Matrix_Exponentiation

Number Theory/Matrix_Exponentiation.cpp

@@ -0,0 +1,92 @@
+#include <bits/stdc++.h>
+#define ll long long int
+
+using namespace std;
+
+const int M = (int)1e9+7;
+struct Mat{
+    ll m[2][2];
+
+    Mat(){
+        memset(m,0,sizeof(m));
+    }
+
+    void identity(){
+        for(int idx = 0 ; idx < 2 ; idx++ ){
+            m[idx][idx] = 1;
+        }
+    }
+};
+
+Mat operator* (Mat m1,Mat m2){
+    Mat res;
+
+    for(int i = 0 ; i < 2 ; i++ ){
+        for(int j = 0 ; j < 2 ; j++ ){
+            for(int k = 0 ; k < 2 ; k++ ){
+                res.m[i][j] += m1.m[i][k]*m2.m[k][j];
+                res.m[i][j] %= M;
+            }
+        }
+    }
+
+    return res;
+}
+
+Mat power(Mat X,ll n){
+    Mat res;
+    res.identity();
+
+    ll b = n;
+    while(b){
+        if( b&1 ) res = res*X;
+        X = X*X;
+        b >>= 1;
+    }
+
+    return res;
+}
+
+ll fibo(ll n){
+
+    if( n < 2 ) return n;
+    Mat res;
+
+    Mat X;
+    X.m[0][1] = 1 , X.m[1][0] = 1 , X.m[1][1] = 1;
+
+    res = power(X,n);
+
+    ll fn[2][1];
+    fn[0][0]=0,fn[1][0]=1;
+
+    ll fn1[2][1];
+
+    for(int i = 0 ; i < 2 ; i++ ){
+        for(int j = 0 ; j < 1 ; j++ ){
+            for(int k = 0 ; k < 2 ; k++ ){
+                fn1[i][j] = res.m[i][k]*fn[k][j];
+                fn1[i][j]%=M;
+            }
+        }
+    }
+
+    return fn1[0][0];
+}
+
+ll modSub(ll a,ll b){
+    return ((a%M)-(b%M)+M)%M;
+}
+
+int main(){
+    int t;
+    cin>>t;
+
+    while(t--){
+        ll n,m;
+        cin>>n>>m;
+
+        cout << modSub(fibo(m+2),fibo(n+1)) << '\n';
+    }
+    return 0;
+}