Fast Exponentiation Algorithms Added

src/main/cpp/algorithms/math/Binary_Exponentiation.cpp

@@ -0,0 +1,29 @@
+#include<bits/stdc++.h>
+#define ll long long
+
+using namespace std;
+
+ll power(ll a,ll n)
+{
+    ll res=1;
+
+    while(n)
+    {
+        if(n&1)
+        {
+            res=res*a;
+            n--;
+        }
+        a*=a;
+        n/=2;
+    }
+    return res;
+}
+
+int main()
+{
+    ll a,n;
+    cin>>a>>n;
+    cout<<power(a,n);
+    return 0;
+}

src/main/cpp/algorithms/math/Matrix_exponentiation.cpp

@@ -0,0 +1,80 @@
+//for more info refer : https://www.spoj.com/problems/MPOW/
+#include<bits/stdc++.h>
+#define ll long long
+#define MOD 1000000007
+using namespace std;
+#define N 51
+ll mat[51][51],I[51][51];
+void show(ll A[][N],int dim)
+{
+    for(int i=0;i<dim;i++)
+    {
+        for(int j=0;j<dim;j++)
+            cout<<A[i][j]<<" ";
+        cout<<"\n";
+    }
+
+}
+void mul(ll A[][N],ll B[][N],int dim)
+{
+    ll res[dim][dim];
+    for(int i=0;i<dim;i++)
+    {
+
+        for(int j=0;j<dim;j++)
+        {
+            res[i][j]=0;
+            for(int k=0;k<dim;k++)
+                res[i][j]=(res[i][j]%MOD+(A[i][k]%MOD * B[k][j]%MOD)% MOD)%MOD;
+        }
+    }
+    for(int i=0;i<dim;i++)
+    {
+        for(int j=0;j<dim;j++)
+        {
+            A[i][j]=res[i][j];
+        }
+    }
+}
+void power(ll A[][N],int dim,int n)
+{
+    for(int i=0;i<dim;i++)
+    {
+        for(int j=0;j<dim;j++)
+            if(i==j)
+            I[i][j]=1;
+        else I[i][j]=0;
+
+    }
+    while(n)
+    {
+        if(n%2)
+            mul(I,A,dim),n--;
+        else
+            mul(A,A,dim),n/=2;
+
+    }
+    show(I,dim);
+}
+
+int main()
+{
+    int t;
+    cin>>t;
+    while(t--)
+    {
+        int m,n;
+        cin>>m>>n;
+        for(int i=0;i<m;i++)
+        {
+            for(int j=0;j<m;j++)
+                cin>>mat[i][j];
+
+        }
+        power(mat,m,n);
+
+
+    }
+    return 0;
+
+}