add FPS

Author: snuke

README.md

@@ -26,6 +26,7 @@ AtCoder解説放送ライブラリ集
 |Combination|[comb.cpp](comb.cpp)|nCkをmod素数で求める|
 |Matrix|[mat.cpp](mat.cpp)|行列|
 |素数|[prime.cpp](prime.cpp)|素数列挙と素因数分解|
+|FPS|[fps.cpp](fps.cpp)|形式的べき級数|
 
 ### グラフ
 |名前|コード|説明|

fps.cpp

@@ -0,0 +1,38 @@
+// Formal Power Series
+using vm = vector<mint>;
+struct fps : vm {
+#define d (*this)
+#define s int(vm::size())
+  template<class...Args> fps(Args...args): vm(args...) {}
+  fps(initializer_list<mint> a): vm(a.begin(),a.end()) {}
+  void rsz(int n) { if (s < n) resize(n);}
+  mint& operator[](int i) { rsz(i+1); return vm::operator[](i);}
+  mint operator[](int i) const { return i<s ? vm::operator[](i) : 0;}
+  mint operator()(mint x) const {
+    mint r;
+    for (int i = s-1; i >= 0; --i) r = r*x+d[i];
+    return r;
+  }
+  fps operator-() const { fps r(d); rep(i,s) r[i] = -r[i]; return r;}
+  fps& operator+=(const fps& a) { rsz(a.size()); rep(i,a.size()) d[i] += a[i]; return d;}
+  fps& operator-=(const fps& a) { rsz(a.size()); rep(i,a.size()) d[i] -= a[i]; return d;}
+  fps& operator*=(const fps& a) { return d = convolution(d, a);}
+  fps& operator*=(mint a) { rep(i,s) d[i] *= a; return *this;}
+  fps& operator/=(mint a) { rep(i,s) d[i] /= a; return *this;}
+  fps operator+(const fps& a) const { return fps(d) += a;}
+  fps operator-(const fps& a) const { return fps(d) -= a;}
+  fps operator*(const fps& a) const { return fps(d) *= a;}
+  fps operator*(mint a) const { return fps(d) *= a;}
+  fps operator/(mint a) const { return fps(d) /= a;}
+  fps integ() const {
+    fps r;
+    rep(i,s) r[i+1] = d[i]/(i+1);
+    return r;
+  }
+#undef s
+#undef d
+};
+ostream& operator<<(ostream&o,const fps&a) {
+  rep(i,a.size()) o<<(i?" ":"")<<a[i].val();
+  return o;
+}