任意 mod 畳み込み

fps/any_mod.hpp

@@ -0,0 +1,77 @@
+#pragma once
+#include <vector>
+#include <atcoder/convolution>
+#include <cassert>
+
+namespace po167{
+//https://kopricky.github.io/code/Computation_Advanced/garner.html
+template<typename T>
+T mod_add(const T a, const T b, const T mod){
+    return (a + b) % mod;
+}
+
+template<typename T>
+T mod_mul(const T a, const T b, const T mod){
+    return a * b % mod;
+}
+
+template<typename T>
+T mod_inv(T a, T mod){
+    T u[] = {a, 1, 0}, v[] = {mod, 0, 1}, t;
+    while(*v){
+        t = *u / *v;
+        std::swap(u[0] -= t * v[0], v[0]);
+        std::swap(u[1] -= t * v[1], v[1]);
+        std::swap(u[2] -= t * v[2], v[2]);
+    }
+    u[1] %= mod;
+    return (u[1] < 0) ? (u[1] + mod) : u[1];
+}
+
+template<typename T>
+T garner(const std::vector<T>& a, std::vector<T> p, const T mod){
+    const unsigned int sz = a.size();
+    std::vector<T> kp(sz + 1, 0), rmult(sz + 1, 1);
+    p.push_back(mod);
+    for(unsigned int i = 0; i < sz; ++i){
+        T x = mod_mul(a[i] - kp[i], mod_inv(rmult[i], p[i]), p[i]);
+        x = (x < 0) ? (x + p[i]) : x;
+        for(unsigned int j = i + 1; j < sz + 1; ++j){
+            kp[j] = mod_add(kp[j], rmult[j] * x, p[j]);
+            rmult[j] = mod_mul(rmult[j], p[i], p[j]);
+        }
+    }
+    return kp[sz];
+}
+
+const long long _mod0=754974721;
+const long long _mod1=167772161;
+const long long _mod2=469762049;
+std::vector<long long> _MOD={_mod0,_mod1,_mod2};
+std::vector<long long> convolution_any_mod(std::vector<long long> a,std::vector<long long> b,long long pmod){
+	for(auto &x:a) x = (x % pmod + pmod) % pmod;
+	for(auto &x:b) x = (x % pmod + pmod) % pmod;
+	std::vector<std::vector<long long>> res(3);
+	res[0] = atcoder::convolution<_mod0>(a,b);
+	res[1] = atcoder::convolution<_mod1>(a,b);
+	res[2] = atcoder::convolution<_mod2>(a,b);
+	for(int i=0;i<(int)res[0].size();i++){
+		std::vector<long long> q(3);
+		for(int j=0;j<3;j++) q[j] = res[j][i];
+		res[0][i] = garner(q, _MOD, pmod);
+	}
+	return res[0];
+}
+template<typename T>
+std::vector<T> convolution_mint(std::vector<T> a, std::vector<T> b){
+    std::vector<long long> A, B;
+    A.reserve(a.size()), B.reserve(b.size());
+    for (auto x : a) A.push_back(x.val());
+    for (auto x : b) B.push_back(x.val());
+    std::vector<long long> C = convolution_any_mod(A, B, T::mod());
+    std::vector<T> c;
+    c.reserve(C.size());
+    for (auto x : C) c.push_back(x);
+    return c;
+}
+};