fftslowbasic.cpp

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define pb push_back
#define mp make_pair
#define all(a) begin(a),end(a)
#define FOR(x,val,to) for(int x=(val);x<int((to));++x)
#define FORE(x,val,to) for(auto x=(val);x<=(to);++x)
#define FORR(x,arr) for(auto &x: arr)
#define FORS(x,plus,arr) for(auto x = begin(arr)+(plus); x != end(arr); ++x)
#define FORREV(x,plus,arr) for(auto x = (arr).rbegin()+(plus); x !=(arr).rend(); ++x)
#define REE(s_) {cout<<s_<<'\n';exit(0);}
#define GET(arr) for(auto &i: (arr)) sc(i)
#define whatis(x) cerr << #x << " is " << x << endl;
#define e1 first
#define e2 second
#define INF 0x7f7f7f7f
typedef std::pair<int,int> pi;
typedef std::vector<int> vi;
typedef std::vector<std::string> vs;
typedef int64_t ll;
typedef uint64_t ull;
#define umap unordered_map
#define uset unordered_set
using namespace std;
using namespace __gnu_pbds;

#ifdef _WIN32
#define getchar_unlocked() _getchar_nolock()
#define _CRT_DISABLE_PERFCRIT_LOCKS
#endif
template<class L, class R> ostream& operator<<(ostream &os, map<L, R> P) { for(auto const &vv: P)os<<"("<<vv.first<<","<<vv.second<<")"; return os; }
template<class T> ostream& operator<<(ostream &os, set<T> V) { os<<"[";for(auto const &vv:V)os<<vv<<","; os<<"]"; return os; }
template<class T> ostream& operator<<(ostream &os, vector<T> V) { os<<"[";for(auto const &vv:V)os<<vv<<","; os<<"]"; return os; }
template<class L, class R> ostream& operator<<(ostream &os, pair<L, R> P) { os<<"("<<P.first<<","<<P.second<<")"; return os; }
inline int fstoi(const string &str){auto it=str.begin();bool neg=0;int num=0;if(*it=='-')neg=1;else num=*it-'0';++it;while(it<str.end()) num=num*10+(*it++-'0');if(neg)num*=-1;return num;}
inline void getch(char &x){while(x = getchar_unlocked(), x < 33){;}}
inline void getstr(string &str){str.clear(); char cur;while(cur=getchar_unlocked(),cur<33){;}while(cur>32){str+=cur;cur=getchar_unlocked();}}
template<typename T> inline bool sc(T &num){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){if(c == EOF) return false;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; return true;}template<typename T, typename ...Args> inline void sc(T &num, Args &...args){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; sc(args...); }
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; //s.find_by_order(), s.order_of_key() <- works like lower_bound
template<typename T> using ordered_map = tree<T, int, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

//basic slow fft - use better template if possible
//change to LL in most cases

typedef complex<double> cd;

void fft(vector<cd> &a, bool invert){
    int n = a.size();
    if(n == 1) return;
    vector<cd> a0(n/2),a1(n/2);
    for(int i = 0,j=0; i < n; i += 2, ++j){
        a0[j] = a[i];
        a1[j] = a[i+1];
    }
    fft(a0,invert);
    fft(a1,invert);
    double ang = 2*M_PI/n*(invert?-1:1);
    cd w(1), wn(cos(ang),sin(ang));
    for(int i = 0; i < n/2; ++i){
        a[i] = a0[i]+w*a1[i];
        a[i+n/2] = a0[i]-w*a1[i];
        if(invert){
            a[i] /= 2;
            a[i+n/2] /= 2;
        }
        w *= wn;
    }
}

vector<int> multiply(const vector<int> a, const vector<int> b){
    vector<cd> fa(a.begin(),a.end()), fb(b.begin(),b.end());
    int k = 0;
    while((1 << k) < (int)(a.size()+b.size()-1)) ++k;
    int n = 1 << k;
    fa.resize(n,0), fb.resize(n,0);
    fft(fa,0);
    fft(fb,0);
    for(int i = 0; i < n; ++i){
        fa[i] *= fb[i];
    }
    fft(fa,1);
    vector<int> res(n);
    for(int i = 0; i < n; ++i){
        res[i] = int(fa[i].real()+0.5);
    }
    return res;
}

int main(){
    ios_base::sync_with_stdio(0);cin.tie(0);
    vector<int> a = {0,1,3}, b = {5,1,3,2};
    auto ret = multiply(a,b);
    FORR(i,ret) cout << i << ' ';
}