// Example: left = 2, right = 8
// Explanation: F(2) + F(3) + F(4) + F(5) + F(6) + F(7) + F(8) = 1 + 2 + 3 + 5 + 8 + 13 + 21 = 53
// Function to compute Fibonacci numbers up to n
fn fibonacci(n: usize) -> u64 {
if n == 0 {
return 0;
}
if n == 1 {
return 1;
}
let mut prev: u64 = 0;
let mut curr: u64 = 1;
for _i in 2..=n {
let next = prev + curr;
prev = curr;
curr = next;
}
curr
}
// Function to calculate sum of Fibonacci numbers from index L to R (inclusive)
fn sum_fibonacci_range(l: usize, r: usize) -> u64 {
// If the range is invalid (e.g., L > R), return 0
if l > r {
return 0;
}
/*
Mathematical identity:
Sum(F_L + F_(L+1) + ... + F_R) = F_(R+2) - F_(L+1)
Explanation:
- The sum of the first n Fibonacci numbers is F_(n+2) - 1.
- So, the sum from F_L to F_R can be derived by subtracting:
(sum of first R terms) - (sum of first (L-1) terms)
= (F_(R+2) - 1) - (F_(L+1) - 1)
= F_(R+2) - F_(L+1)
*/
fibonacci(r + 2) - fibonacci(l + 1)
}
fn main() {
let left: usize = 2;
let right: usize = 8;
let result = sum_fibonacci_range(left, right);
println!("Sum of Fibonacci numbers from index {} to {} = {}", left, right, result);
}
/*
run:
Sum of Fibonacci numbers from index 2 to 8 = 53
*/
