_3) = (6, 7)$. Indeed, $s_1 = 0$ is strictly lexicographically smaller than $s_3s_4s_5 = 010$, and $s_3s_4s_5 = 010$ is strictly lexicographically smaller than $s_6s_7 = 10$.
For $K \geq 4$, there is no sequence $\big((L_1, R_1), (L_2, R_2), \ldots, (L_K, R_K)\big)$ satisfying the condition.

Sample Input 2

30
000011001110101001011110001001

Sample Output 2

9

问题描述

给你一个长度为 N 的字符串 $S = s_1 s_2 \ldots s_N$，由 0 和 1 组成。

找到最大的整数 $K$，使得存在一个整数对序列 $\big((L_1, R_1), (L_2, R_2), \ldots, (L_K, R_K)\big)$ 满足以下三个条件。

• 对于每个 $i = 1, 2, \ldots, K$，都有 $1 \leq L_i \leq R_i \leq N$。
• 对于 $i = 1, 2, \ldots, K-1$，都有 $R_i \lt L_{i+1}$。
• 字符串 $s_{L_i}s_{L_i+1} \ldots s_{R_i}$ 严格字典序小于 字符串 $s_{L_{i+1}}s_{L_{i+1}+1}\ldots s_{R_{i+1}}$。

限制条件

• $1 \leq N \leq 2.5 \times 10^4$
• $N$ 是一个整数。
• $S$ 是一个长度为 $N$ 的字符串，由 0 和 1 组成。

输入

输入从标准输入中给出，格式如下：

$N$
$S$

输出

打印答案。

样例输入 1

7
0101010

样例输出 1

3

对于 $K = 3$，一个满足条件的序列是 $(L_1, R_1) = (1, 1), (L_2, R_2) = (3, 5), (L_3, R_3) = (6, 7)$。 确实，$s_1 = 0$ 严格字典序小于 $s_3s_4s_5 = 010$，且 $s_3s_4s_5 = 010$ 严格字典序小于 $s_6s_7 = 10$。

对于 $K \geq 4$，不存在满足条件的序列 $\big((L_1, R_1), (L_2, R_2), \ldots, (L_K, R_K)\big)$。

样例输入 2

30
000011001110101001011110001001

样例输出 2

9