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data structures - How to implement a queue in Go?

The current Go library doesn't provide the queue container. To implement a simple queue, I use circle array as the underlying data structure. It follows algorithms mentioned in TAOCP:

Insert Y into queue X: X[R]<-Y; R<-(R+1)%M; if R=F then OVERFLOW.
Delete Y from queue X: if F=R then UNDERFLOW; Y<-X[F]; F<-(F+1) % M.
F: Front, R: Rear, M: Array length.

Following is the code:

package main

import (
    "fmt"
)

type Queue struct {
    len        int 
    head, tail int 
    q          []int
}

func New(n int) *Queue {
    return &Queue{n, 0, 0, make([]int, n)} 
}

func (p *Queue) Enqueue(x int) bool {
    p.q[p.tail] = x 
    p.tail = (p.tail + 1) % p.len
    return p.head != p.tail
}

func (p *Queue) Dequeue() (int, bool) {
    if p.head == p.tail {
        return 0, false
    }   
    x := p.q[p.head]
    p.head = (p.head + 1) % p.len
    return x, true
}

func main() {
    q := New(10)
    for i := 1; i < 13; i++ {
        fmt.Println(i, q.Enqueue(i))
    }   
    fmt.Println()
    for i := 1; i < 13; i++ {
        fmt.Println(q.Dequeue())
    }   
}

But the output is obviously wrong:

1 true 2 true 3 true 4 true 5 true 6 true 7 true 8 true 9 true 10 false 11 true 12 true

11 true 12 true 0 false 0 false 0 false 0 false 0 false 0 false 0 false 0 false 0 false 0 false

I think I need one more field to make the code work properly. What do you suggest?

The improved code has a small shortcoming: an array of size n can contain only n-1 elements.

package main

import (
    "fmt"
)

type Queue struct {
    len        int 
    head, tail int 
    q          []int
}

func New(n int) *Queue {
    return &Queue{n, 0, 0, make([]int, n)} 
}

func (p *Queue) Enqueue(x int) bool {
    p.q[p.tail] = x 
    ntail := (p.tail + 1) % p.len
    ok := false
    if ntail != p.head {
        p.tail = ntail
        ok = true
    }   
    return ok
}

func (p *Queue) Dequeue() (int, bool) {
    if p.head == p.tail {
        return 0, false
    }   
    x := p.q[p.head]
    p.head = (p.head + 1) % p.len
    return x, true
}

func main() {
    q := New(10)
    for i := 1; i < 13; i++ {
        fmt.Println(i, q.Enqueue(i))
    }   
    fmt.Println()
    for i := 1; i < 13; i++ {
        fmt.Println(q.Dequeue())
    }   
}
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