Codeforces 197C 找最大子串（字典序可以不连续）

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本文介绍了一种算法，用于寻找给定字符串中字典序最大的子序列。通过逆向遍历字符串并记录最大字符的方式，高效地解决了这一问题。

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http://codeforces.com/problemset/problem/197/C

You've got string s, consisting of only lowercase English letters. Find its lexicographically maximum subsequence.

We'll call a non-empty string s[p₁p₂... p_k] = s_p₁s_p₂... s_{p_k}(1 ≤ p₁ < p₂ < ... < p_k ≤ |s|) a subsequence of string s = s₁s₂... s_|s|.

String x = x₁x₂... x_|x| is lexicographically larger than string y = y₁y₂... y_|y|, if either |x| > |y| and x₁ = y₁, x₂ = y₂, ... , x_|y| = y_|y|, or exists such number r (r < |x|, r < |y|), that x₁ = y₁, x₂ = y₂, ... , x_r = y_r and x_r + 1 > y_r + 1. Characters in lines are compared like their ASCII codes.

Input

The single line contains a non-empty string s, consisting only of lowercase English letters. The string's length doesn't exceed 10⁵.

Output

Print the lexicographically maximum subsequence of string s.

Sample test(s)

Input

ababba

Output

bbba

Input

abbcbccacbbcbaaba

Output

cccccbba

Note

Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters).

The first sample: aBaBBA

The second sample: abbCbCCaCbbCBaaBA

题意：

输入一个字符串找出这个字符串按字典序排列的最大子串

1 ≤ p₁ < p₂ < ... < p_k ≤ |s| 根据这个条件可以看出可以是不连续的子串千万注意细节条件仔细分析每一个条件大多数时候每一个条件都有肯定的作用

所以千万注意细节提取出每个条件

思路：

很容易看出假如 abcaaccbcac

首先遍历一遍找到最大字符c 最大字串的第一个字符设为c 再从其后开始即aaccbcac

再遍历一遍找到最大字符c 最大字串的第二个字符设为c 如此下去直到最后一个即可

直接暴力显然会超时

有stable_sort 仍旧会超时

这时候可以用逆向思维从后面往前找

By hnust_xiehonghao, contest: Codeforces Round #124 (Div. 2), problem: (C) Lexicographically Maximum Subsequence, Accepted, #

#include<stdio.h>
#include<string.h>
char s[1000000];
char ans[1000000];
int main()
{
	int i,len,cnt;
	char max=0;
    while(scanf("%s",s)!=EOF)
	{
		max=0;cnt=1000000-1;
		len=strlen(s);
		for(i=len-1;i>=0;i--)
		{
			if(s[i]>=max) {max=s[i]; ans[cnt--]=s[i];}
		}
	//	puts(ans);
		//ans[cnt]=0;
		for(i=cnt+1;i<1000000;i++)
			printf("%c",ans[i]);
		printf("\n");
		 
	}
	return 0;
}