Fuzzy Search

#include <bits/stdc++.h>

#define PI acos(-1)

const int N = 200010;

using namespace std;

struct EX
{
    double real,i;
    EX operator+(const EX tmp)const{return (EX){real+tmp.real, i+tmp.i};};
    EX operator-(const EX tmp)const{return (EX){real-tmp.real, i-tmp.i};};
    EX operator*(const EX tmp)const{return (EX){real*tmp.real - i*tmp.i, real*tmp.i + i*tmp.real};};
};

int R[N<<2];

void DFT(EX a[],int n,int tp_k)
{
    for(int i=0;i<n;i++) if(i<R[i]) swap(a[i],a[R[i]]);
    for(int d=1;d<n;d<<=1)
    {
        EX wn = (EX){cos(PI/d), sin(PI/d)*tp_k};
        for(int i=0;i<n;i += (d<<1))
        {
            EX wt = (EX){1,0};
            for(int k=0;k<d;k++, wt = wt*wn)
            {
                EX A0 = a[i+k], A1 = wt * a[i+k+d];
                a[i+k] = A0+A1;
                a[i+k+d] = A0-A1;
            }
        }
    }
    if(tp_k==-1)
        for(int i=0;i<n;i++) a[i] = (EX){a[i].real/n, a[i].i/n};
}

int n,m,K;
EX A[N<<2],B[N<<2],C[N<<2];
char S[N],S2[N];
bool del[N];

void calc(char ch,int tot)
{
    memset(B,0,sizeof(B));
    memset(A,0,sizeof(A));
    int cnt_S2 = 0;
    for(int i=0;i<m;i++) if(S2[i]==ch) B[m-i] = (EX){1,0}, cnt_S2++;
    int tp = -1;
    for(int i=0;i<n;i++)
    {
        if(S[i]==ch) tp = i;
        if(tp!=-1 && i-tp<=K) A[i] = (EX){1,0};
    }
    tp = -1;
    for(int i=n-1;i>=0;i--)
    {
        if(S[i]==ch) tp = i;
        if(tp!=-1 && tp-i<=K) A[i] = (EX){1,0};
    }
    DFT(A,tot,1);
    DFT(B,tot,1);
    for(int i=0;i<tot;i++) C[i] = A[i]*B[i];
    DFT(C,tot,-1);
    for(int i=0;i<n;i++)
    {
        int tmp = C[i+m].real+0.5;
        if(tmp<cnt_S2) del[i] = 1;
    }
}

int main()
{
    scanf("%d%d%d",&n,&m,&K);
    scanf("%s%s",S,S2);
    int L = 0,tot;
    while((1<<L)<n+m) L++;
    tot = (1<<L);
    for(int i=1;i<tot;i++) R[i]=(R[i>>1]>>1)|((i&1)<<(L-1));
    calc(‘A‘,tot);
    calc(‘T‘,tot);
    calc(‘C‘,tot);
    calc(‘G‘,tot);
    int ans = 0;
    for(int i=0;i<=n-m;i++) if(!del[i]) ans++;
    printf("%d\n",ans);
    return 0;
}