import Foundation
// 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
func fibonacci(_ n: Int) -> UInt64 {
if n == 0 { return 0 }
if n == 1 { return 1 }
var prev: UInt64 = 0
var curr: UInt64 = 1
for _ in 2...n {
let next = prev + curr
prev = curr
curr = next
}
return curr
}
// Function to calculate sum of Fibonacci numbers from index L to R (inclusive)
func sumFibonacciRange(_ L: Int, _ R: Int) -> UInt64 {
// 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)
*/
return fibonacci(R + 2) - fibonacci(L + 1)
}
// Main program
let left = 2
let right = 8
let result = sumFibonacciRange(left, right)
print("Sum of Fibonacci numbers from index \(left) to \(right) = \(result)")
/*
run:
Sum of Fibonacci numbers from index 2 to 8 = 53
*/
