我正在尝试实现一个可解决此问题的程序：
如果给您一个特定的数字（例如：268） 和另外6个数字（例如：2,4,5,25,75,100）
如何找到可以给出确切答案或最接近答案的操作？
您可以使用以下操作来回答前面的示例：75 * 4-25-5-2 = 268
规则：
有没有比写下全部可能性并采取最接近的可能性更好的解决方案？因为此答案将迫使我编写太多行代码，谢谢！
实际上，蛮力解决方案实际上不是那么多代码
（编辑：略微更改了代码，因为某些规则没有得到适当考虑）
import java.util.ArrayList; import java.util.Arrays; import java.util.List; public class NumberPuzzle { public static void main(String[] args) { List<Integer> numbers = Arrays.asList(2,4,5,25,75,100); Integer result = 268; solve(numbers, result); } private static void solve(List<Integer> numbers, Integer result) { List<Node> nodes = new ArrayList<Node>(); for (int i=0; i<numbers.size(); i++) { Integer number = numbers.get(i); nodes.add(new Node(number)); } System.out.println(nodes); List<Node> all = create(nodes); System.out.println("Found "+all.size()+" combinations"); List<Node> best = new ArrayList<Node>(); Integer minDifference = Integer.MAX_VALUE; for (Node n : all) { //System.out.println(n); Integer e = n.evaluate(); Integer difference = Math.abs(e - result); if (difference < minDifference) { best.clear(); minDifference = difference; best.add(n); } else if (difference.equals(minDifference)) { best.add(n); } } for (Node n : best) { System.out.println(n+" = "+n.evaluate()); } } private static List<Node> create(List<Node> nodes) { if (nodes.size() == 1) { return nodes; } List<Node> result = new ArrayList<Node>(nodes); for (int i=0; i<nodes.size(); i++) { List<Node> copy = new ArrayList<Node>(nodes); Node node = copy.remove(i); List<Node> others = create(copy); for (int j=0; j<others.size(); j++) { Node other = others.get(j); result.add(new Node(node, '+', other)); result.add(new Node(node, '*', other)); result.add(new Node(node, '-', other)); result.add(new Node(other, '-', node)); Integer vNode = node.evaluate(); Integer vOther = other.evaluate(); if (vOther != 0 && vNode % vOther == 0) { result.add(new Node(node, '/', other)); } if (vNode != 0 && vOther % vNode == 0) { result.add(new Node(other, '/', node)); } } } return result; } static class Node { Integer value; Node left; Character op; Node right; Node(Node left, Character op, Node right) { this.left = left; this.op = op; this.right = right; } Node(Integer value) { this.value = value; } Integer evaluate() { if (op != null) { Integer lv = left.evaluate(); Integer rv = right.evaluate(); switch (op) { case '+': return lv + rv; case '-': return lv - rv; case '*': return lv * rv; case '/': return rv.equals(0) ? Integer.MAX_VALUE : lv / rv; } } return value; } @Override public String toString() { if (op == null) { return String.valueOf(value); } return "("+left.toString()+op+right.toString()+")"; } } }
