Leetcode - Different Ways to Add Parentheses

Given a string of numbers and operators, return all possible results from computing all the different possible ways to group numbers and operators. The valid operators are +, - and *.
Example 2
Input: "2*3-4*5"

(2*(3-(4*5))) = -34
((2*3)-(4*5)) = -14
((2*(3-4))*5) = -10
(2*((3-4)*5)) = -10
(((2*3)-4)*5) = 10
Output: [-34, -14, -10, -10, 10]

[分析] 这题参考[url]https://leetcode.com/discuss/48488/c-4ms-recursive-method[/url] 。 思路类似Unique Binary Search Trees II，以某个运算符为分界线，递归计算左右两边可能的值，然后根据当前运算符归并结果。纯粹的递归含有冗余计算，可同时保留中间结果来提高效率。

public class Solution {
    // method 2: dp
    public List<Integer> diffWaysToCompute(String input) {
        HashMap<String, List<Integer>> dpMap = new HashMap<String, List<Integer>>();
        return computeWithDP(input, dpMap);
    }
    public List<Integer> computeWithDP(String input, HashMap<String, List<Integer>> dpMap) {
        List<Integer> result = new ArrayList<Integer>();
        if (input == null || input.length() == 0) return result;
        int N = input.length();
        for (int i = 0; i < N; i++) {
            char c = input.charAt(i);
            if (c == '+' || c == '-' || c == '*') {
                String leftSubStr = input.substring(0, i);
                String rightSubStr = input.substring(i + 1, N);
                List<Integer> left = dpMap.get(leftSubStr);
                if (left == null)
                    left = computeWithDP(leftSubStr, dpMap);
                List<Integer> right = dpMap.get(rightSubStr);
                if (right == null)
                    right = computeWithDP(rightSubStr, dpMap);
                for (int op1: left) {
                    for (int op2: right) {
                        if (c == '+')
                            result.add(op1 + op2);
                        else if (c == '-')
                            result.add(op1 - op2);
                        else
                            result.add(op1 * op2);
                    }
                }
            }
        }
        if (result.isEmpty())
            result.add(Integer.parseInt(input));
        dpMap.put(input, result);
        return result;
    }

    // method 1: recursive
    public List<Integer> diffWaysToCompute1(String input) {
        List<Integer> result = new ArrayList<Integer>();
        if (input == null || input.length() == 0) return result;
        int N = input.length();
        for (int i = 0; i < N; i++) {
            char c = input.charAt(i);
            if (c == '+' || c == '-' || c == '*') {
                List<Integer> left = diffWaysToCompute(input.substring(0, i));
                List<Integer> right = diffWaysToCompute(input.substring(i + 1, N));
                for (int op1 : left) {
                    for (int op2 : right) {
                        if (c == '+')
                            result.add(op1 + op2);
                        else if (c == '-')
                            result.add(op1 - op2);
                        else
                            result.add(op1 * op2);
                    }
                }
            }
        }
        // if the string contains only number
        if (result.isEmpty())
            result.add(Integer.parseInt(input));
        return result;
    }
}