数节点、量深度

（每道题开头都有同一段：T() 是上一站 lexer 的替身——源码里 token 之间用空格分开，它切成 (kind, text, line, col)；show() 把树写成一行：二元运算全加括号，语句之间用 |。）

用完整 parser 解析 x = 1 + 2 * 3 ;，数树里有几个节点、最深几层：

KEYWORDS = ("let", "if", "else", "while")
CMP = (">=", "<=", "==", "!=", "<", ">")

def T(src):
    toks = []
    for ln, line in enumerate(src.split("\n"), 1):
        pos = 0
        for w in line.split():
            pos = line.index(w, pos)
            if w in KEYWORDS:
                k = "KEYWORD"
            elif w[0] == '"':
                k = "STRING"
            elif w.isdigit():
                k = "NUMBER"
            elif w[0].isalpha() or w[0] == "_":
                k = "IDENT"
            else:
                k = "OP"
            toks.append((k, w, ln, pos + 1))
            pos += len(w)
    toks.append(("EOF", "", ln, pos + 1))
    return toks

class ParseError(Exception):
    def __init__(self, want, got, line, col):
        super().__init__("期待「" + want + "」遇到「" + got + "」@" + str(line) + ":" + str(col))
        self.want, self.got, self.line, self.col = want, got, line, col

def show(n):
    if n[0] == "num" or n[0] == "var":
        return str(n[1])
    if n[0] == "str":
        return '"' + n[1] + '"'
    if n[0] == "bin":
        return "(" + show(n[2]) + n[1] + show(n[3]) + ")"
    if n[0] == "let":
        return "let:" + n[1] + "=" + show(n[2])
    if n[0] == "assign":
        return n[1] + "=" + show(n[2])
    if n[0] == "if":
        s = "if[" + show(n[1]) + "]{" + ";".join(show(x) for x in n[2]) + "}"
        if n[3] is not None:
            s += "else{" + ";".join(show(x) for x in n[3]) + "}"
        return s
    if n[0] == "while":
        return "while[" + show(n[1]) + "]{" + ";".join(show(x) for x in n[2]) + "}"
    if n[0] == "program":
        return "|".join(show(x) for x in n[1])
    return "?"

class Parser:
    def __init__(self, toks):
        self.toks = toks
        self.i = 0

    def peek(self):
        return self.toks[self.i]

    def advance(self):
        t = self.toks[self.i]
        self.i += 1
        return t

    def at(self, text):
        return self.peek()[1] == text

    def expect(self, text):
        t = self.peek()
        if t[1] != text:
            raise ParseError(text, t[1] or "文件结尾", t[2], t[3])
        return self.advance()

    def expect_kind(self, kind):
        t = self.peek()
        if t[0] != kind:
            raise ParseError(kind, t[1] or "文件结尾", t[2], t[3])
        return self.advance()

    def program(self):
        stmts = []
        while self.peek()[0] != "EOF":
            stmts.append(self.stmt())
        return ("program", stmts)

    def stmt(self):
        if self.at("let"):
            self.advance()
            name = self.expect_kind("IDENT")[1]
            self.expect("=")
            e = self.expr()
            self.expect(";")
            return ("let", name, e)
        if self.at("if"):
            self.advance()
            self.expect("(")
            c = self.expr()
            self.expect(")")
            body = self.block()
            alt = None
            if self.at("else"):
                self.advance()
                alt = self.block()
            return ("if", c, body, alt)
        if self.at("while"):
            self.advance()
            self.expect("(")
            c = self.expr()
            self.expect(")")
            return ("while", c, self.block())
        name = self.expect_kind("IDENT")[1]
        self.expect("=")
        e = self.expr()
        self.expect(";")
        return ("assign", name, e)

    def block(self):
        self.expect("{")
        stmts = []
        while not self.at("}"):
            if self.peek()[0] == "EOF":
                self.expect("}")
            stmts.append(self.stmt())
        self.expect("}")
        return stmts

    def expr(self):
        return self.comparison()

    def comparison(self):
        left = self.sum_()
        if self.peek()[1] in CMP:
            op = self.advance()[1]
            right = self.sum_()
            return ("bin", op, left, right)
        return left

    def sum_(self):
        left = self.term()
        while self.peek()[1] in ("+", "-"):
            op = self.advance()[1]
            right = self.term()
            left = ("bin", op, left, right)
        return left

    def term(self):
        left = self.factor()
        while self.peek()[1] in ("*", "/"):
            op = self.advance()[1]
            right = self.factor()
            left = ("bin", op, left, right)
        return left

    def factor(self):
        t = self.peek()
        if t[0] == "NUMBER":
            self.advance()
            return ("num", int(t[1]))
        if t[0] == "STRING":
            self.advance()
            return ("str", t[1][1:-1])
        if t[0] == "IDENT":
            self.advance()
            return ("var", t[1])
        if t[1] == "(":
            self.advance()
            e = self.expr()
            self.expect(")")
            return e
        raise ParseError("表达式", t[1] or "文件结尾", t[2], t[3])

def kids(n):
    if n[0] == "bin":
        return [n[2], n[3]]
    if n[0] in ("let", "assign"):
        return [n[2]]
    if n[0] == "if":
        return [n[1]] + n[2] + (n[3] or [])
    if n[0] == "while":
        return [n[1]] + n[2]
    if n[0] == "program":
        return n[1]
    return []

def count(n):
    return 1 + sum(count(k) for k in kids(n))

def depth(n):
    return 1 + max([depth(k) for k in kids(n)] + [0])

node = Parser(T("x = 1 + 2 * 3 ;")).stmt()
print(str(count(node)) + "/" + str(depth(node)))