From 0f26e3b754e01464df2cfef35f419f0a56cc8eef Mon Sep 17 00:00:00 2001
From: "Paulo H. Lamounier" <53798700+Nanashii76@users.noreply.github.com>
Date: Sun, 25 Feb 2024 14:03:11 -0300
Subject: [PATCH] Introduction to Linear recurrences and Matrix

---
 .../binaryExponetiation.cpp                   | 38 ++++++++++++++++
 .../enxugando_gelo_no_sol.cpp                 | 44 +++++++++++++++++++
 .../modularBinaryExponetation.cpp             | 32 ++++++++++++++
 3 files changed, 114 insertions(+)
 create mode 100644 theory/linear_recurrences_matrix_expo/binaryExponetiation.cpp
 create mode 100644 theory/linear_recurrences_matrix_expo/enxugando_gelo_no_sol.cpp
 create mode 100644 theory/linear_recurrences_matrix_expo/modularBinaryExponetation.cpp

diff --git a/theory/linear_recurrences_matrix_expo/binaryExponetiation.cpp b/theory/linear_recurrences_matrix_expo/binaryExponetiation.cpp
new file mode 100644
index 0000000..31b2cec
--- /dev/null
+++ b/theory/linear_recurrences_matrix_expo/binaryExponetiation.cpp
@@ -0,0 +1,38 @@
+#include <iostream>
+
+int binaryPower(int a, int b) {
+
+    if (a == 0)
+        return 0;
+
+    int res = 1;
+    while(b) {
+        if(b&1)
+            res *= a;
+        a*=a;
+        b = b>>1;
+    }
+
+    return res;
+
+}
+
+
+int main(void) {
+
+    std::cout << binaryPower(2,10) << std::endl;
+
+
+}
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/theory/linear_recurrences_matrix_expo/enxugando_gelo_no_sol.cpp b/theory/linear_recurrences_matrix_expo/enxugando_gelo_no_sol.cpp
new file mode 100644
index 0000000..1977811
--- /dev/null
+++ b/theory/linear_recurrences_matrix_expo/enxugando_gelo_no_sol.cpp
@@ -0,0 +1,44 @@
+#include <iostream>
+
+typedef long long ll;
+
+const int mod = 1e9+7;
+
+ll mfac(int i) {
+    
+    int m = i+2;
+    int ans = 1;
+    
+    for(int i = 0; i < 3; ++i) {
+        m %= mod;
+        ans *= m-i;
+        ans %= mod;
+    }
+    
+    return ans;
+    
+}
+
+ll solve(int n) {
+    
+    int ans = 0;
+    
+    while(n > 0) {
+        ans += mfac(n);
+        n--;
+    }
+    
+    return ans;
+}
+
+
+int32_t main(void) {
+    
+    int n;
+    std::cin >> n;
+    std::cout << solve(n) << std::endl;
+    
+    
+}
+
+
diff --git a/theory/linear_recurrences_matrix_expo/modularBinaryExponetation.cpp b/theory/linear_recurrences_matrix_expo/modularBinaryExponetation.cpp
new file mode 100644
index 0000000..93581d2
--- /dev/null
+++ b/theory/linear_recurrences_matrix_expo/modularBinaryExponetation.cpp
@@ -0,0 +1,32 @@
+#include <iostream>
+
+#define int long long int
+
+// Constant isn't necessary
+const int mod = 1e9 + 7;
+
+int binaryExponentation(int a, int b) {
+
+    if (a == 0)
+        return 0;
+    
+    int ans = 1;
+    while(b) {
+        if(b&1)
+            ans *= a, ans %= mod;
+        a*=a;
+        a %= mod;
+        b = b>>1;
+    }
+
+    return ans;
+
+}
+
+int32_t main ( void ){
+
+    std::cout << binaryExponentation(10,20) << std::endl;
+
+}
+
+