Project Euler Problem 25 1000-digit Fibonacci number

1000-digit Fibonacci number

Problem 25

The Fibonacci sequence is defined by the recurrence relation:

F_n = F_n−1 + F_n−2, where F₁ = 1 and F₂ = 1.

Hence the first 12 terms will be:

F₁ = 1

F₂ = 1

F₃ = 2

F₄ = 3

F₅ = 5

F₆ = 8

F₇ = 13

F₈ = 21

F₉ = 34

F₁₀ = 55

F₁₁ = 89

F₁₂ = 144

The 12th term, F₁₂, is the first term to contain three digits.

What is the index of the first term in the Fibonacci sequence to contain 1000 digits?

C++:

#include <iostream>
#include <cstring>

using namespace std;

const int MAXN = 1000;

char f1[MAXN+2], f2[MAXN+2];

int fibadd(char f1[], char f2[], int digits)
{
    int carry = 0, i;
    for(i=1; i<=digits || carry; i++) {
        f1[i] += f2[i] + carry;
        carry = f1[i] / 10;
        f1[i] %= 10;
    }
    return f1[i] ? i : i - 1;
}

int main()
{
    int n, digits;

    while(cin >> n && n<= MAXN) {
        memset(f1, 0, sizeof(f1));
        memset(f2, 0, sizeof(f2));

        f1[1] = 1;
        f2[1] = 1;
        digits = 1;

        if(digits >= n) {
            cout << digits << endl;
        } else {
            for(int i=3;;) {
                digits = fibadd(f1, f2, digits);
                if(digits >= n) {
                    cout << i << endl;
                    break;
                }
                i++;

                digits = fibadd(f2, f1, digits);
                if(digits >= n) {
                    cout << i << endl;
                    break;
                }
                i++;
            }
        }

    }

    return 0;
}