// 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
fun fibonacci(n: Int): ULong {
if (n == 0) return 0u
if (n == 1) return 1u
var prev: ULong = 0u
var curr: ULong = 1u
for (i in 2..n) {
val next = prev + curr
prev = curr
curr = next
}
return curr
}
// Function to calculate sum of Fibonacci numbers from index L to R (inclusive)
fun sumFibonacciRange(L: Int, R: Int): ULong {
// If the range is invalid (e.g., L > R), return 0
if (L > R) return 0u
/*
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)
}
fun main() {
val left = 2
val right = 8
val result = sumFibonacciRange(left, right)
println("Sum of Fibonacci numbers from index $left to $right = $result")
}
/*
run:
Sum of Fibonacci numbers from index 2 to 8 = 53
*/
