FFT

---

1 HDU 1402 A * B Problem Plus

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <cctype>
#include <ctime>
#include <ext/rope>

using namespace std;
using namespace __gnu_cxx;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define eps 1e-9
#define SZ(x) ((int)x.size())

typedef long long ll;
typedef pair<int, int> pii;

#define PI acos(-1.0)
const int maxn = 1e5 + 10;
struct Complex {
    double x, y;
    Complex(double _x = 0.0, double _y = 0.0) { x = _x; y = _y; }
    Complex operator - (const Complex &b) const { return Complex(x - b.x, y - b.y); }
    Complex operator + (const Complex &b) const { return Complex(x + b.x, y + b.y); }
    Complex operator * (const Complex &b) const { return Complex(x * b.x - y * b.y, x * b.y + y * b.x); }
};
char str_A[maxn], str_B[maxn];
Complex A[maxn * 4], B[maxn * 4], ans[maxn * 4];
int ans_final[maxn * 4], len_final = 0;
int N, M, n = 1;

void fft(Complex a[], int len, int oper) {
    for (int i = 1, j = 0; i < len - 1; ++i) {
        for (int s = len; ~j & s;) { j ^= s >>= 1; }
        if (i < j) { swap(a[i], a[j]); }
    }
    Complex omega_m, omega, t, u;
    int m, m2;
    for (int d = 0; (1 << d) < len; ++d) {
        m = (1 << d); m2 = m << 1;
        omega_m = Complex(cos(PI / m * oper), sin(PI / m * oper));
        for (int i = 0; i < len; i += m2) {
            omega = Complex(1, 0);
            for (int j = 0; j < m; ++j) {
                u = a[i + j]; t = omega * a[i + j + m];
                a[i + j] = u + t; a[i + j + m] = u - t;
                omega = omega * omega_m;
            }
        }
    }
    if (oper == -1) { REP(i, N + M - 1) { a[i].x /= len; } }
}


int main() {
#ifdef __AiR_H
    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
#endif // __AiR_H
    while (scanf("%s %s", str_A, str_B) != EOF) {
        memset(ans, 0, sizeof(ans)); memset(ans_final, 0, sizeof(ans_final));
        N = strlen(str_A); M = strlen(str_B); n = 1;
        while (n < N + M - 1) { n <<= 1; }
        REP(i, N) { A[i] = Complex(str_A[N - 1 - i] - '0', 0); }
        for (int i = N; i < n; ++i) { A[i] = Complex(0, 0); }
        REP(i, M) { B[i] = Complex(str_B[M - 1 - i] - '0', 0); }
        for (int i = M; i < n; ++i) { B[i] = Complex(0, 0); }
        fft(A, n, 1); fft(B, n, 1);
        REP(i, n) { ans[i] = A[i] * B[i]; }
        fft(ans, n, -1);
        REP(i, N + M) { ans_final[i] = ans[i].x + 0.5; }
        REP(i, N + M - 1) { ans_final[i + 1] += ans_final[i] / 10; ans_final[i] %= 10; }
        len_final = N + M - 1;
        if (ans_final[len_final]) { ++len_final; }
        while (ans_final[len_final - 1] == 0 && len_final > 1) { --len_final; }
        for (int i = len_final - 1; i > 0; --i) { printf("%d", ans_final[i]); } printf("%d
", ans_final[0]);
    }
    return 0;
}

2 HDU 4609 3-idiots

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <cctype>
#include <ctime>
#include <ext/rope>

using namespace std;
using namespace __gnu_cxx;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define eps 1e-9
#define SZ(x) ((int)x.size())

typedef long long ll;
typedef pair<int, int> pii;

#define PI acos(-1.0)
const int maxn = 1e5 + 10;
struct Complex {
    double x, y;
    Complex(double _x = 0.0, double _y = 0.0) { x = _x; y = _y; }
    Complex operator - (const Complex &b) const { return Complex(x - b.x, y - b.y); }
    Complex operator + (const Complex &b) const { return Complex(x + b.x, y + b.y); }
    Complex operator * (const Complex &b) const { return Complex(x * b.x - y * b.y, x * b.y + y * b.x); }
};
int T, n_t, N, M, n;
Complex A[maxn * 4], B[maxn * 4], mul[maxn * 4];
int a[maxn];
ll ans[maxn * 4], sum[maxn * 4];

void fft(Complex a[], int len, int oper) {
    for (int i = 1, j = 0; i < len - 1; ++i) {
        for (int s = len; ~j & s;) { j ^= s >>= 1; }
        if (i < j) { swap(a[i], a[j]); }
    }
    Complex omega_m, omega, t, u;
    int m, m2;
    for (int d = 0; (1 << d) < len; ++d) {
        m = (1 << d); m2 = m << 1;
        omega_m = Complex(cos(PI / m * oper), sin(PI / m * oper));
        for (int i = 0; i < len; i += m2) {
            omega = Complex(1, 0);
            for (int j = 0; j < m; ++j) {
                u = a[i + j]; t = omega * a[i + j + m];
                a[i + j] = u + t; a[i + j + m] = u - t;
                omega = omega * omega_m;
            }
        }
    }
    if (oper == -1) { REP(i, N + M - 1) { a[i].x /= len; } }
}
void init() {
    memset(A, 0 ,sizeof(A)); memset(B, 0, sizeof(B));
    memset(mul, 0, sizeof(mul)); memset(ans, 0, sizeof(ans)); n = 1;
}

