Question

So I’m learning C++. I’ve got my ‘C++ Programming Language’ and ‘Effective C++’ out and I’m running through Project Euler. Problem 1…dunzo. Problem 2…not so much. I’m working in VS2008 on a Win32 Console App.

Whats the Sum of all even terms of the Fibonacci Sequence under 4 million?

It wasn’t working so I cut down to a test case of 100…

Here’s what I wrote…

// Problem2.cpp : Defines the entry point for the console application. //  #include 'stdafx.h' using namespace std;  int _tmain(int argc, _TCHAR* argv[]) {     cout << 'Project Euler Problem 2:\n\n';     cout << 'Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:\n\n';     cout << '1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...\n\n';     cout << 'Find the sum of all the even-valued terms in the sequence which do not exceed four million.\n\n';     cout << 'Answer:  ' << Solve(); }  double Solve() {     int FibIndex = 0;     double result = 0.0;     double currentFib = GenerateNthFibonacciNumber(FibIndex);     while (currentFib < 100.0){         cout << currentFib << ' ' << (int)currentFib << ' ' << (int)currentFib % 2 << '\n';         if ((int)currentFib % 2 == 0){             result += currentFib;             cout<<(int)currentFib;         }         currentFib = GenerateNthFibonacciNumber(++FibIndex);     }     return result; }  double GenerateNthFibonacciNumber(const int n){     //This generates the nth Fibonacci Number using Binet's Formula     const double PHI = (1.0 + sqrt(5.0)) / 2.0;     return ((pow(PHI,n)-pow(-1.0/PHI,n)) / sqrt(5.0)); } 

And here’s the output…

Project Euler Problem 2:

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

Find the sum of all the even-valued terms in the sequence which do not exceed four million.

0 0 0
1 1 1
1 1 1
2 2 0
3 3 1
5 5 1
8 8 0
13 13 1
21 21 1
34 34 0
55 54 0
89 89 1
Answer: 99

So I have three columns of debug code…the number returned from the generate function, (int)generatedNumber, and (int)generatedNumber % 2

So on the 11th term we have

55,54,0

Why does (int)55 = 54?

Answer 1

Casting to int truncates the number – same as if you’d called floor(currentFib). So even if currentFib is 54.999999… (a number so close to 55 that it will be rounded up when printed), (int)currentFib will produce 54.