[Golang] 1000-digit Fibonacci number - Problem 25 - Project Euler
Problem: [1]
The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.Hence the first 12 terms will be:
F1 = 1F2 = 1F3 = 2F4 = 3F5 = 5F6 = 8F7 = 13F8 = 21F9 = 34F10 = 55F11 = 89F12 = 144The 12th term, F12, is the first term to contain three digits.
What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
Solution:
We use large number addition [2] to calcualte Fibonacci number. The answer is 4782.
package main
import (
"fmt"
)
const MaxDigits = 1200
const BASE = 10
func MakePositiveInt(s string) (n [MaxDigits]int) {
// make n zero
for i := 0; i < MaxDigits; i++ {
n[i] = 0
}
for index, digit := range s {
i := len(s) - index - 1
switch digit {
case '0':
n[i] = 0
case '1':
n[i] = 1
case '2':
n[i] = 2
case '3':
n[i] = 3
case '4':
n[i] = 4
case '5':
n[i] = 5
case '6':
n[i] = 6
case '7':
n[i] = 7
case '8':
n[i] = 8
case '9':
n[i] = 9
default:
panic("invalid digit in number string")
}
}
return
}
func AddPositiveInt(a, b [MaxDigits]int) (c [MaxDigits]int) {
var carry, sum = 0, 0
// make c zero
for i := 0; i < MaxDigits; i++ {
c[i] = 0
}
for i := 0; i < MaxDigits; i++ {
sum = a[i] + b[i] + carry
if sum >= BASE {
carry = 1
sum -= BASE
} else {
carry = 0
}
c[i] = sum
}
if carry != 0 {
panic("overflow in addition")
}
return
}
func PositiveIntToString(a [MaxDigits]int) (result string) {
isLeadingZero := true
for i := MaxDigits - 1; i >= 0; i-- {
if isLeadingZero && a[i] == 0 {
continue
} else {
isLeadingZero = false
switch a[i] {
case 0:
result += "0"
case 1:
result += "1"
case 2:
result += "2"
case 3:
result += "3"
case 4:
result += "4"
case 5:
result += "5"
case 6:
result += "6"
case 7:
result += "7"
case 8:
result += "8"
case 9:
result += "9"
default:
panic("invalid digit in int array")
}
}
}
return
}
func main() {
Fn1 := MakePositiveInt(`1`)
Fn2 := MakePositiveInt(`1`)
Fn := AddPositiveInt(Fn1, Fn2)
index := 3
for len(PositiveIntToString(Fn)) < 1000 {
Fn2 = Fn1
Fn1 = Fn
Fn = AddPositiveInt(Fn1, Fn2)
index++
}
fmt.Println(PositiveIntToString(Fn))
fmt.Println("index: ", index)
}
Tested on: Go Playground
References:
[1] | 1000-digit Fibonacci number - Problem 25 - Project Euler |
[2] | [Golang] Large Positive Integer Addition |