Competitive-Programming-Problems/FFT.cpp at master · JorgeIba/Competitive-Programming-Problems · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
#include <bits/stdc++.h>
#define endl '\n'
#define lli long long int
#define ld long double
#define forn(i,n) for (int i = 0; i < n; i++)
#define all(v) v.begin(), v.end()
#define fastIO(); ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define SZ(s) int(s.size())

using namespace std;

#define cd complex<ld>

#include <bits/stdc++.h>

#define endl '\n'
#define lli long long int
#define ld long double
#define forn(i,n) for (int i = 0; i < n; i++)
#define all(v) v.begin(), v.end()
#define fastIO(); ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define SZ(s) int(s.size())

using namespace std;

typedef vector<lli> VLL;
typedef vector<int> VI;

typedef complex<ld> cd;
const ld PI = acos(-1);

int nearestPowerTwo(int n)
{
    int r = 1;
    while(r < n) r<<=1;
    return r;
}

const int LOG = 16, maxN = 3e4;
cd wp[16][maxN]; // wn[i][j] = w_{2^i}^j
cd wn[16][maxN];

void init()
{
    for(int i = 0; i<LOG; i++)
    {
        int n = pow(2, i);
        cd wnp = polar((ld)1, 2*PI/n);
        cd wnn = polar((ld)1, -2*PI/n);
        wp[i][0] = 1;
        wn[i][0] = 1;
        for(int j = 1; j<maxN; j++)
        {
            wp[i][j] = wp[i][j-1]*wnp;
            wn[i][j] = wn[i][j-1]*wnn;
        }
    }
}

void fft(vector<cd> &A, bool inv)
{
    int n = SZ(A);
    for(int i = 1, j = 0; i < n - 1; ++i){
		for(int k = n >> 1; (j ^= k) < k; k >>= 1);
		if(i < j) swap(A[i], A[j]);
	}

    for(int k = 2; k<=n; k<<=1)
    {
        int loga = log2(k);
        for(int i = 0; i<n; i+=k)
        {
            for(int j = 0; j<k/2; j++)
            {
                cd u = A[i+j], v = A[i+j+k/2] * (inv?wn[loga][j]:wp[loga][j]);
                A[i+j] = u + v;
                A[i+j+k/2] = u - v;
            }
        }
    }
    if(inv)
        for(auto &x: A) x/=n;
}


vector<lli> multiply(vector<lli> &A, vector<lli> &B)
{
    int n = SZ(A) + SZ(B) - 1, sz = nearestPowerTwo(n);
    vector<cd> FA(sz), FB(sz);
    for(int i = 0; i<SZ(A); i++) FA[i] = A[i];
    for(int i = 0; i<SZ(B); i++) FB[i] = B[i];
    fft(FA, false);
    fft(FB, false);
    vector<cd> C(sz);
    for(int i = 0; i<sz; i++) C[i] = FA[i]*FB[i];
    fft(C, true);
    vector<lli> ans(n);
    for(int i = 0; i<n; i++) ans[i] = (lli)(round(C[i].real()));
    return ans;
}


void solve () {

    lli n; cin>>n;
    vector<cd> A(n+1), B(n+1);

    for(int i = 0; i<=n; i++) cin>>A[i];
    for(int i = 0; i<=n; i++) cin>>B[i];

    auto C = multiply(A, B);

    for(auto c: C)
    {
        cout << (lli)(round(c.real())) << " ";
    }
    cout << endl;
    return;
}

int main()
{
    fastIO();
    lli t; cin>>t;
    while(t--)
    {
        solve();
    }
    return 0;
}