小鸟游六花

vanishment this world

发表于

一、埃拉托斯特尼筛法

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const int MAX_N = 1010;
using ll = long long;
bool is_prime[MAX_N];
vector<int> primes;
int init = []() {
    for (int i = 0; i < MAX_N; ++i) {
        is_prime[i] = true;
    }
    is_prime[0] = is_prime[1] = false;
    for (int i = 2; i < MAX_N; ++i) {
        if (!is_prime[i]) {
            continue;
        }
        primes.push_back(i);
        for (int j = i; j <= (MAX_N - 1) / i; ++j) {
            is_prime[i * j] = false;
        }
    }
    return 0;
} ();
bool check_prime(ll x) {
    if (x < MAX_N) {
        return is_prime[x];
    }
    for (ll p : primes) {
        if (p * p > x) {
            return true;
        }
        if (x % p == 0) {
            return false;
        }
    }
    return true; 
}

发表于

一、算法实现

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template<typename T, int M>
struct matrix_t {
    using row = vector<T>;
    using mat = vector<row>;
    using ll = long long;
    static void mul(const mat& a, const mat& b, mat& c) {
        auto m = a.size(), p = a[0].size(), n = b[0].size();
        for (int i = 0; i < m; ++i) {
            for (int k = 0; k < p; ++k) {
                for (int j = 0; j < n; ++j) {
                    c[i][j] = (c[i][j] + (ll)a[i][k] * b[k][j]) % M;
                }
            }
        }
    }
    static mat mul(const mat& a, const mat& b) {
        auto m = a.size(), n = b[0].size();
        mat c = vector<row>(m, row(n, 0));
        mul(a, b, c);
        return c;
    }
    static mat qpow(mat a, ll k) {
        auto n = a.size();
        mat ans = vector<row>(n, row(n, 0));
        for (int i = 0; i < n; ++i) {
            ans[i][i] = 1;
        }
        while (k) {
            if (k & 1) {
                ans = mul(a, ans);
            }
            k >>= 1;
            a = mul(a, a);
        }
        return ans;
    }
};
const int M = 1e9 + 7;
using matrix = matrix_t<int, M>;
class Solution {
public:
    int fib(int n) {
         vector<vector<int>> mat = {{0, 1}, {1, 1}};
         vector<vector<int>> vec = {{0, 1}};
         mat = matrix::qpow(mat, n);
         return matrix::mul(vec, mat)[0][0];
    }
};

发表于

一、算法实现

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using ll = long long;
template<typename T, typename F>
struct disjoint_sparse_table {
    int n;
    vector<int> log2;
    vector<vector<T>> mat;
    F func;
    disjoint_sparse_table(const vector<T>& arr, const F& f) : n(int(arr.size())), func(f) {
        build_log2();
        mat.push_back(arr);
        int k = log2[n];
        for (int i = 1; i <= k; ++i) {
            mat.emplace_back(n);
            for (int j = 0; j < n - (1 << (i - 1)); ++j) {
                mat[i][j] = func(mat[i - 1][j], mat[i - 1][j + (1 << (i - 1))]);
            }
        }
    }
    void build_log2() {
        log2.resize(n + 5, 0);
        log2[1] = 0;
        log2[2] = 1;
        for (int i = 3; i <= n; ++i) log2[i] = log2[i >> 1] + 1;
    }
    T query(int l, int r) {
        int k = log2[r - l + 1];
        return func(mat[k][l], mat[k][r - (1 << k) + 1]);
    }
};
/*
        disjoint_sparse_table st(nums, [](int a, int b) {
            return gcd(a, b);
        });
*/
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