一块40克的砝码,摔成4块,利用天平,刚好可以称出1~40g所有整数克,问:这4块分别是多少克
1 public static void main(String[] args) {
2 List<Integer> list = new ArrayList<>();//记录每组数的值 每组数a<=b<=c<=d
3 List<Integer> rlist = new ArrayList<>();//记录最后的结果
4
5 for(int i = 1; i <= 10 ; i++) {
6 for(int j = i; j <= 13 ; j++) {
7 for(int k = j; k <= 19 ; k++) {
8 list.add(i);
9 list.add(j);
10 list.add(k);
11 list.add(40-i-j-k);
12 }
13 }
14 }
15
16 int a,b,c,d;
17 int len = list.size()/4;
18 for (int i = 0; i < len; i++) {
19 a = list.get(4*i);
20 b = list.get(4*i+1);
21 c = list.get(4*i+2);
22 d = list.get(4*i+3);
23 if(result(a, b, c, d)) {
24 rlist.add(a);
25 rlist.add(b);
26 rlist.add(c);
27 rlist.add(d);
28 }
29 }
30 len = rlist.size()/4;
31 for(int i = 0; i < len; i++) {
32 System.out.println("40 = "+rlist.get(4*i)+" + "+rlist.get(4*i+1)+" + "+rlist.get(4*i+2)+" + "+rlist.get(4*i+3));
33 }
34 }
35
36 public static boolean result(int a,int b,int c,int d){
37 TreeSet<Integer> set = new TreeSet<>();
38 int[] arr = {-1,0,1};
39 for (int i = 0; i < arr.length; i++) {
40 for (int j = 0; j < arr.length; j++) {
41 for (int k = 0; k < arr.length; k++) {
42 for (int l = 0; l < arr.length; l++) {
43 int sum = a*arr[i]+b*arr[j]+c*arr[k]+d*arr[l];
44
45 if(sum > 0) set.add(sum);
46 }
47 }
48 }
49 }
50 if(set.size() == 40)
51 return true;
52 else
53 return false;
54 }