fps division

fps/FPS_division.hpp

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+#pragma once
+#include <vector>
+#include <atcoder/convolution>
+
+#include "FPS_inv.hpp"
+namespace po167{
+template<class T>
+// f = g * res.first + res.second
+// |res.first| <= |f| - |g| + 1
+// |res.second| <= |g| - 1
+std::pair<std::vector<T>, std::vector<T>>
+FPS_division(std::vector<T> f, std::vector<T> g){
+    assert(!f.empty() && f.back() != 0);
+    assert(!g.empty() && g.back() != 0);
+    if (f.size() < g.size()){
+        return {{}, f};
+    }
+    // rev(f) / rev(g) = rev(q) (mod x ^ {|f| - |g| + 1})
+    std::vector<T> r = f;
+    std::reverse(f.begin(), f.end());
+    std::reverse(g.begin(), g.end());
+    int z = (int)f.size() - (int)g.size() + 1;
+    f.resize(z);
+    std::vector<T> q = atcoder::convolution(f, FPS_inv(g, z));
+    q.resize(z);
+    std::reverse(g.begin(), g.end());
+    std::reverse(q.begin(), q.end());
+    f = atcoder::convolution(q, g);
+    for (int i = 0; i < (int)f.size(); i++) r[i] -= f[i];
+    while (!q.empty() && q.back() == 0) q.pop_back();
+    while (!r.empty() && r.back() == 0) r.pop_back();
+    return {q, r};
+}
+}

test/fps/division.test.cpp

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+#define PROBLEM "https://judge.yosupo.jp/problem/division_of_polynomials"
+
+#include "../../fps/FPS_division.hpp"
+
+#include <vector>
+#include <iostream>
+#include <atcoder/modint>
+
+int main(){
+    int N, M, a;
+    std::cin >> N >> M;
+    std::vector<atcoder::modint998244353> f(N), g(M);
+    for (int i = 0; i < N; i++){
+        std::cin >> a;
+        f[i] = a;
+    }
+    for (int i = 0; i < M; i++){
+        std::cin >> a;
+        g[i] = a;
+    }
+    auto ans = po167::FPS_division(f, g);
+    std::cout << ans.first.size() << " " << ans.second.size() << "\n";
+    for (int i = 0; i < (int)ans.first.size(); i++){
+        if (i) std::cout << " ";
+        std::cout << ans.first[i].val();
+    }
+    std::cout << "\n";
+    for (int i = 0; i < (int)ans.second.size(); i++){
+        if (i) std::cout << " ";
+        std::cout << ans.second[i].val();
+    }
+    std::cout << "\n";
+}