算法原理参考编程之美1.16章节解法2：

下面是java源码：子问题为S[i] U= Fork(f(x),f(i-x));

import java.util.HashMap;

import java.util.HashSet;

import java.util.Map;

import java.util.Scanner;

import java.util.Set;

class Elem{

public double res;

public String info;

public Elem(double r,String i){

res = r;

info = i;

}

}

public class CalculateAnswer {

private final int N = 4;

private final int res = 24;

private int[] A;

private Map> map;

private Set answers;

public CalculateAnswer(int[] a) {

A = a;

map = new HashMap>();

answers = new HashSet();

}

public void run() {

for(int i=0;i

Set set = new HashSet();

map.put(i,set);

}

for(int i=0;i

Elem e = new Elem(A[i], A[i]+"");

Set set = new HashSet();

set.add(e);

map.put(1<

}

for (int i = 1; i < (1 << N); i++) {

fork(i);

}

Set mSet = map.get((1<

for(Elem e:mSet){

if(e.res==res) {

answers.add(e.info);

}

}

if(answers.size()==0){

System.out.println("无解");

}

else {

for(String s:answers)

System.out.println(s);

System.out.println("共有"+answers.size()+"个解");

}

}

public Set fork(int m) {

Set mSet = map.get(m);

if(mSet.size()>0)

return mSet;

else {

for(int x = 1; x <= m ; x++) {

if((x&m)==x){

Set s1 = fork(x);

Set s2 = fork(m-x);

for(Elem e1: s1) {

for(Elem e2:s2) {

String str = "("+e1.info+"+"+e2.info+")";

mSet.add(new Elem(e1.res+e2.res, str));

str = "("+ e1.info+"-"+e2.info+")";

mSet.add(new Elem(e1.res-e2.res, str));

str = "("+ e2.info+"-"+e1.info+")";

mSet.add(new Elem(e2.res-e1.res, str));

str = "("+ e1.info+"*"+e2.info+")";

mSet.add(new Elem(e1.res*e2.res, str));

if(e1.res!=0) {

str = "("+ e2.info+"/"+e1.info+")";

mSet.add(new Elem(e2.res/e1.res, str));

}

if(e2.res!=0){

str = "("+ e1.info+"/"+e2.info+")";

mSet.add(new Elem(e1.res/e2.res, str));

}

}

}

}

}

return mSet;

}

}

public static void main(String[] args) {

int[] a = new int[4];

Scanner sc = new Scanner(System.in);

for(int i = 0;i<4;i++) {

a[i] = sc.nextInt();

}

CalculateAnswer cal = new CalculateAnswer(a);

cal.run();

sc.close();

}

}