Matrices

Matrix Addition.
Matrix Multiplication.
Recursive Matrix Exponentiation.
Iterative Matrix Exponentiation.

Author: Muhammad-Magdi

Matrices.cpp

@@ -0,0 +1,73 @@
+#include <cstdio>
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+typedef long long ll;
+
+#define row vector<ll>
+#define matrix vector<row>
+#define ROWS(v)  (v).size()
+#define COLS(v)  (v)[0].size()
+
+const int N = 5e4+5, OO = 0x3f3f3f3f, MOD = 1e9+7;
+
+inline ll fixMod(ll a, ll m){
+  return (a%m+m)%m;
+}
+
+void printMatrix(const matrix& m){
+  for(auto r : m){
+    for(auto x : r){
+      cout << x << " ";
+    }
+    cout << endl;
+  }
+}
+
+matrix identity(int n){
+  matrix ret(n ,row(n, 0));
+  for(int i = 0 ; i < n ; ++i)  ret[i][i] = 1;
+  return ret;
+}
+
+matrix add(const matrix& a, const matrix& b){
+  matrix ret(ROWS(a), row(COLS(a), 0));
+  for(int i = 0 ; i < ROWS(a) ; ++i)
+    for(int j = 0 ; i  < COLS(a) ; ++j)
+      ret[i][j] = a[i][j] + b[i][j];
+  return ret;
+}
+
+matrix multiply(const matrix& a, const matrix& b){
+  matrix ret(ROWS(a), row(COLS(b), 0));
+  for(int r = 0 ; r < ROWS(a) ; ++r)
+    for(int k = 0 ; k < COLS(a) ; ++k)
+      if(a[r][k])for(int c = 0 ; c < COLS(b) ; ++c)
+        ret[r][c] = (ret[r][c] + (a[r][k]*b[k][c])%MOD)%MOD;
+  return ret;
+}
+
+matrix power(const matrix& a, ll p){
+  if(!p)  return identity(ROWS(a));
+  matrix m = power(a, p>>1);
+  m = multiply(m, m);
+  if(p&1) m = multiply(m, a);
+  return m;
+}
+
+matrix powerI(const matrix& a, ll p){
+  matrix ret = identity(ROWS(a)), t = a;
+  while(p){
+    if(p&1) ret = multiply(ret, t);
+    t = multiply(t, t);
+    p >>= 1;
+  }
+  return ret;
+}
+
+int main(){
+
+  return 0;
+}