Codeforces Round #166 (Div. 2)D. Good Substrings（字符串散列）

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最新推荐文章于 2024-07-25 21:12:06 发布

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本文探讨了一种利用哈希函数优化字符串匹配效率的方法，并通过具体代码实例展示了如何在给定条件下查找特定类型的好子串。通过统计字符串中好字母的数量，并结合哈希值快速判断子串是否满足条件，实现高效计算不同长度子串的个数。

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You've got string s, consisting of small English letters. Some of the English letters are good, the rest are bad.

A substring s[l...r] (1 ≤ l ≤ r ≤ |s|) of string s = s₁s₂...s_|s| (where |s| is the length of string s) is string s_ls_l + 1...s_r.

The substring s[l...r] is good, if among the letters s_l, s_l + 1, ..., s_r there are at most k bad ones (look at the sample's explanation to understand it more clear).

Your task is to find the number of distinct good substrings of the given string s. Two substrings s[x...y] and s[p...q] are considered distinct if their content is different, i.e. s[x...y] ≠ s[p...q].

Input

The first line of the input is the non-empty string s, consisting of small English letters, the string's length is at most 1500 characters.

The second line of the input is the string of characters "0" and "1", the length is exactly 26 characters. If the i-th character of this string equals "1", then the i-th English letter is good, otherwise it's bad. That is, the first character of this string corresponds to letter "a", the second one corresponds to letter "b" and so on.

The third line of the input consists a single integer k (0 ≤ k ≤ |s|) — the maximum acceptable number of bad characters in a good substring.

Output

Print a single integer — the number of distinct good substrings of string s.

Sample test(s)

Input

ababab
01000000000000000000000000
1

Output

Input

acbacbacaa
00000000000000000000000000
2

Output

Note

In the first example there are following good substrings: "a", "ab", "b", "ba", "bab".

In the second example there are following good substrings: "a", "aa", "ac", "b", "ba", "c", "ca", "cb".

直接比较字符串的运算量大，因而构造哈希函数将字符串映射为整数，便于比较。

AC Code：

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <set>
 4 #include <cstring>
 5 
 6 using namespace std;
 7 
 8 char str[1505], flag[27];  //flag用于记录字母是否good one
 9 int Dad_Count[1505], k;
10 const long long seed[3] = {13131, 10007, 11137};  //用于生成哈希值,设置三个值降低冲突率
11 const int MOD = 1000000007;
12 
13 int main()
14 {
15     while(scanf("%s %s %d", str, flag, &k) != EOF)
16     {
17         int len = strlen(str);
18         Dad_Count[0] = (flag[str[0]-'a'] == '0');
19         for(int i = 1; i < len; i++)  //统计[str_0, str_i]中坏字母的个数
20             Dad_Count[i] = Dad_Count[i-1] + ('0' == flag[str[i]-'a']);
21         set<long long> Substr;
22         for(int i = 0; i < len; i++)
23         {
24             long long HashVal = str[i] - 'a' + 1;
25             for(int j = i; j < len; j++)
26             {
27                 if(j == i)
28                 {
29                     if(('0' == flag[str[i]-'a']) <= k)
30                     {
31                         int key = (str[i] - 'a');
32                         Substr.insert(key);
33                     }
34                 }
35                 else
36                 {
37                     //注意判断边界：flag[str[i]-'a'] == '0'
38                     int cnt = Dad_Count[j] - Dad_Count[i] + (flag[str[i]-'a'] == '0');
39                     if(cnt > k) break;
40                     HashVal += ((HashVal * seed[str[j]%3] + (str[j] - 'a')) % MOD);  //%MOD是防止溢出
41                     Substr.insert(HashVal);
42                 }
43             }
44         }
45         printf("%d\n", Substr.size());
46     }
47     return 0;
48 }