Given a string of numbers and a number of multiplication operators, what is the highest number one can calculate?

Question

This was an interview question I had and I was embarrassingly pretty stumped by it. Wanted to know if anyone could think up an answer to it and provide the big O notation for it

Answer 1

here's another Java solution. (I know it's correct for "312" and 1 multiplication and I think it works for others...

You'll have to remember how to obtain the complexity of recursive methods on your own, haha.

package test;

import java.util.ArrayList;
import java.util.List;

public class BiggestNumberMultiply {

    private static class NumberSplit{
        String[] numbers;
        long result;
        NumberSplit(String[] numbers){
            this.numbers=numbers.clone();
            result=1;
            for(String n:numbers){
                result*=Integer.parseInt(n);
            }
        }
        @Override
        public String toString() {
            StringBuffer sb=new StringBuffer();
            for(String n:numbers){
                sb.append(n).append("*");
            }
            sb.replace(sb.length()-1, sb.length(), "=")
                .append(result);
            return sb.toString();
        }
    }

    public static void main(String[] args) {
        String numbers = "312";
        int numMults=1;

        int numSplits=numMults;

        List splits = new ArrayList();
        splitNumbersRecursive(splits, new String[numSplits+1], numbers, numSplits);
        NumberSplit maxSplit = splits.get(0);
        for(NumberSplit ns:splits){
            System.out.println(ns);
            if(ns.result>maxSplit.result){
                maxSplit = ns;
            }
        }
        System.out.println("The maximum is "+maxSplit);
    }

    private static void splitNumbersRecursive(List list, String[] splits, String numbers, int numSplits){
        if(numSplits==0){
            splits[splits.length-1] = numbers;
            return;
        }
        for(int i=1; i<=numbers.length()-numSplits; i++){
            splits[splits.length-numSplits-1] = numbers.substring(0,i);
            splitNumbersRecursive(list, splits, numbers.substring(i), numSplits-1);
            list.add(new NumberSplit(splits));
        }
    }
}