70: libreoj #2424 区间dp

$des$

$sol$

$f_{i, j, k} => a => [1, i], b => [1, j], a_i = b_j | a_i != b_j , a_i => 0 / 1 $
$g_{i, j, k} => a => [1, i], b => [1, j], a_i = b_j, a_i => 1$
转移时：
$a_i = b_j => g_{i, j, k} = g_{i - 1, j - 1, k} + f_{i - 1, j - 1, k - 1}$
$a_i != b_j => g_{i, j, k} = 0$
$f_{i, j, k} = g_{i - 1, j, k} + f_{i - 1, j, k}$

$code$

#include <bits/stdc++.h>

using namespace std;

#define gc getchar()
inline int read() {
    int x = ; char c = gc;
    while(c < '' || c > '') c = gc;
    while(c >= '' && c <= '') x = x *  + c - '', c = gc;
    return x;
}

const int Mod = 1e9 + ;

const int N = ;

int n, m, k_;
int f[][N][N], g[][N][N];
char a[], b[N];    

int main() {
    cin >> n >> m >> k_;
    scanf("%s%s", a + , b + );
    f[][][] = ;
    int cur = ;
    for(int i = ; i <= n; i ++, cur ^= ) {
        f[cur][][] = ;
        for(int j = ; j <= m; j ++) {
            for(int k = ; k <= k_; k ++) {
                if(a[i] == b[j]) g[cur][j][k] = (g[cur ^ ][j - ][k] + f[cur ^ ][j - ][k - ]) % Mod;
                else g[cur][j][k] = ;
                f[cur][j][k] = (g[cur][j][k] + f[cur ^ ][j][k]) % Mod;
            }
        }
    }

    cout << f[cur ^ ][m][k_];
    return ;
}