UVa 12219

链接：

https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=3371

题意：

可以用表达式树来表示一个表达式。在本题中，运算符均为二元的，且运算符和运算数均用1～4个小写字母表示。
例如，a(b(f(a,a),b(f(a,a),f)),f(b(f(a,a),b(f(a,a),f)),f))可以表示为a(b(f(a,4),b(3,f)),f(2,6))，
其中各个结点按照出现顺序编号为1，2，3，…，即编号k表示目前为止写下的第k个结点。
输入一个长度不超过50000的表达式，输出一个等价的，结点最少的图。

分析：

用一个map把子树映射成编号1, 2,…。这样一来，子树就可以用根的名字（字符串）和左右子结点编号表示。
然后构造表达式树并判断地输出即可。

代码：

//HashMap version
import java.io.*;
import java.util.*;
import static java.util.Arrays.*;
import static java.lang.Character.*;

class Node {
    String s;
    int lch, rch;
    
    @Override
    public int hashCode() {
        final int prime = 31;
        int result = 1;
        result = prime * result + lch;
        result = prime * result + rch;
        result = prime * result + ((s == null) ? 0 : s.hashCode());
        return result;
    }
    
    @Override
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Node other = (Node) obj;
        if (lch != other.lch)
            return false;
        if (rch != other.rch)
            return false;
        if (s == null) {
            if (other.s != null)
                return false;
        } else if (!s.equals(other.s))
            return false;
        return true;
    }
}

public class Main {
    Scanner cin = new Scanner(new BufferedInputStream(System.in));
    final int UP = 50000 + 5;
    int p, nextNode;
    char s[];
    boolean vis[] = new boolean[UP];
    Node node[] = new Node[UP];
    HashMap<Node,Integer> map = new HashMap<Node,Integer>();
    
    { for(int i = 0; i < UP; i++) node[i] = new Node(); }
    
    int parse() {
        int id = ++nextNode;
        node[id].s = "";
        node[id].lch = node[id].rch = 0;
        while(isLetter(s[p])) {
            node[id].s += s[p];
            p++;
        }
        if(s[p] == '(') {
            p++;  node[id].lch = parse();  p++;  node[id].rch = parse();  p++;
        }
        if(map.containsKey(node[id])) {
            nextNode--;
            return map.get(node[id]);
        }
        map.put(node[id], id);
        return id;
    }
    
    void output(int id) {
        if(vis[id]) {
            System.out.print(id);
            return;
        }
        vis[id] = true;
        System.out.print(node[id].s);
        if(node[id].lch != 0) {
            System.out.print('(');
            output(node[id].lch);
            System.out.print(',');
            output(node[id].rch);
            System.out.print(')');
        }
    }
    
    void MAIN() {
        int T = cin.nextInt();
        while(T --> 0) {
            s = (cin.next() + "").toCharArray();
            p = nextNode = 0;
            fill(vis, false);
            map.clear();
            output(parse());
            System.out.println();
        }
    }
    
    public static void main(String args[]) { new Main().MAIN(); }
}

//TreeMap version
import java.io.*;
import java.util.*;
import static java.util.Arrays.*;
import static java.lang.Character.*;

class Node implements Comparable<Node> {
    String s;
    int hash, lch, rch;
    
    @Override
    public int compareTo(Node that) {
        if(hash != that.hash) return hash - that.hash;
        if(lch != that.lch) return lch - that.lch;
        return rch - that.rch;
    }
}

public class Main {
    Scanner cin = new Scanner(new BufferedInputStream(System.in));
    final int UP = 50000 + 5;
    int p, nextNode;
    char s[];
    boolean vis[] = new boolean[UP];
    Node node[] = new Node[UP];
    TreeMap<Node,Integer> map = new TreeMap<Node,Integer>();
    
    { for(int i = 0; i < UP; i++) node[i] = new Node(); }
    
    int parse() {
        int id = ++nextNode;
        node[id].s = "";
        node[id].hash = node[id].lch = node[id].rch = 0;
        while(isLetter(s[p])) {
            node[id].hash = node[id].hash * 29 + s[p] - 'a' + 1;
            node[id].s += s[p];
            p++;
        }
        if(s[p] == '(') {
            p++;  node[id].lch = parse();  p++;  node[id].rch = parse();  p++;
        }
        if(map.containsKey(node[id])) {
            nextNode--;
            return map.get(node[id]);
        }
        map.put(node[id], id);
        return id;
    }
    
    void output(int id) {
        if(vis[id]) {
            System.out.print(id);
            return;
        }
        vis[id] = true;
        System.out.print(node[id].s);
        if(node[id].lch != 0) {
            System.out.print('(');
            output(node[id].lch);
            System.out.print(',');
            output(node[id].rch);
            System.out.print(')');
        }
    }
    
    void MAIN() {
        int T = cin.nextInt();
        while(T --> 0) {
            s = (cin.next() + "").toCharArray();
            p = nextNode = 0;
            fill(vis, false);
            map.clear();
            output(parse());
            System.out.println();
        }
    }
    
    public static void main(String args[]) { new Main().MAIN(); }
}