动态规划的题目总结（长期更新）

 

字符串匹配的DP：

 

CF 358 D. Alyona and Strings

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

After returned from forest, Alyona started reading a book. She noticed strings s and t, lengths of which are n and m respectively. As usual, reading bored Alyona and she decided to pay her attention to strings s and t, which she considered very similar.

Alyona has her favourite positive integer k and because she is too small, k does not exceed 10. The girl wants now to choose k disjoint non-empty substrings of string s such that these strings appear as disjoint substrings of string t and in the same order as they do in string s. She is also interested in that their length is maximum possible among all variants.

Formally, Alyona wants to find a sequence of k non-empty strings p₁, p₂, p₃, ..., p_k satisfying following conditions:

• s can be represented as concatenation a₁p₁a₂p₂... a_kp_ka_k + 1, where a₁, a₂, ..., a_k + 1 is a sequence of arbitrary strings (some of them may be possibly empty);
• t can be represented as concatenation b₁p₁b₂p₂... b_kp_kb_k + 1, where b₁, b₂, ..., b_k + 1 is a sequence of arbitrary strings (some of them may be possibly empty);
• sum of the lengths of strings in sequence is maximum possible.

Please help Alyona solve this complicated problem and find at least the sum of the lengths of the strings in a desired sequence.

A substring of a string is a subsequence of consecutive characters of the string.

Input

In the first line of the input three integers n, m, k (1 ≤ n, m ≤ 1000, 1 ≤ k ≤ 10) are given — the length of the string s, the length of the string t and Alyona's favourite number respectively.

The second line of the input contains string s, consisting of lowercase English letters.

The third line of the input contains string t, consisting of lowercase English letters.

Output

In the only line print the only non-negative integer — the sum of the lengths of the strings in a desired sequence.

It is guaranteed, that at least one desired sequence exists.

Examples

Input

3 2 2
abc
ab

Output

2

Input

9 12 4
bbaaababb
abbbabbaaaba

Output

7

Note

The following image describes the answer for the second sample case:

 

　　这道题弄清楚状态就不难做了。

　　dp数组

　　　　第一维：s字串匹配到的位置。

　　　　第二维：t字串匹配到的位置。

　　　　第三维：当前匹配到第几个。

　　　　第四维：是否中断过 1-否 0-是

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
const int maxn=1010;
int n,m,K;
int dp[maxn][maxn][11][2];
char s[maxn],t[maxn];
int main(){
    scanf("%d%d%d",&n,&m,&K);
    scanf("%s%s",s+1,t+1);
    for(int k=1;k<=K;k++)
    for(int i=1;i<=n;i++)
    for(int j=1;j<=m;j++){
        if(s[i]==t[j])
            dp[i][j][k][1]=max(dp[i-1][j-1][k-1][0],dp[i-1][j-1][k][1])+1;    
        dp[i][j][k][0]=max(dp[i][j][k][1],max(dp[i][j-1][k][0],dp[i-1][j][k][0]));
    }
    printf("%d\n",dp[n][m][K][0]);    
    return 0;    
}