A1093 Count PAT's (25 point(s))

递推计算PAT个数

1. 原文

原题

The string APPAPT contains two PAT‘s as substrings. The first one is formed by the 2nd, the 4th, and the 6th characters, and the second one is formed by the 3rd, the 4th, and the 6th characters.

Now given any string, you are supposed to tell the number of PAT‘s contained in the string.

Input Specification:

Each input file contains one test case. For each case, there is only one line giving a string of no more than 105characters containing only P, A, or T.

output Specification:

For each test case, print in one line the number of PAT‘s contained in the string. Since the result may be a huge number, you only have to output the result moded by 1000000007.

Sample Input:

APPAPT

Sample output:

2

2. 解析

统计每个字符所在位置之前的P 个数，leftP[i]++;

从后到前，统计T 个数，righT++;

当字符为A时，统计个数ans=(ans+leftP[i]*righT)%mod;

3. AC代码

#include<cstdio>
char str[100010];
int leftP[100010]={};
const int mod=1000000007;
int main()
{
	scanf("%s",str);
	int len=0;
	for (int i = 0; str[i] != '\0'; ++i)
	{
		len++;
		if (i>0)
		{
			leftP[i]=leftP[i-1];
		}
		if (str[i]=='P')
		{
			leftP[i]++;
		}
	}
	int righT=0; int ans=0;
	for (int i = len-1; i >= 0 ; i--)
	{
		if (str[i]=='T')
		{
			righT++;
		}else if(str[i]=='A'){
			ans=(ans+leftP[i]*righT)%mod;
		}
	}
	printf("%d\n", ans);
	return 0;
}