Is my golang func run time analysis correct? - algorithm

Question

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This code snippet is for give two slice of binary number a1 and a2 to return sum slice r1, and I want to figure out how long spend with this code snippet figure out the result.
and I figure out the factorial result.
Is my analysis right?
my analysis for time complexity is:
cn + (n*n!) + c
the Code is:
func BinaryPlus(a1 []int, a2 []int) []int {
var r1 = make([]int, len(a1), 2*(len(a1)))
for i := 0; i < len(a1); i++ {
r1[i] = a1[i] + a2[i]
}
// 二分反转
ReverseSlice(r1)
r1 = append(r1, 0)
final := 0
for i := 0; final != 1; i++ {
isOver := 1
for j := 0; j < len(r1); j++ {
if r1[j] > 1 {
r1[j] = r1[j] % 2
r1[j+1] += 1
if r1[j+1] > 1 {
isOver = 0
}
}
}
if isOver == 1 {
final = 1
}
}
// 二分反转
ReverseSlice(r1)
return r1
}
func ReverseSlice(s interface{}) {
n := reflect.ValueOf(s).Len()
swap := reflect.Swapper(s)
for i, j := 0, n-1; i < j; i, j = i+1, j-1 {
swap(i, j)
}
}

Answer 1

It is not entirely clear that your code, as written, is correct. The size cap for your result array could be too small. Consider the case that len(a2) > 2*len(a1): the r1 := make(...) will not reserve enough in this case. Further, the initial for loop will miss adding in the more significant bits of a2.
Binary addition should have no more than O(n) complexity. You can do it with a single for loop. n = 1+max(len(a1),len(a2)):
package main
import (
"fmt"
"reflect"
)
func BinaryPlus(a1 []int, a2 []int) []int {
reserve := len(a1) + 1
if x := len(a2) + 1; x > reserve {
reserve = x
}
hold := 0
maxBit := 1
ans := make([]int, reserve)
for i := 1; i <= reserve; i++ {
hold = hold / 2
if i <= len(a1) {
hold += a1[len(a1)-i]
}
if i <= len(a2) {
hold += a2[len(a2)-i]
}
ans[reserve-i] = hold & 1
if hold != 0 && i > maxBit {
maxBit = i
}
}
return ans[reserve-maxBit:]
}
func main() {
tests := []struct {
a, b, want []int
}{
{
a: []int{1},
b: []int{0},
want: []int{1},
},
{
a: []int{1, 0},
b: []int{0, 0, 1},
want: []int{1, 1},
},
{
a: []int{1, 0, 0, 1},
b: []int{1, 1, 1, 1, 0},
want: []int{1, 0, 0, 1, 1, 1},
},
{
a: []int{0, 0},
b: []int{0, 0, 0, 0, 0},
want: []int{0},
},
}
bad := false
for i := 0; i < len(tests); i++ {
t := tests[i]
c := BinaryPlus(t.a, t.b)
if !reflect.DeepEqual(c, t.want) {
fmt.Println(t.a, "+", t.b, "=", c, "; wanted:", t.want)
bad = true
}
}
if bad {
fmt.Println("FAILED")
} else {
fmt.Println("PASSED")
}
}