add fibo_sum.cpp

math/fibonacci_sum.cpp

@@ -0,0 +1,129 @@
+/**
+ * @file
+ * @brief An algorithm to calculate the sum of Fibonacci Sequence: \f$\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\f$
+ * @details An algorithm to calculate the sum of Fibonacci Sequence: \f$\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\f$ where \f$\mathrm{F}(i)\f$
+ * denotes the i-th Fibonacci Number . Note that F(0) = 0 and F(1) = 1. 
+ * The value of the sum is calculated using matrix exponentiation.
+ *
+ * @author [Sarthak Sahu](https://github.com/SarthakSahu1009)
+ */
+
+#include <iostream> /// for std::cin and std::cout
+#include <cassert>  /// for assert
+#include <vector>   /// for std::vector
+
+/**
+ * @namespace math
+ * @brief Mathematical algorithms
+ */
+namespace math{
+    
+    /**
+     * Function to multiply two matrices
+     * @param T matrix 1
+     * @param A martix 2
+     * @returns resultant matrix
+     */
+    std::vector<std::vector<int> > multiply(std::vector<std::vector<int> > T, std::vector<std::vector<int> > A) {
+    
+        std::vector<std::vector<int> > result(2,std::vector<int>(2));
+        
+        // multiplying matrices
+        for(int i=0;i<2;i++) {
+            for(int j=0;j<2;j++) {
+                result[i][j]=0;
+                for(int k=0;k<2;k++) {
+                    result[i][j]=(result[i][j]+(T[i][k]*A[k][j]));
+                }
+            }
+        }
+        
+        return result;
+    }
+ 
+    /**
+     * Function to compute A^n where A is a matrix.
+     * @param T matrix
+     * @param ex power
+     * @returns resultant matrix
+     */
+    std::vector<std::vector<int> > power(std::vector<std::vector<int> > T, int ex) {
+        
+        std::vector<std::vector<int> > A{{1,1},{1,0}};
+        if(ex == 0 || ex == 1) {
+            return T;
+        }
+        
+        T = power(T,ex/2);
+        T = multiply(T,T);
+        if(ex&1) {
+            T = multiply(T,A);
+        }
+        return T;
+    }
+    
+    /**
+     * Function to compute sum of fibonacci sequence from 0 to n.
+     * @param n number
+     * @returns int ans, the sum of sequence
+     */
+    int result(int n) {
+        std::vector<std::vector<int> > T{{1,1},{1,0}};
+        T = power(T,n);
+        int ans=T[0][1];
+        ans = (ans - 1);
+        return ans;
+    }
+    
+    /**
+     * Function to compute sum of fibonacci sequence from n to m.
+     * @param n start of sequence
+     * @param m end of sequence
+     * @returns int the sum of sequence
+     */
+    int fiboSum(int n,int m){
+        return (result(m+2) - result(n+1));
+    }
+}//namespace math
+ 
+/**
+ * Function for testing fiboSum function.
+ * test cases and assert statement.
+ * @returns `void`
+*/
+static void test() {
+    int n = 0, m = 3;
+    int test_1 = math::fiboSum(n,m);
+    assert(test_1 == 4);
+    std::cout << "Passed Test 1!" << std::endl;
+
+    n = 3; m = 5;
+    int test_2 = math::fiboSum(n,m);
+    assert(test_2 == 10);
+    std::cout << "Passed Test 2!" << std::endl;
+
+    n = 5; m = 7;
+    int test_3 = math::fiboSum(n,m);
+    assert(test_3 == 26);
+    std::cout << "Passed Test 3!" << std::endl;
+
+    n = 7; m = 10;
+    int test_4 = math::fiboSum(n,m);
+    assert(test_4 == 123);
+    std::cout << "Passed Test 4!" << std::endl;
+
+    n = 9; m = 12;
+    int test_5 = math::fiboSum(n,m);
+    assert(test_5 == 322);
+    std::cout << "Passed Test 5!" << std::endl;
+} 
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main()
+{
+    test();
+    return 0;
+}