mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
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136 lines
3.9 KiB
C++
136 lines
3.9 KiB
C++
/**
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* @file
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* @brief An algorithm to calculate the sum of [Fibonacci Sequence](https://en.wikipedia.org/wiki/Fibonacci_number): \f$\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\f$
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* @details An algorithm to calculate the sum of Fibonacci Sequence: \f$\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\f$ where \f$\mathrm{F}(i)\f$
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* denotes the i-th Fibonacci Number . Note that F(0) = 0 and F(1) = 1.
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* The value of the sum is calculated using matrix exponentiation.
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* @source https://stackoverflow.com/questions/4357223/finding-the-sum-of-fibonacci-numbers
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* @author [Sarthak Sahu](https://github.com/SarthakSahu1009)
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*/
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#include <iostream> /// for std::cin and std::cout
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#include <cassert> /// for assert
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#include <vector> /// for std::vector
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/**
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* @namespace math
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* @brief Mathematical algorithms
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*/
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namespace math {
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/**
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* @namespace fibonacci_sum
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* @brief Functions for the sum of the Fibonacci Sequence: \f$\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\f$
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*/
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namespace fibonacci_sum {
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/**
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* Function to multiply two matrices
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* @param T matrix 1
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* @param A martix 2
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* @returns resultant matrix
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*/
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std::vector<std::vector<int> > multiply(std::vector<std::vector<int> > T, std::vector<std::vector<int> > A) {
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std::vector<std::vector<int> > result(2,std::vector<int>(2));
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// multiplying matrices
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for(int i=0;i<2;i++) {
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for(int j=0;j<2;j++) {
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result[i][j]=0;
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for(int k=0;k<2;k++) {
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result[i][j]=(result[i][j]+(T[i][k]*A[k][j]));
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}
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}
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}
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return result;
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}
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/**
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* Function to compute A^n where A is a matrix.
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* @param T matrix
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* @param ex power
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* @returns resultant matrix
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*/
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std::vector<std::vector<int> > power(std::vector<std::vector<int> > T, int ex) {
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std::vector<std::vector<int> > A{{1,1},{1,0}};
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if(ex == 0 || ex == 1) {
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return T;
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}
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T = power(T,ex/2);
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T = multiply(T,T);
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if(ex&1) {
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T = multiply(T,A);
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}
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return T;
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}
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/**
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* Function to compute sum of fibonacci sequence from 0 to n.
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* @param n number
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* @returns int ans, the sum of sequence
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*/
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int result(int n) {
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std::vector<std::vector<int> > T{{1,1},{1,0}};
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T = power(T,n);
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int ans=T[0][1];
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ans = (ans - 1);
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return ans;
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}
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/**
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* Function to compute sum of fibonacci sequence from n to m.
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* @param n start of sequence
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* @param m end of sequence
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* @returns int the sum of sequence
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*/
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int fiboSum(int n,int m){
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return (result(m+2) - result(n+1));
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}
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} // namespace fibonacci_sum
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} // namespace math
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/**
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* Function for testing fiboSum function.
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* test cases and assert statement.
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* @returns `void`
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*/
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static void test() {
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int n = 0, m = 3;
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int test_1 = math::fibonacci_sum::fiboSum(n,m);
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assert(test_1 == 4);
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std::cout << "Passed Test 1!" << std::endl;
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n = 3; m = 5;
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int test_2 = math::fibonacci_sum::fiboSum(n,m);
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assert(test_2 == 10);
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std::cout << "Passed Test 2!" << std::endl;
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n = 5; m = 7;
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int test_3 = math::fibonacci_sum::fiboSum(n,m);
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assert(test_3 == 26);
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std::cout << "Passed Test 3!" << std::endl;
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n = 7; m = 10;
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int test_4 = math::fibonacci_sum::fiboSum(n,m);
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assert(test_4 == 123);
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std::cout << "Passed Test 4!" << std::endl;
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n = 9; m = 12;
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int test_5 = math::fibonacci_sum::fiboSum(n,m);
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assert(test_5 == 322);
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std::cout << "Passed Test 5!" << std::endl;
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}
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/**
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* @brief Main function
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* @returns 0 on exit
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*/
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int main()
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{
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test(); // execute the tests
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return 0;
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}
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