Mountain Subsequences（dp）

思路：

遍历两次求得每个字符左侧的递增子序列数和右侧的递减子序列数。

最后再遍历一遍每个字符左右序列数相乘。

代码：

#include<iostream>#include<cstdio>#include<cstring>using namespace std;const int maxn = 1e5+5;const int mod = 2012;char str[maxn];int n, a[maxn], l[maxn], r[maxn], dp[maxn];int main(void){    while(cin >> n)    {        scanf(" %s", str);        for(int i = 0; i < n; i++)            a[i] = str[i]-'a';        memset(l, 0, sizeof(l));        memset(r, 0, sizeof(r));        memset(dp, 0, sizeof(dp));        for(int i = 0; i < n; i++)        {            for(int j = 0; j < a[i]; j++)                l[i] = (l[i]+dp[j])%mod;    //l[i]统计前i个能组成结尾小于a[i]的方案数            dp[a[i]] = (dp[a[i]]+l[i]+1)%mod;   //dp[a[i]]统计当前位置以a[i]字符结尾的方案数        }        memset(dp, 0, sizeof(dp));        for(int i = n-1; i >= 0; i--)        {            for(int j = 0; j < a[i]; j++)                r[i] = (r[i]+dp[j])%mod;            dp[a[i]] = (dp[a[i]]+r[i]+1)%mod;        }        int ans = 0;        for(int i = 0; i < n; i++)            ans = (ans+l[i]*r[i])%mod;        PRintf("%d/n", ans);    }    return 0;}
Mountain Subsequences
Time Limit: 1000MS Memory Limit: 65536KBSubmit Statistic Discuss
Problem Description
Coco is a beautiful ACMer girl living in a very beautiful mountain. There are many trees and flowers on the mountain, and there are many animals and birds also. Coco like the mountain so much that she now name some letter sequences as Mountain Subsequences.
 
A Mountain Subsequence is defined as following:
1. If the length of the subsequence is n, there should be a max value letter, and the subsequence should like this, a1 < ...< ai < ai+1 < Amax > aj > aj+1 > ... > an
2. It should have at least 3 elements, and in the left of the max value letter there should have at least one element, the same as in the right.
3. The value of the letter is the ASCII value.
 
Given a letter sequence, Coco wants to know how many Mountain Subsequences exist.
Input
Input contains multiple test cases.
For each case there is a number n (1<= n <= 100000) which means the length of the letter sequence in the first line, and the next line contains the letter sequence.
Please note that the letter sequence only contain lowercase letters. 
Output
For each case please output the number of the mountain subsequences module 2012.
Example Input
4abca
Example Output
4
Hint
The 4 mountain subsequences are:
aba, aca, bca, abca