Update

Author: scanof

code/.vscode/settings.json

@@ -3,6 +3,8 @@
     "iomanip": "cpp",
     "vector": "cpp",
     "cmath": "cpp",
-    "iostream": "cpp"
+    "iostream": "cpp",
+    "numeric": "cpp",
+    "tuple": "cpp"
   }
 }

code/math/CRT.cpp

@@ -1,29 +1,55 @@
-/*
-OVERFLOW!!!
-p = p1*p2*...*pk, pi pairwise coprime
+#include <bits/stdc++.h>
 
-a = a1 mod p1
-a = a2 mod p2
-..
-a = ak mod pk
+#define fi first
+#define se second
 
-This function returns
-a = x1 + x2*p1 + x3*p1*p2 + ... + xk*p1*p2*...*pk-1
+using namespace std;
 
-O(k^2)
-*/
+typedef long long ll;
+typedef pair<ll,ll> pll;
 
-ll CRT(vector<ll> &a, vector<ll> &p){
-  vector<ll> x(sz(p));
-  ll ans = 0, prod = 1;
-  forn(i, sz(p)){
-    x[i] = a[i];
-    forn(j,i){
-      x[i] = 1LL*(x[i] - x[j])*binpow(p[j], p[i] - 2, p[i])%p[i];
-      x[i] = (x[i] + p[i])%p[i];
-    }
-    ans+= 1LL*x[i]*prod;
-    prod *= p[i];
-  }
-  return ans;
+pll extendedEuclid(ll a, ll b){ // a * x + b * y = __gcd(a,b)
+	ll x,y;
+	if (b==0) return {1,0};
+	auto p=extendedEuclid(b,a%b);
+	x=p.se;
+	y=p.fi-(a/b)*x;
+	if(a*x+b*y==-__gcd(a,b)) x=-x, y=-y;
+	return {x,y};
+}
+pair<pll,pll> diophantine(ll a,ll b, ll r) {
+  //a*x+b*y=r where r is multiple of __gcd(a,b);
+	ll d=__gcd(a,b);
+  a/=d; b/=d; r/=d;
+	auto p = extendedEuclid(a,b);
+	p.fi*=r; p.se*=r;
+	// assert(a*p.fi+b*p.se==r);
+	return {p,{-b,a}}; // solutions: p+t*ans.se
+}
+ll inv(ll a, ll m) {
+	assert(__gcd(a,m)==1);
+	ll x = diophantine(a,m,1).fi.fi;
+	return ((x%m)+m)%m;
+}
+#define MOD(a,m) (((a)%m+m)%m)
+pll sol(tuple<ll,ll,ll> c){ //requires inv, diophantine
+  ll a=get<0>(c), x1=get<1>(c), m=get<2>(c), d=__gcd(a,m);
+  if(d==1) return pll(MOD(x1*inv(a,m),m), m);
+  else return x1%d ? pll({-1LL,-1LL}) : sol(make_tuple(a/d,x1/d,m/d));
+}
+pair<ll,ll> crt(vector< tuple<ll,ll,ll> > &cond) { // returns: (sol, lcm)
+	ll x1=0,m1=1,x2,m2;
+	for(auto &t: cond){
+		tie(x2,m2)=sol(t);
+		if((x1-x2)%__gcd(m1,m2))return {-1,-1};
+		if(m1==m2)continue;
+		ll k=diophantine(m2,-m1,x1-x2).fi.se,l=m1*(m2/__gcd(m1,m2));
+		x1=MOD((__int128_t)m1*k+x1,l); m1=l;
+	}
+	return sol(make_tuple(1,x1,m1));
+} //cond[i]={ai,bi,mi} ai*xi=bi (mi); assumes lcm fits in ll
+
+int main(){
+  // cout << "NO" << endl;
+  return 0;
 }

code/math/berlekamp_massey.cpp

@@ -0,0 +1,63 @@
+// taken from https://codeforces.com/blog/entry/61306
+struct ber_ma{
+	vi BM(vi &x){
+		vi ls,cur; int lf,ld;
+		forn(i,sz(x)){
+			ll t=0;
+			forn(j,sz(cur)) t=(t+x[i-j-1]*(ll)cur[j])%mod;
+			if((t-x[i])%mod==0) continue; 
+			if(!sz(cur)){
+				cur.resize(i+1);
+				lf=i; ld=(t-x[i])%mod;
+				continue;
+			}
+			ll k=-(x[i]-t)*inv(ld,mod);
+			vi c(i-lf-1); c.pb(k);
+			forn(j,sz(ls)) c.pb(-ls[j]*k%mod);
+			if(sz(c)<sz(cur)) c.resize(sz(cur));
+			forn(j,sz(cur)) c[j]=(c[j]+cur[j])%mod;
+			if(i-lf+sz(ls)>=sz(cur)) ls=cur,lf=i,ld=(t-x[i])%mod;
+			cur=c;
+		}
+		forn(i,sz(cur)) cur[i]=(cur[i]%mod+mod)%mod;
+		return cur;
+	}
+	
+	int m; //length of recurrence
+	//a: first terms
+	//h: relation
+	vector<ll> a, h, t_, s, t;
+	//calculate p*q mod f
+	inline vector<ll> mull(vector<ll> p, vector<ll> q){
+		forn(i,2*m) t_[i]=0;
+		forn(i,m) if(p[i])
+			forn(j,m)
+				t_[i+j]=(t_[i+j]+p[i]*q[j])%mod;
+		for(int i=2*m-1;i>=m;--i) if(t_[i])
+			forn(j,m)
+				t_[i-j-1]=(t_[i-j-1]+t_[i]*h[j])%mod;
+		forn(i,m) p[i]=t_[i];
+		return p;
+	}
+	inline ll calc(ll k){
+    if(k < sz(a)) return a[k];
+		forn(i,m) s[i]=t[i]=0;
+		s[0]=1; 
+		if(m!=1) t[1]=1; 
+		else t[0]=h[0];
+		
+		while(k){
+			if(k&1LL) s = mull(s,t);
+			t = mull(t,t); k/=2;
+		}
+		ll su=0;
+		forn(i,m) su=(su+s[i]*a[i])%mod;
+		return (su%mod+mod)%mod;
+	}
+	ber_ma(vi &x){
+		vi v = BM(x); m=sz(v);
+		h.resize(m), a.resize(m), s.resize(m);
+		t.resize(m), t_.resize(2*m);
+		forn(i,m) h[i]=v[i],a[i]=x[i];
+	}	
+};

contents.txt

@@ -95,6 +95,7 @@ math/CRT.cpp	Chinese Remainder Theorem
 math/simplex.cpp	Simplex
 math/gaussjordan.cpp	Gauss Jordan
 math/gaussjordan_modular.cpp	Gauss Jordan Modular
+math/berlekamp_massey.cpp	Berlekamp Massey
 
 [Dynamic Programming]
 dynamic-programming/edit_distance.cpp	Edit Distance