CodingHardcod-g646

Subject Number theoryLevel Senior–Staff~35 minCommon in Algorithms & data structures interviewsIndustries Software development

Question

Compute the n-th Fibonacci number modulo m using the fast-doubling method (O(log n)), where F(0)=0, F(1)=1. Constraints: 0 <= n <= 10^18, 1 <= m <= 10^9. A linear loop would be far too slow for n near 10^18, so use the doubling identities F(2k)=F(k)*(2*F(k+1)-F(k)) and F(2k+1)=F(k+1)^2+F(k)^2.

Implement

fib_mod(n: int, m: int) → int

Examples

in[10,1000000007]out55

What a strong answer looks like

State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.

Learn the concepts

Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.

Run or narrate your approach, then ask the coach.