Matrix Exponentiation, Linear Recurrence

Author: ivorynoise

SUMSUMS-d.cpp

@@ -0,0 +1,82 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+typedef long long int ll;
+typedef vector<vector<ll> > vii;
+typedef vector<ll> vi;
+
+const int m = 98765431;
+int k;
+vi b;
+
+//matrix mul
+vii mul(const vii& A, const vii& B) {
+	vii C(k, vi(k, 0));
+
+	for (int r = 0; r < k; ++r) {
+		for (int c = 0; c < k; ++c) {
+			for (int x = 0; x < k; ++x) {
+				C[r][c] += (A[r][x] * B[x][c]) % m;
+				C[r][c] %= m;
+			}
+		}
+	}
+	return C;
+}
+
+//matrix exponentiation
+vii pow(vii& A, int n) {
+	if (n <= 1) return A;
+
+	//if odd
+	if (n & 1) return mul(A, pow(A, n - 1));
+
+	vii ans = pow(A, n / 2);
+	return mul(ans, ans);
+}
+
+
+vi sol(int n){
+	//TLE since k could be of the range 50000
+	
+	//creating transformation mat
+	vii t(k, vi(k, 0));
+
+	if (n < 1) return b;
+
+	for(int i = 0; i < k; ++i){
+		for(int j = 0; j < k; ++j){
+			if (i != j) t[i][j] = 1;
+		}
+	}
+
+	vii tn = pow(t, n);
+	vi ans;
+	ll x = 0;
+
+	for(int r = 0; r < k; ++r){
+		for(int c = 0; c < k; ++c){
+			x += (tn[r][c] * b[c]) % m;
+			x %= m; 
+		}
+		ans.push_back(x);
+		x = 0;
+	}
+	return ans;
+}
+
+
+int main(){
+	cin >> k;
+	int n; cin >> n;
+	b.resize(k);
+
+	for(int i = 0; i < k; ++i){
+		cin >> b[i];
+	}
+
+	vi ans = sol(n);
+	for(int i = 0; i < k; ++i){
+		cout << ans[i] << "\n";
+	}
+}