旧版链接 https://blog.csdn.net/hhhhhhhhhhkkkkkkkkkk/article/details/19990287
按照这个标题搜进来的各位是不是以为这也是和课本一样的内容呢，其实这是我看了两天课本才理解出来的内容啊，绝对和课本不一样。 课本上LR(1)项目集族的构造内容如下
以S′→·S，#属于初始项目集中，把’#‘号作为向前搜索符，表示活前缀为γ(若γ是有关S产生式的某一右部)要归约成S时，必须面临输入符为’#'号才行。我们对初始项目S′→·S，# 求闭包后再用转换函数逐步求出整个文法的LR(1)项目集族。具体构造步骤如下：
(1) 构造LR(1)项目集的闭包函数。
a)假定I是一个项目集， I 的任何项目都属于CLOSURE(I)。
b) 若有项目 A→α·Bβ,a 属于CLOSURE(I)，B→γ是文法中的产生式，β∈V*，b∈FIRST(βa)， 则 B→·γ,b 也属于CLOSURE(I)中。
c) 重复b)直到CLOSURE(I)不再增大为止。
大家是不是看的一头雾水呢。课本上还给出了一个例子：
文法：

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.edge-pattern-dashed{stroke-dasharray:3}#mermaid-svg-ZXzwQo4LHBkhLak8 .edge-pattern-dotted{stroke-dasharray:2}#mermaid-svg-ZXzwQo4LHBkhLak8 .marker{fill:#333}#mermaid-svg-ZXzwQo4LHBkhLak8 .marker.cross{stroke:#333}:root { --mermaid-font-family: "trebuchet ms", verdana, arial;}#mermaid-svg-ZXzwQo4LHBkhLak8 {color: rgba(0, 0, 0, 0.75);font: ;}

0 S'->S
1 S->aAd
2 S->bAc
3 S->aec
4 S->bed
5 A->e

项目集簇：

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S
a
b
A
e
A
e
d
c
c
d
I0:
S'->.S,#
S->.aAd,#
S->.bAc,#
S->.aec,#
S->.bed,#
I1:
S'->S.,#
I2:
S->a.<font color=#F00>A</font><font color=#0F0>d</font><font color=#080>,#</font>
S->a.ec,#
<font color=#F00>A</font>->.e,<font color=#0F0>d</font>
I3:
S->b.<font color=#F00>A</font><font color=#0F0>c</font><font color=#080>,#</font>
S->b.ed,#
<font color=#F00>A</font>->.e,<font color=#0F0>c</font>
I4:
S->aA.d,#
I5:
S->ae.c,#
A->e.,<font color=#F0F>d</font>
I6:
S->bA.c,#
I7:
S->be.d,#
A->e.,<font color=#F0F>c</font>
I8:
S->aAd.,#
I9:
S->aec.,#
I10:
S->bAc.,#
I11:
S->bed.,#

大家是不是在想I2中

A->e.,d

后的d，
I7中

A->e.,c

后的c是怎么来的呢？

课本的答案是对的，但是写法很是让我们一头雾水，下面让我们来看看答案是怎么出来的：

  • 1.一开始，S’是整个句子，所以后面理所当然跟句子结束符#。
    然后S后面是‘ε’（就是什么都没有）所以β=ε，
    接着逗号后面是‘#’即a=#，
    这样FIRST(βa)=FIRST(ε#)={#}。这就是I0中S后面#号的来历。

  • 2.在I2:S->a. Ad,#中
    A的后面是d,所以FIRST(d#)={d}（就是“d#”的第一个终结符d)，所以接下来A的后面跟的是d如图中绿色所示。

