package main
import (
"fmt"
)
// 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, curr uint64 = 0, 1
for i := 2; i <= n; i++ {
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, 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)
}
func main() {
left, right := 2, 8
result := sumFibonacciRange(left, right)
fmt.Printf("Sum of Fibonacci numbers from index %d to %d = %d\n", left, right, result)
}
/*
run:
Sum of Fibonacci numbers from index 2 to 8 = 53
*/
