Code from a friend to solve the float number with operators - maximum number for [1, 12, -3] is 37.

FloatNumberOperators.java

package google;

import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Set;

public class NumbersWithOperators {
    char[] ops = {'+', '-', '*', '/'};

    public double GetMaxNumber(double[] nums){
        if(nums == null || nums.length == 0){
            return 0;
        }
        List<Double> list = helper(nums, 0, nums.length - 1);
        double maxDouble = Double.MIN_VALUE;
        for(double ele : list){
            maxDouble = ele > maxDouble ? ele : maxDouble;
        }
        return maxDouble;
    }

    private List<Double> helper(double[] nums, int start, int end){
        List<Double> rst = new LinkedList<>();
        if(start == end){
            rst.add(nums[start]);
        }
        else if(start + 1 == end){
            List<Double> l1 = helper(nums, start, start);
            List<Double> l2 = helper(nums, end, end);
            rst = getCombinationResult(l1, l2);
        }
        else{
            Set<Double> set = new HashSet<>();
            for(int pos = start; pos <= end - 1; pos++){
                List<Double> l1 = helper(nums, start, pos);
                List<Double> l2 = helper(nums, pos + 1, end);
                set.addAll(getCombinationResult(l1, l2));
            }
            rst.addAll(set);
        }
        return rst;
    }

    private List<Double> getCombinationResult(List<Double> l1, List<Double> l2){
        Set<Double> set = new HashSet<>();
        for(Double d1 : l1){
            for(Double d2 : l2){
                set.addAll(operate(d1, d2));
            }
        }
        return new LinkedList<>(set);
    }

    private List<Double> operate(double num1, double num2){
        Set<Double> set = new HashSet<>();
        for(char op : ops){
            switch (op){
                case '+':
                    set.add(num1 + num2);
                case '-':
                    set.add(num1 - num2);
                case '*':
                    set.add(num1 * num2);
                case '/':
                    if(num2 != 0){
                        set.add(num1 / num2);
                    }
            }
        }
        return new LinkedList<>(set);
    }

    public static void main(String[] args){
        NumbersWithOperators test = new NumbersWithOperators();
        double[] nums = {1, 12, -3};
        double rst = test.GetMaxNumber(nums);
        System.out.println(rst);
    }
}