  • 3.在确定了A的逗号后面的搜索符后，基本上就可以直接照搬下去了，如图中的紫色所示。（其实#号一直都在照搬来着，大家注意到没？）

下面再讲一点FIRST(β)的计算。

  • 1.如果β的第一个字符是终结符，如：
β=aAbbC
β=eBbbD

那么

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.taskTextOutsideRight.clickable{cursor:pointer;fill:#003163 !important;font-weight:bold}#mermaid-svg-H6Td79aY0ozn7GqW .taskText0,#mermaid-svg-H6Td79aY0ozn7GqW .taskText1,#mermaid-svg-H6Td79aY0ozn7GqW .taskText2,#mermaid-svg-H6Td79aY0ozn7GqW .taskText3{fill:#fff}#mermaid-svg-H6Td79aY0ozn7GqW .task0,#mermaid-svg-H6Td79aY0ozn7GqW .task1,#mermaid-svg-H6Td79aY0ozn7GqW .task2,#mermaid-svg-H6Td79aY0ozn7GqW .task3{fill:#8a90dd;stroke:#534fbc}#mermaid-svg-H6Td79aY0ozn7GqW .taskTextOutside0,#mermaid-svg-H6Td79aY0ozn7GqW .taskTextOutside2{fill:#000}#mermaid-svg-H6Td79aY0ozn7GqW .taskTextOutside1,#mermaid-svg-H6Td79aY0ozn7GqW .taskTextOutside3{fill:#000}#mermaid-svg-H6Td79aY0ozn7GqW .active0,#mermaid-svg-H6Td79aY0ozn7GqW .active1,#mermaid-svg-H6Td79aY0ozn7GqW .active2,#mermaid-svg-H6Td79aY0ozn7GqW .active3{fill:#bfc7ff;stroke:#534fbc}#mermaid-svg-H6Td79aY0ozn7GqW .activeText0,#mermaid-svg-H6Td79aY0ozn7GqW .activeText1,#mermaid-svg-H6Td79aY0ozn7GqW .activeText2,#mermaid-svg-H6Td79aY0ozn7GqW 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.edge-pattern-dashed{stroke-dasharray:3}#mermaid-svg-H6Td79aY0ozn7GqW .edge-pattern-dotted{stroke-dasharray:2}#mermaid-svg-H6Td79aY0ozn7GqW .marker{fill:#333}#mermaid-svg-H6Td79aY0ozn7GqW .marker.cross{stroke:#333}:root { --mermaid-font-family: "trebuchet ms", verdana, arial;}#mermaid-svg-H6Td79aY0ozn7GqW {color: rgba(0, 0, 0, 0.75);font: ;}

β
aAbbC
eBbbD
a
e
a,e

即：

FIRST(β)
=FIRST(aAbbC)+FIRST(eBbbD)
={a}+{e}={a,e};   （‘+’代表‘并’，那个符号不好打，用‘+’来代替了。​）
  • 2.如果β的第一个字符是非终结符，如：
β=AEbC
A=DBac
D=ε
B=ea
B=bd
E=ε

那么:

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β
AEbC
(DBac)EbC
((ε)Bac)EbC
(εBac)EbC
(Bac)EbC
εEbC
(Bac)EbC
(E)bC
(Bac)EbC
(ε)bC
(Bac)EbC
bC
((ea)ac)EbC
((bd)ac)EbC
b
(eac)EbC
(bac)EbC
b
eEbC
bEbC
b
e
b
e,b

即：

FIRST(β)
=FIRST(AEbC)
=FIRST(FIRST(A)EbC)
=FIRST(FIRST(DBac)EbC)
=FIRST(FIRST(FIRST(D)Bac)EbC)
=FIRST(FIRST(εBac)EbC)        （ε表示空，如果不是空，就结束了，但是空还要计算ε后面的Bac）
=FIRST(FIRST(εBac)EbC)+FIRST(FIRST(Bac)EbC)
=FIRST(εEbC)+FIRST(FIRST(Bac)EbC)
=FIRST(FIRST(E)bC)+FIRST(FIRST(Bac)EbC)
={εbC}+FIRST(FIRST(Bac)EbC)
={bC}+FIRST(FIRST(FIRST(ea)ac)EbC)+FIRST(FIRST(FIRST(bd)ac)EbC)        （由于B有两个推导式，所以分开来写并求并集，‘+’代表‘并’）
={b}+FIRST(FIRST(eac)EbC)+FIRST(FIRST(bac)EbC)
={b}+FIRST(eEbC)+FIRST(bEbC)
={b}+{e}+{b}
={e,b}

为了普遍性，我把β搞的复杂了点，多看几遍，你就会了。如果不会，在下面留言。我可是看了两天才看懂的。

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