NOIP2015 Day2 T2 子串

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https://blog.sengxian.com/solutions/noip-2015-day2
三维DP，空间会爆，缩范围可拿70巨分。

#include<cstdio>#include<iostream>using namespace std;const int maxn = 550;const int maxm = 55;const int mod = 1000000007;int n, m, K;char a[maxn], b[maxm];int f[maxn][maxm][maxm], s[maxn][maxm][maxm];int main(){    cin >> n >> m >> K;    scanf("%s", a+1);    scanf("%s", b+1);    s[0][0][0] = 1;    for(int i = 1; i <= n; i++){        s[i][0][0] = 1;        for(int j = 1; j <= m; j++){            if(a[i] == b[j])                for(int k = 1; k <= min(K, j); k++){                    f[i][j][k] = (s[i-1][j-1][k-1] + f[i-1][j-1][k]) % mod;                    s[i][j][k] = (s[i-1][j][k] + f[i][j][k]) % mod;                }            else                for(int k = 1; k <= min(K, j); k++)                    s[i][j][k] = s[i-1][j][k];        }    }    cout << s[n][m][K] << endl;    return 0;}

三维可像01背包一样压缩为二维，方法是倒序枚举j,k，这样可以调用i-1时的j,k，如此可拿100巨分。

#include<cstdio>#include<iostream>using namespace std;const int maxn = 1050;const int maxm = 220;const int mod = 1000000007;int n, m, K;char a[maxn], b[maxm];int f[maxm][maxm], s[maxm][maxm];int main(){    cin >> n >> m >> K;    scanf("%s", a+1);    scanf("%s", b+1);    s[0][0] = 1;    for(int i = 1; i <= n; i++){        //s[i][0][0] = 1;        for(int j = m; j >= 1; j--){            if(a[i] == b[j])                for(int k = min(K, j); k >= 1; k--){                    f[j][k] = (s[j-1][k-1] + f[j-1][k]) % mod;                    s[j][k] = (s[j][k] + f[j][k]) % mod;                }            else                fill(f[j], f[j] + min(K, j) + 1, 0);        }    }    cout << s[m][K] << endl;    return 0;}

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