它找到了很多解决方案。
（编辑：根据更改的代码进行了更新）
(2*(4+(5+(25+100)))) = 268 (2*(4+(5+(100+25)))) = 268 (2*(4+(25+(5+100)))) = 268 (2*(4+(25+(100+5)))) = 268 (2*(4+(100+(5+25)))) = 268 (2*(4+(100+(25+5)))) = 268 ((5*(4-(25-75)))-2) = 268 ((5*(4+(75-25)))-2) = 268 (2*(5+(4+(25+100)))) = 268 ((5*(4+(25-(75-100))))-2) = 268 ((5*(4-((75-100)-25)))-2) = 268 ((5*(4+(25+(100-75))))-2) = 268 ((5*(4+(25+(100-75))))-2) = 268 ((5*(4+(25-(75-100))))-2) = 268 ((5*(4-((75-100)-25)))-2) = 268 ((5*(4+(75-25)))-2) = 268 ((5*(4-(25-75)))-2) = 268 ((5*(4-(75-(25+100))))-2) = 268 ((5*(4+((25+100)-75)))-2) = 268 ((5*(4-(75-(100+25))))-2) = 268 ((5*(4+((100+25)-75)))-2) = 268 (2*(5+(4+(100+25)))) = 268 ((5*(4+(100+(25-75))))-2) = 268 ((5*(4+(100-(75-25))))-2) = 268 ((5*(4-((75-25)-100)))-2) = 268 ((5*(4+(100-(75-25))))-2) = 268 ((5*(4-((75-25)-100)))-2) = 268 ((5*(4+(100+(25-75))))-2) = 268 ((5*((4+75)-25))-2) = 268 ((((4*75)-25)-5)-2) = 268 (2*(5+(25+(4+100)))) = 268 ((5*(25+(4-(75-100))))-2) = 268 ((5*(25-((75-100)-4)))-2) = 268 ((5*(25+(4+(100-75))))-2) = 268 ((5*(25+(4+(100-75))))-2) = 268 ((5*(25+(4-(75-100))))-2) = 268 ((5*(25-((75-100)-4)))-2) = 268 ((5*((75+4)-25))-2) = 268 ((((75*4)-25)-5)-2) = 268 ((5*(25-(75-(4+100))))-2) = 268 ((5*(25+((4+100)-75)))-2) = 268 ((5*(25-(75-(100+4))))-2) = 268 ((5*(25+((100+4)-75)))-2) = 268 (2*(5+(25+(100+4)))) = 268 ((5*(25+(100+(4-75))))-2) = 268 ((5*(25+(100-(75-4))))-2) = 268 ((5*(25-((75-4)-100)))-2) = 268 ((5*(25+(100-(75-4))))-2) = 268 ((5*(25-((75-4)-100)))-2) = 268 ((5*(25+(100+(4-75))))-2) = 268 ((5*(75+(4-25)))-2) = 268 ((5*(75-(25-4)))-2) = 268 ((5*((4+(25+100))-75))-2) = 268 ((5*((4+(100+25))-75))-2) = 268 ((5*(75-(25-4)))-2) = 268 ((5*(75+(4-25)))-2) = 268 ((5*((25+(4+100))-75))-2) = 268 ((5*((25+(100+4))-75))-2) = 268 ((5*((100+(4+25))-75))-2) = 268 (((75+(100+(4*25)))-5)-2) = 268 ((5*((100+(25+4))-75))-2) = 268 (((75+(100+(25*4)))-5)-2) = 268 (2*(5+(100+(4+25)))) = 268 ((5*(100+(4+(25-75))))-2) = 268 ((5*(100+(4-(75-25))))-2) = 268 ((5*(100-((75-25)-4)))-2) = 268 ((5*(100+(4-(75-25))))-2) = 268 ((5*(100-((75-25)-4)))-2) = 268 ((5*(100+(4+(25-75))))-2) = 268 (2*(5+(100+(25+4)))) = 268 ((5*(100+(25+(4-75))))-2) = 268 ((5*(100+(25-(75-4))))-2) = 268 ((5*(100-((75-4)-25)))-2) = 268 ((5*(100+(25-(75-4))))-2) = 268 ((5*(100-((75-4)-25)))-2) = 268 ((5*(100+(25+(4-75))))-2) = 268 ((5*(100-(75-(4+25))))-2) = 268 ((5*(100+((4+25)-75)))-2) = 268 (((100+(75+(4*25)))-5)-2) = 268 ((5*(100-(75-(25+4))))-2) = 