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

The java version, though Python already showed its functional advantage and beat me:

private static class Solution {
    BigInteger product;
    String expression;
}

private static Solution solve(String digits, int multiplications) {
    if (digits.length() < multiplications + 1) {
        return null; // No solutions
    }
    if (multiplications == 0) {
        Solution solution = new Solution();
        solution.product = new BigInteger(digits);
        solution.expression = digits;
        return solution;
    }
    // Position of first '*':
    Solution max = null;
    for (int i = 1; i < digits.length() - (multiplications - 1); ++i) {
        BigInteger n = new BigInteger(digits.substring(0, i));
        Solution solutionRest = solve(digits.substring(i), multiplications - 1);
        n = n.multiply(solutionRest.product);
        if (max == null || n.compareTo(max.product) > 0) {
            solutionRest.product = n;
            solutionRest.expression = digits.substring(0, i) + "*"
                + solutionRest.expression;
            max = solutionRest;
        }
    }
    return max;
}

private static void test(String digits, int multiplications) {
    Solution solution = solve(digits, multiplications);
    System.out.printf("%s %d -> %s = %s%n", digits, multiplications,
            solution.expression, solution.product.toString());
}

public static void main(String[] args) {
    test("1826456903521651", 5);
}

Output

1826456903521651 5 -> 182*645*6*903*521*651 = 215719207032420