Project Euler Solution 2

Problem Statement#

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

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, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

Solution#

To solve this problem, let us see Fibonacci sequence whose values do not exceed 10.

note

The Fibonacci sequence starts with 0 and 1.
Add the previous two numbers p and c to get the new Fibonacci number.
But our problem is to add only even numbers in the Fibonacci sequence that do not exceed four million, so each time a new Fibonacci number is found, check if the number is even and is not exceeding four million.

Finding Fibonacci values whose values do not exceed 10.

note

p and c represents previous and current terms in the Fibonacci sequence

p = 0

c = 1

0 + 1 = 1

p = 1

c = 1

1 + 1 = 2

p = 1

c = 2

1 + 2 = 3

p = 2

c = 3

2 + 3 = 5

p = 3

c = 5

3 + 5 = 8

p = 5

c = 8

5 + 8 = 13 exceeds 10

In this case 2 and 8 are even, so the sum of even valued terms in the Fibonacci sequence that do not exceed 10 is 2 + 8 = 10.

Implementation#

#include <stdio.h>
int MAX_NUM = 4000000;
int main(){    int new_f, prev_f, curr_number, sum;    new_f = 0;    prev_f = 0;    curr_number = 1;    sum = 0;    while (new_f <= MAX_NUM)    {        new_f = curr_number + prev_f;        if ((new_f <= MAX_NUM) && (new_f % 2) == 0) sum = sum + new_f;        prev_f = curr_number;        curr_number = new_f;    }    printf("%d", sum);    return 0;}

Sample Output#

Sample Output