268 ((5*(100+((25+4)-75)))-2) = 268 (((100+(75+(25*4)))-5)-2) = 268 (2*(25+(4+(5+100)))) = 268 (2*(25+(4+(100+5)))) = 268 ((((4*75)-5)-25)-2) = 268 (2*(25+(5+(4+100)))) = 268 ((((75*4)-5)-25)-2) = 268 (2*(25+(5+(100+4)))) = 268 (2*(25+(100+(4+5)))) = 268 (2*(25+(100+(5+4)))) = 268 ((((5*(4+75))-100)-25)-2) = 268 ((((5*(75+4))-100)-25)-2) = 268 ((75-(5-(100+(4*25))))-2) = 268 ((75+((100+(4*25))-5))-2) = 268 ((75-(5-(100+(25*4))))-2) = 268 ((75+((100+(25*4))-5))-2) = 268 ((75+(100-(5-(4*25))))-2) = 268 ((75-((5-(4*25))-100))-2) = 268 ((75+(100+((4*25)-5)))-2) = 268 ((75+(100-(5-(25*4))))-2) = 268 ((75-((5-(25*4))-100))-2) = 268 ((75+(100+((25*4)-5)))-2) = 268 (2*(100+(4+(5+25)))) = 268 (2*(100+(4+(25+5)))) = 268 (2*(100+(5+(4+25)))) = 268 (2*(100+(5+(25+4)))) = 268 ((100-(5-(75+(4*25))))-2) = 268 ((100+((75+(4*25))-5))-2) = 268 ((100-(5-(75+(25*4))))-2) = 268 ((100+((75+(25*4))-5))-2) = 268 (2*(100+(25+(4+5)))) = 268 (2*(100+(25+(5+4)))) = 268 ((((5*(4+75))-25)-100)-2) = 268 ((((5*(75+4))-25)-100)-2) = 268 ((100+(75-(5-(4*25))))-2) = 268 ((100-((5-(4*25))-75))-2) = 268 ((100+(75+((4*25)-5)))-2) = 268 ((100+(75-(5-(25*4))))-2) = 268 ((100-((5-(25*4))-75))-2) = 268 ((100+(75+((25*4)-5)))-2) = 268 (((100*((75-5)-2))/25)-4) = 268 (((100*((75-5)-2))/25)-4) = 268 (((100*((75-2)-5))/25)-4) = 268 (((100*((75-2)-5))/25)-4) = 268 (((100*(75-(2+5)))/25)-4) = 268 (((100*(75-(5+2)))/25)-4) = 268 (4*(75-(2*(100/25)))) = 268 (4*(75-(2*(100/25)))) = 268 (4*(75-((2*100)/25))) = 268 (4*(75-((100*2)/25))) = 268 ((((4*75)-25)-2)-5) = 268 ((((75*4)-25)-2)-5) = 268 (((75+(100+(4*25)))-2)-5) = 268 (((75+(100+(25*4)))-2)-5) = 268 (((100+(75+(4*25)))-2)-5) = 268 (((100+(75+(25*4)))-2)-5) = 268 ((((4*75)-2)-25)-5) = 268 ((((75*4)-2)-25)-5) = 268 ((75-(2-(100+(4*25))))-5) = 268 ((75+((100+(4*25))-2))-5) = 268 ((75-(2-(100+(25*4))))-5) = 268 ((75+((100+(25*4))-2))-5) = 268 ((75+(100-(2-(4*25))))-5) = 268 ((75-((2-(4*25))-100))-5) = 268 ((75+(100+((4*25)-2)))-5) = 268 ((75+(100-(2-(25*4))))-5) = 268 ((75-((2-(25*4))-100))-5) = 268 ((75+(100+((25*4)-2)))-5) = 268 ((100-(2-(75+(4*25))))-5) = 268 ((100+((75+(4*25))-2))-5) = 268 ((100-(2-(75+(25*4))))-5) = 268 ((100+((75+(25*4))-2))-5) = 268 ((100+(75-(2-(4*25))))-5) = 268 ((100-((2-(4*25))-75))-5) = 268 ((100+(75+((4*25)-2)))-5) = 268 ((100+(75-(2-(25*4))))-5) = 268 ((100-((2-(25*4))-75))-5) = 268 ((100+(75+((25*4)-2)))-5) = 268 ((((4*75)-5)-2)-25) = 268 ((((75*4)-5)-2)-25) = 268 ((((5*(4+75))-100)-2)-25) = 268 ((((5*(75+4))-100)-2)-25) = 268 ((((4*75)-2)-5)-25) = 268 ((((75*4)-2)-5)-25) = 268 ((75+(2*(4+(5+100))))-25) = 268 ((75+(2*(4+(100+5))))-25) = 268 ((75+(2*(5+(4+100))))-25) = 268 ((75+(2*(5+(100+4))))-25) = 268 ((75+(2*(100+(4+5))))-25) = 268 ((75+(2*(100+(5+4))))-25) = 268 ((((5*(4+75))-2)-100)-25) = 268 ((((5*(75+4))-2)-100)-25) = 268 ((100*(75-(2*4)))/25) = 268 ((100*(75-(4*2)))/25) = 268 (75-(2+(5-(100+(4*25))))) = 268 (75-(2-((100+(4*25))-5))) = 268 (75+(((100+(4*25))-5)-2)) = 268 (75-(2+(5-(100+(25*4))))) = 268 (75-(2-((100+(25*4))-5))) = 268 (75+(((100+(25*4))-5)-2)) = 268 (75-(2-(100-(5-(4*25))))) = 268 (75+((100-(5-(4*25)))-2)) = 268 (75-(2+((5-(4*25))-100))) = 268 (75-(2-(100+((4*25)-5)))) = 268 (75+((100+((4*25)-5))-2)) = 268 (75-(2-(100-(5-(25*4))))) = 268 (75+((100-(5-(25*4)))-2)) = 268 (75-(2+((5-(25*4))-100))) = 268 (75-(2-(100+((25*4)-5)))) = 268 (75+((100+((25*4)-5))-2)) = 268 (75-(5+(2-(100+(4*25))))) = 268 (75-(5-((100+(4*25))-2))) = 268 (75+(((100+(4*25))-2)-5)) = 268 (75-(5+(2-(100+(25*4))))) = 268 (75-(5-((100+(25*4))-2))) = 268 (75+(((100+(25*4))-2)-5)) = 268 (75-(5-(100-(2-(4*25))))) = 268 (75+((100-(2-(4*25)))-5)) = 268 (75-(5+((2-(4*25))-100))) = 268 (75-(5-(100+((4*25)-2)))) = 268 (75+((100+((4*25)-2))-5)) = 268 (75-(5-(100-(2-(25*4))))) = 268 (75+((100-(2-(25*4)))-5)) = 268 (75-(5+((2-(25*4))-100))) = 268 (75-(5-(100+((25*4)-2)))) = 268 (75+((100+((25*4)-2))-5)) = 268 (75-(25-(2*(4+(5+100))))) = 268 (75+((2*(4+(5+100)))-25)) = 268 (75-(25-(2*(4+(100+5))))) = 268 (75+((2*(4+(100+5)))-25)) = 268 (75-(25-(2*(5+(4+100))))) = 268 (75+((2*(5+(4+100)))-25)) = 268 (75-(25-(2*(5+(100+4))))) = 268 (75+((2*(5+(100+4)))-25)) = 268 (75-(25-(2*(100+(4+5))))) = 268 (75+((2*(100+(4+5)))-25)) = 268 (75-(25-(2*(100+(5+4))))) = 268 (75+((2*(100+(5+4)))-25)) = 268 (75+(100-(2+(5-(4*25))))) = 268 (75-((2+(5-(4*25)))-100)) = 268 (75+(100-(2-((4*25)-5)))) = 268 (75-((2-((4*25)-5))-100)) = 268 (75+(100+(((4*25)-5)-2))) = 268 (75+(100-(2+(5-(25*4))))) = 268 (75-((2+(5-(25*4)))-100)) = 268 (75+(100-(2-((25*4)-5)))) = 268 (75-((2-((25*4)-5))-100)) = 268 (75+(100+(((25*4)-5)-2))) = 268 (75+(100-(5+(2-(4*25))))) = 268 (75-((5+(2-(4*25)))-100)) = 268 (75+(100-(5-((4*25)-2)))) = 268 (75-((5-((4*25)-2))-100)) = 268 (75+(100+(((4*25)-2)-5))) = 268 (75+(100-(5+(2-(25*4))))) = 268 (75-((5+(2-(25*4)))-100)) = 268 (75+(100-(5-((25*4)-2)))) = 268 (75-((5-((25*4)-2))-100)) = 268 (75+(100+(((25*4)-2)-5))) = 268 (100+(2*(4+(5+75)))) = 268 (100+(2*(4+(75+5)))) = 268 (100+(2*(4+(75+(25/5))))) = 268 (100+(2*(4+(75+(25/5))))) = 268 (100+(2*(5+(4+75)))) = 268 (100+(2*(5+(75+4)))) = 