多点評価等比数列

fps/Multipoint_Evaluation_Geo.hpp

@@ -0,0 +1,59 @@
+#include "FPS_cyclic_convolution.hpp"
+namespace po167{
+template <class T>
+// return {f(ar^0), f(ar^1), f(ar^2), ... f(ar^{len - 1})}
+std::vector<T> Multipoint_Evaluation_Geo(
+    std::vector<T> f,
+    T a, T r, int len = -1
+){
+    if (len == -1) len = f.size();
+    if (r == 0){
+        T tmp = 1;
+        std::vector<T> res(len, f[0]);
+        for (int i = 1; i < (int)f.size(); i++){
+            tmp *= a;
+            res[0] += tmp * f[i];
+        }
+        return res;
+    }
+    /*
+    X[k] = sum (fi * (ar^k)^i)
+         = sum (fi * a^i * r^{ki})
+         = sum (fi * a^i * r^t[k + i] * r^-t[k] * r^-t[i])
+         = r^-t[k] sum r^t[k + i](fi * a^i * r^-t[i])
+    */
+    int n = f.size();
+    T invr = (T)(1) / (T)(r);
+    T tmp = 1, tmpr1 = 1, tmpr2 = 1;
+    for (int i = 0; i < n; i++){
+        f[i] *= tmp * tmpr2;
+        tmpr2 *= tmpr1;
+        tmpr1 *= invr;
+        tmp *= a;
+    }
+    std::vector<T> g(n + len - 1);
+    tmpr1 = 1, tmpr2 = 1;
+    for (int i = 0; i < n + len - 1; i++){
+        g[i] = tmpr2;
+        tmpr2 *= tmpr1;
+        tmpr1 *= r;
+    }
+    std::reverse(f.begin(), f.end());
+    int size = 1;
+    while (size < n + len - 1) size *= 2;
+    f.resize(size);
+    g.resize(size);
+    f = po167::FPS_cyclic_convolution(f, g);
+    std::vector<T> res(len);
+    for (int i = n - 1; i < n + len - 1; i++){
+        res[i - n + 1] = f[i];
+    }
+    tmpr1 = 1, tmpr2 = 1;
+    for (int i = 0; i < len; i++){
+        res[i] *= tmpr2;
+        tmpr2 *= tmpr1;
+        tmpr1 *= invr;
+    }
+    return res;
+}
+}

test/fps/multpoint_evalution_geo.test.cpp

@@ -0,0 +1,22 @@
+#define PROBLEM "https://judge.yosupo.jp/problem/multipoint_evaluation_on_geometric_sequence"
+#include "../../fps/Multipoint_Evaluation_Geo.hpp"
+
+#include <iostream>
+int main(){
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+    using mint = atcoder::modint998244353;
+
+    int N, M, a, r;
+    std::cin >> N >> M >> a >> r;
+    std::vector<mint> c(N);
+    int b;
+    for (auto &x : c){
+        std::cin >> b;
+        x = b;
+    }
+    auto ans = po167::Multipoint_Evaluation_Geo(c, (mint)(a), (mint)(r), M);
+    for (int i = 0; i < (int)ans.size(); i++){
+        std::cout << ans[i].val() << (i + 1 == (int)ans.size() ? "\n" : " ");
+    }
+}