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koosaga/berlekamp_massey.cpp

Last active June 28, 2025 12:30
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Revisions

  1. koosaga revised this gist May 17, 2019. 1 changed file with 15 additions and 4 deletions.
    19 changes: 15 additions & 4 deletions berlekamp_massey.cpp
    View file
    Original file line number Diff line number Diff line change
    @@ -1,3 +1,14 @@
    const int mod = 998244353;
    using lint = long long;
    lint ipow(lint x, lint p){
    lint ret = 1, piv = x;
    while(p){
    if(p & 1) ret = ret * piv % mod;
    piv = piv * piv % mod;
    p >>= 1;
    }
    return ret;
    }
    vector<int> berlekamp_massey(vector<int> x){
    vector<int> ls, cur;
    int lf, ld;
    @@ -69,8 +80,8 @@ int guess_nth_term(vector<int> x, lint n){
    return get_nth(v, x, n);
    }
    struct elem{int x, y, v;}; // A_(x, y) <- v, 0-based. no duplicate please..
    vector<int> get_min_poly(int n, vector<elem> M){
    // smallest poly P such that A^i = sum_{j < i} {A^j \times P_j}
    vector<int> get_min_poly(int n, vector<elem> M){
    // smallest poly P such that A^i = sum_{j < i} {A^j \times P_j}
    vector<int> rnd1, rnd2;
    mt19937 rng(0x14004);
    auto randint = [&rng](int lb, int ub){
    @@ -99,7 +110,7 @@ vector<int> get_min_poly(int n, vector<elem> M){
    reverse(sol.begin(), sol.end());
    return sol;
    }
    lint det(int n, vector<elem> M){
    lint det(int n, vector<elem> M){
    vector<int> rnd;
    mt19937 rng(0x14004);
    auto randint = [&rng](int lb, int ub){
    @@ -113,4 +124,4 @@ lint det(int n, vector<elem> M){
    if(n % 2 == 0) sol = mod - sol;
    for(auto &i : rnd) sol = 1ll * sol * ipow(i, mod - 2) % mod;
    return sol;
    }
    }
  2. koosaga created this gist May 17, 2019.
    116 changes: 116 additions & 0 deletions berlekamp_massey.cpp
    View file
    Original file line number Diff line number Diff line change
    @@ -0,0 +1,116 @@
    vector<int> berlekamp_massey(vector<int> x){
    vector<int> ls, cur;
    int lf, ld;
    for(int i=0; i<x.size(); i++){
    lint t = 0;
    for(int j=0; j<cur.size(); j++){
    t = (t + 1ll * x[i-j-1] * cur[j]) % mod;
    }
    if((t - x[i]) % mod == 0) continue;
    if(cur.empty()){
    cur.resize(i+1);
    lf = i;
    ld = (t - x[i]) % mod;
    continue;
    }
    lint k = -(x[i] - t) * ipow(ld, mod - 2) % mod;
    vector<int> c(i-lf-1);
    c.push_back(k);
    for(auto &j : ls) c.push_back(-j * k % mod);
    if(c.size() < cur.size()) c.resize(cur.size());
    for(int j=0; j<cur.size(); j++){
    c[j] = (c[j] + cur[j]) % mod;
    }
    if(i-lf+(int)ls.size()>=(int)cur.size()){
    tie(ls, lf, ld) = make_tuple(cur, i, (t - x[i]) % mod);
    }
    cur = c;
    }
    for(auto &i : cur) i = (i % mod + mod) % mod;
    return cur;
    }
    int get_nth(vector<int> rec, vector<int> dp, lint n){
    int m = rec.size();
    vector<int> s(m), t(m);
    s[0] = 1;
    if(m != 1) t[1] = 1;
    else t[0] = rec[0];
    auto mul = [&rec](vector<int> v, vector<int> w){
    int m = v.size();
    vector<int> t(2 * m);
    for(int j=0; j<m; j++){
    for(int k=0; k<m; k++){
    t[j+k] += 1ll * v[j] * w[k] % mod;
    if(t[j+k] >= mod) t[j+k] -= mod;
    }
    }
    for(int j=2*m-1; j>=m; j--){
    for(int k=1; k<=m; k++){
    t[j-k] += 1ll * t[j] * rec[k-1] % mod;
    if(t[j-k] >= mod) t[j-k] -= mod;
    }
    }
    t.resize(m);
    return t;
    };
    while(n){
    if(n & 1) s = mul(s, t);
    t = mul(t, t);
    n >>= 1;
    }
    lint ret = 0;
    for(int i=0; i<m; i++) ret += 1ll * s[i] * dp[i] % mod;
    return ret % mod;
    }
    int guess_nth_term(vector<int> x, lint n){
    if(n < x.size()) return x[n];
    vector<int> v = berlekamp_massey(x);
    if(v.empty()) return 0;
    return get_nth(v, x, n);
    }
    struct elem{int x, y, v;}; // A_(x, y) <- v, 0-based. no duplicate please..
    vector<int> get_min_poly(int n, vector<elem> M){
    // smallest poly P such that A^i = sum_{j < i} {A^j \times P_j}
    vector<int> rnd1, rnd2;
    mt19937 rng(0x14004);
    auto randint = [&rng](int lb, int ub){
    return uniform_int_distribution<int>(lb, ub)(rng);
    };
    for(int i=0; i<n; i++){
    rnd1.push_back(randint(1, mod - 1));
    rnd2.push_back(randint(1, mod - 1));
    }
    vector<int> gobs;
    for(int i=0; i<2*n+2; i++){
    int tmp = 0;
    for(int j=0; j<n; j++){
    tmp += 1ll * rnd2[j] * rnd1[j] % mod;
    if(tmp >= mod) tmp -= mod;
    }
    gobs.push_back(tmp);
    vector<int> nxt(n);
    for(auto &i : M){
    nxt[i.x] += 1ll * i.v * rnd1[i.y] % mod;
    if(nxt[i.x] >= mod) nxt[i.x] -= mod;
    }
    rnd1 = nxt;
    }
    auto sol = berlekamp_massey(gobs);
    reverse(sol.begin(), sol.end());
    return sol;
    }
    lint det(int n, vector<elem> M){
    vector<int> rnd;
    mt19937 rng(0x14004);
    auto randint = [&rng](int lb, int ub){
    return uniform_int_distribution<int>(lb, ub)(rng);
    };
    for(int i=0; i<n; i++) rnd.push_back(randint(1, mod - 1));
    for(auto &i : M){
    i.v = 1ll * i.v * rnd[i.y] % mod;
    }
    auto sol = get_min_poly(n, M)[0];
    if(n % 2 == 0) sol = mod - sol;
    for(auto &i : rnd) sol = 1ll * sol * ipow(i, mod - 2) % mod;
    return sol;
    }