将递归函数转换为尾递归

Question

我有以下递归函数来计算循环双向链表中值为 20 的所有节点。我需要将其转换为尾递归函数以防止安全问题。请帮我做同样的事情。谢谢

int count(node *start)
{
    return count_helper(start, start);
}
int count_helper(node *current, node *start)
{
    int c;
    c = 0;
    if(current == NULL)
        return 0;
    if((current->roll_no) == 20)
        c = 1;
    if(current->next == start) return c;
    return (c + count_helper(current->next, start));
}

Answer 1

为了利用尾递归，递归调用必须是最后执行的事情。目前，唯一阻碍这一目标的就是添加。因此，要转换函数，必须移动该添加部分。实现此目的的常见方法是将变量 c 作为参数传递给递归辅助函数，如下所示:

int count(node *start)
{
    return count_helper(start,start,0);
}

int count_helper(node *current, node *start, int c)
{
    if(current == NULL)
        return c;
    if((current->roll_no) == 20)
        c+=1;
    if(current->next == start)
        return c;
    return count_helper(current->next, start,c);
}

展开如下(使用 gcc 4.6.1，由 gcc -S -O2 生成):

count_helper:
.LFB23:
    .cfi_startproc
    pushl   %ebx
    .cfi_def_cfa_offset 8
    .cfi_offset 3, -8
    movl    8(%esp), %edx
    movl    12(%esp), %ebx
    movl    16(%esp), %eax
    testl   %edx, %edx
    jne     .L15
    jmp     .L10
    .p2align 4,,7
    .p2align 3
.L14:
    testl   %edx, %edx
    je      .L10
.L15:
    xorl    %ecx, %ecx
    cmpl    $20, 4(%edx)
    movl    (%edx), %edx
    sete    %cl
    addl    %ecx, %eax
    cmpl    %ebx, %edx
    jne     .L14         # <-- this is the key line right here
.L10:
    popl    %ebx
    .cfi_def_cfa_offset 4
    .cfi_restore 3
    ret
    .cfi_endproc

将其与您的原始版本进行比较(在没有 -O2 的情况下完成，显然编译器也找到了一种方法使您的原始尾部递归，尽管在这个过程中它把它弄乱了很多，我可以几乎没有读过):

count_helper:
.LFB1:
    .cfi_startproc
    pushl   %ebp
    .cfi_def_cfa_offset 8
    .cfi_offset 5, -8
    movl    %esp, %ebp
    .cfi_def_cfa_register 5
    subl    $40, %esp
    movl    $0, -12(%ebp)
    cmpl    $0, 8(%ebp)
    jne     .L3
    movl    $0, %eax
    jmp     .L4
.L3:
    movl    8(%ebp), %eax
    movl    4(%eax), %eax
    cmpl    $20, %eax
    jne     .L5
    movl    $1, -12(%ebp)
.L5:
    movl    8(%ebp), %eax
    movl    (%eax), %eax
    cmpl    12(%ebp), %eax
    jne     .L6
    movl    -12(%ebp), %eax
    jmp     .L4
.L6:
    movl    8(%ebp), %eax
    movl    (%eax), %eax
    movl    12(%ebp), %edx
    movl    %edx, 4(%esp)
    movl    %eax, (%esp)
    call    count_helper     # <-- this is the key line right here
    addl    -12(%ebp), %eax
.L4:
    leave
    .cfi_restore 5
    .cfi_def_cfa 4, 4
    ret
    .cfi_endproc