268 (100-(2+(5-(75+(4*25))))) = 268 (100-(2-((75+(4*25))-5))) = 268 (100+(((75+(4*25))-5)-2)) = 268 (100-(2+(5-(75+(25*4))))) = 268 (100-(2-((75+(25*4))-5))) = 268 (100+(((75+(25*4))-5)-2)) = 268 ((((5*(4+75))-25)-2)-100) = 268 ((((5*(75+4))-25)-2)-100) = 268 (100+(2*(75+(4+5)))) = 268 (100+(2*(75+(4+(25/5))))) = 268 (100+(2*(75+(4+(25/5))))) = 268 (100+(2*(75+(5+4)))) = 268 (100-(2-(75-(5-(4*25))))) = 268 (100+((75-(5-(4*25)))-2)) = 268 (100-(2+((5-(4*25))-75))) = 268 (100-(2-(75+((4*25)-5)))) = 268 (100+((75+((4*25)-5))-2)) = 268 (100-(2-(75-(5-(25*4))))) = 268 (100+((75-(5-(25*4)))-2)) = 268 (100-(2+((5-(25*4))-75))) = 268 (100-(2-(75+((25*4)-5)))) = 268 (100+((75+((25*4)-5))-2)) = 268 (100+(4*(2+(25+(75/5))))) = 268 (100+(4*(2+(25+(75/5))))) = 268 (100+(4*(25+(2+(75/5))))) = 268 (100+(4*(25+(2+(75/5))))) = 268 (100-(5+(2-(75+(4*25))))) = 268 (100-(5-((75+(4*25))-2))) = 268 (100+(((75+(4*25))-2)-5)) = 268 (100-(5+(2-(75+(25*4))))) = 268 (100-(5-((75+(25*4))-2))) = 268 (100+(((75+(25*4))-2)-5)) = 268 (100-(5-(75-(2-(4*25))))) = 268 (100+((75-(2-(4*25)))-5)) = 268 (100-(5+((2-(4*25))-75))) = 268 (100-(5-(75+((4*25)-2)))) = 268 (100+((75+((4*25)-2))-5)) = 268 (100-(5-(75-(2-(25*4))))) = 268 (100+((75-(2-(25*4)))-5)) = 268 (100-(5+((2-(25*4))-75))) = 268 (100-(5-(75+((25*4)-2)))) = 268 (100+((75+((25*4)-2))-5)) = 268 ((((5*(4+75))-2)-25)-100) = 268 ((((5*(75+4))-2)-25)-100) = 268 (100+(75-(2+(5-(4*25))))) = 268 (100-((2+(5-(4*25)))-75)) = 268 (100+(75-(2-((4*25)-5)))) = 268 (100-((2-((4*25)-5))-75)) = 268 (100+(75+(((4*25)-5)-2))) = 268 (100+(75-(2+(5-(25*4))))) = 268 (100-((2+(5-(25*4)))-75)) = 268 (100+(75-(2-((25*4)-5)))) = 268 (100-((2-((25*4)-5))-75)) = 268 (100+(75+(((25*4)-5)-2))) = 268 (100+(75-(5+(2-(4*25))))) = 268 (100-((5+(2-(4*25)))-75)) = 268 (100+(75-(5-((4*25)-2)))) = 268 (100-((5-((4*25)-2))-75)) = 268 (100+(75+(((4*25)-2)-5))) = 268 (100+(75-(5+(2-(25*4))))) = 268 (100-((5+(2-(25*4)))-75)) = 268 (100+(75-(5-((25*4)-2)))) = 268 (100-((5-((25*4)-2))-75)) = 268 (100+(75+(((25*4)-2)-5))) = 268
但是当然，由于可交换性，其中许多都是多余的。
可以轻松避免在蛮力变种中检查过的许多解决方案。第一步之一可能是避免创建包含可交换元素的节点，并可能equals为Node我在此处绘制的速干类实现一种方法，该方法考虑了可交换性，然后使用Sets个Node代替的List。而且，“简单”，“低级”优化也是可能的（例如，找到完美匹配时尽早返回）。
equals
Node
Set
List
关于您的实际问题，是否有解决方案比暴力破解“更好”：我的直觉是答案是否定的，但这取决于应该解决哪个问题。关键点在这里：假定您获得了可用数字的列表以及所需的结果值。并假设不可能从给定的输入值创建结果值。例如，当你有
input = { 1,2,3,4,5,6 } result = 10000000000;
我认为，为了真正 证明 这是不可能的，您 必须 列举所有组合（最后返回“最佳”组合，这里可能是1*2*3*4*5*6）。如果您跳过 任何一种 组合，应该如何确定它并不是 最佳组合 ？
1*2*3*4*5*6
但是再次：这只是一种直觉。也许有人……在数学上涉及更多……可以证明我错了……。
