Gym101667 H. Rock Paper Scissors

 

After each other's characters will win the second string into each other and reverse, string matching is the convolution process.

Cubic convolution can do on enumeration of a character.

#include <bits/stdc++.h>

struct Complex {
    double r, i;
    Complex(){}
    Complex(double r, double i): r(r), i(i) {}
    Complex operator + (const Complex &p) const { return Complex(r + p.r, i + p.i); }
    Complex operator - (const Complex &p) const { return Complex(r - p.r, i - p.i); }
    Complex operator * (const Complex &p) const { return Complex(r * p.r - i * p.i, r * p.i + i * p.r); }
};

const int N = 4e5 + 7;
const double pi = acos(-1.0);
int r[N];

void FFT(Complex a[], int n, int pd) {
    for (int i = 0; i < n; i++)
        if (i < r[i])
            std::swap(a[i], a[r[i]]);
    for (int mid = 1; mid < n; mid <<= 1) {
        Complex wn(cos(pi / mid), pd * sin(pi / mid));
        for (int l = mid << 1, j = 0; j < n; j += l) {
            Complex w(1.0, 0.0);
            for (int k = 0; k < mid; k++, w = w * wn) {
                Complex u = a[k + j], v = w * a[k + j + mid];
                a[k + j] = u + v;
                a[k + j + mid] = u - v;
            }
        }
    }
    if (pd == -1)
        for (int i = 0; i < n; i++)
            a[i] = Complex(a[i].r / n, a[i].i / n);
}

Complex A[N], B[N];
int n, m, limit, sum[N];
char s[N], t[N];

void solve(char ch) {
    for (int i = 0; i < n; i++)
        A[i] = Complex(s[i] == ch ? 1 : 0, 0.0);
    for (int i = n; i < limit; i++)
        A[i] = Complex(0.0, 0.0);
    for (int i = 0; i < m; i++)
        B[i] = Complex(t[i] == ch ? 1.0 : 0.0, 0.0);
    for (int i = m; i < limit; i++)
        B[i] = Complex(0.0, 0.0);
    FFT(A, limit, 1); FFT(B, limit, 1);
    for (int i = 0; i < limit; i++)
        A[i] = A[i] * B[i];
    FFT(A, limit, -1);
    for (int i = 0; i < limit; i++)
        sum[i] += (int)(A[i].r + 0.5);
}

int main () {
    scanf("%d%d", &n, &m);
    scanf("%s", s);
    scanf("%s", t);
    for (int i = 0; i < m; i++) {
        if (t[i] == 'R') t[i] = 'S';
        else if (t[i] == 'S') t[i] = 'P';
        else t[i] = 'R';
    }
    std::reverse(t, t + m);
    int len = n + m;
    int l = 0;
    limit = 1;
    while (limit < len) limit <<= 1, l++;
    for (int i = 0; i < limit; i++)
        r[i] = r[i >> 1] >> 1 | ((i & 1) << (l - 1));
    solve('R');
    solve('S');
    solve('P');
    int ans = 0;
    for (int i = m - 1; i < limit; i++)
        ans = std::max(ans, sum[i]);
    printf("%d\n", ans);
    return 0;
}

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