From e16125495bf7507d682df7ec55617a1438ad3746 Mon Sep 17 00:00:00 2001
From: SaiSatwik <satwik.kuppili@gmail.com>
Date: Fri, 19 Oct 2018 00:11:13 +0530
Subject: [PATCH] Added Polynomial Multiplication using ftt in nlogn complexity
 cpp code

---
 PolyMULftt.cpp | 78 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 78 insertions(+)
 create mode 100644 PolyMULftt.cpp

diff --git a/PolyMULftt.cpp b/PolyMULftt.cpp
new file mode 100644
index 0000000..0fc82b6
--- /dev/null
+++ b/PolyMULftt.cpp
@@ -0,0 +1,78 @@
+#include<bits/stdc++.h>
+#define ll long long
+#define mp make_pair
+#define pb push_back
+#define ff first
+#define ss second
+#define MOD 1000000007
+#define endl '\n'
+#define M_PI 3.14159265358979323846264338327950288
+using namespace std;
+typedef complex<double> cp;
+#define MAXN 32768
+void fft(vector<cp> &a,vector<cp>&b, cp w)
+{
+	int n=a.size();
+	b.resize(n);
+	if(n==1)
+		b[0]=a[0];
+	else
+	{
+		vector<cp> b1(n/2),b2(n/2);
+		for(int i=0;i<n/2;++i)
+		{
+			b1[i]=a[2*i];
+			b2[i]=a[2*i+1];
+		}
+		vector<cp> y1,y2;
+		fft(b1,y1,w*w);
+		fft(b2,y2,w*w);
+		cp wn=cp(1,0);
+		for(int i=0;i<n/2;++i)
+		{
+			b[i]=y1[i]+wn*y2[i];
+			b[i+n/2]=y1[i]-wn*y2[i];
+			wn=wn*w;
+		}
+	}
+}
+int main()
+{
+	ios_base::sync_with_stdio(false);
+	cin.tie(NULL);
+	cout.tie(NULL);
+	int t;
+	cin>>t;
+	while(t--)
+	{
+		int n;
+		cin>>n;
+		vector<cp> p1(MAXN,cp(0,0)),p2(MAXN,cp(0,0)),p3,p4,v;
+		for(int i=0;i<=n;++i)
+		{
+			int x;
+			cin>>x;
+			p1[i]+=cp(x,0);
+		}
+		for(int i=0;i<=n;++i)
+		{
+			int x;
+			cin>>x;
+			p2[i]+=cp(x,0);
+		}
+		double alpha=(double) 2*M_PI/(double) MAXN;
+		cp w=cp(cos(alpha),sin(alpha));
+		fft(p1,p3,w);
+		fft(p2,p4,w);
+		for(int i=0;i<MAXN;++i)
+			p3[i]=p3[i]*p4[i];
+		fft(p3,v,cp(1,0)/w);
+		for(int i=0;i<=2*n;++i)
+		{
+			ll x= round( v[i].real() / (double ) MAXN );
+			cout<<x<<" ";
+		}
+		cout<<endl;
+	}
+	return 0;
+}