int main() {
#ifdef __AiR_H
    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
#endif // __AiR_H
    scanf("%d", &T);
    while (T--) {
        scanf("%d", &n_t); init();
        for (int i = 1; i <= n_t; ++i) {
            scanf("%d", &a[i]); ++A[a[i]].x; ++B[a[i]].x;
        }
        sort(a + 1, a + n_t + 1); N = M = a[n_t] + 1;
        while (n < N + M - 1) { n <<= 1; }
        fft(A, n, 1); fft(B, n, 1);
        for (int i = 0; i < n; ++i) { mul[i] = A[i] * B[i]; } fft(mul, n, -1);
        for (int i = 1; i < N + M; ++i) { ans[i] = (ll)(mul[i].x + 0.5); }
        for (int i = 1; i <= n_t; ++i) { --ans[a[i] + a[i]]; }
        for (int i = 1; i <= N + M; ++i) { ans[i] /= 2; }
        for (int i = 1; i <= N + M; ++i) { sum[i] = sum[i - 1] + ans[i]; }
        ll ans1 = 1ll * n_t * (n_t - 1) * (n_t - 2) / 6, ans2 = 0;
        for (int i = 1; i <= n_t; ++i) {
            ans2 += sum[N + M] - sum[a[i]];
            ans2 -= 1ll * (i - 1) * (n_t - i);
            ans2 -= n_t - 1;
            ans2 -= 1ll * (n_t - i) * (n_t - i - 1) / 2;
        }
        printf("%.7f
", 1.0 * ans2 / ans1);
    }
    return 0;
}

---

---

1 UVALive 4671 K-neighbor substrings

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <queue>
#include <vector>
#include <stack>
#include <map>
#include <set>
#include <cmath>
#include <cctype>
#include <ctime>
#include <ext/rope>

using namespace std;
using namespace __gnu_cxx;

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define eps 1e-9
#define SZ(x) ((int)x.size())
#define PI acos(-1.0)

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
const int maxn = 1e5 + 10;
struct Complex {
    double x, y;
    Complex(double _x = 0.0, double _y = 0.0) { x = _x; y = _y; }
    Complex operator - (const Complex &b) const { return Complex(x - b.x, y - b.y); }
    Complex operator + (const Complex &b) const { return Complex(x + b.x, y + b.y); }
    Complex operator * (const Complex &b) const { return Complex(x * b.x - y * b.y, x * b.y + y * b.x); }
};
ull Hash[maxn], Pow[maxn];
set<ull> s;
int k, len1, len2, Case = 0, N, M, n;
char s1[maxn], s2[maxn];
Complex A[maxn * 4], B[maxn * 4], mul[maxn * 4];
int ans1[maxn * 4], ans2[maxn * 4];

void fft(Complex a[], int len, int oper) {
    for (int i = 1, j = 0; i < len - 1; ++i) {
        for (int s = len; ~j & s;) { j ^= s >>= 1; }
        if (i < j) { swap(a[i], a[j]); }
    }
    Complex omega_m, omega, t, u;
    int m, m2;
    for (int d = 0; (1 << d) < len; ++d) {
        m = (1 << d); m2 = m << 1;
        omega_m = Complex(cos(PI / m * oper), sin(PI / m * oper));
        for (int i = 0; i < len; i += m2) {
            omega = Complex(1, 0);
            for (int j = 0; j < m; ++j) {
                u = a[i + j]; t = omega * a[i + j + m];
                a[i + j] = u + t; a[i + j + m] = u - t;
                omega = omega * omega_m;
            }
        }
    }
    if (oper == -1) { REP(i, N + M - 1) { a[i].x /= len; } }
}
int solve(int ans[], char c) {
    memset(A, 0, sizeof(A)); memset(B, 0, sizeof(B));
    for (int i = 0; i < len1; ++i) {
        if (s1[i] == c) { A[i].x = 1; }
    }
    for (int i = 0; i < len2; ++i) {
        if (s2[i] == c) { B[i].x = 1; }
    }
    fft(A, n, 1); fft(B, n, 1);
    for (int i = 0; i < n; ++i) { mul[i] = A[i] * B[i]; }
    fft(mul, n, -1);
    for (int i = len2 - 1; i < N + M; ++i) { ans[i] = mul[i].x + 0.5; }
}

int main() {
#ifdef __AiR_H
    freopen("in.txt", "r", stdin);
//    freopen("out.txt", "w", stdout);
#endif // __AiR_H
    Pow[0] = 1; ull t; Hash[0] = 0;
    for (int i = 1; i < maxn; ++i) { Pow[i] = Pow[i - 1] * 131; }
    while (scanf("%d", &k) && k != -1) {
        scanf("%s %s", s1, s2); len1 = strlen(s1); len2 = strlen(s2);
        if (len1 < len2) { printf("Case %d: 0
", ++Case); continue; }
        reverse(s2, s2 + len2); s.clear();
        N = len1; M = len2; n = 1; while (n < N + M - 1) { n <<= 1; }
        solve(ans1, 'a'); solve(ans2, 'b');
        for (int i = 0; i < len1; ++i) { Hash[i + 1] = Hash[i] * 131 + s1[i]; }
        for (int i = 0; i <= len1 - len2; ++i) {
            t = Hash[i + len2] - Hash[i] * Pow[len2];
            if (len2 - ans1[i + len2 - 1] - ans2[i + len2 - 1] <= k) {
                s.insert(t);
            }
        }
        printf("Case %d: %d
", ++Case, (int)s.size());
    }
    return 0;
}

---