241. 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 1

Input: "2-1-1".

((2-1)-1) = 0(2-(1-1)) = 2

Output: [0, 2]

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]

Solution 1 Recursive

//Recursivepublic static List<Integer> diffWaysToCompute(String input) {List<Integer> ret = new LinkedList<Integer>();for (int i = 0; i < input.length(); i++) {if (input.charAt(i) == '-' || input.charAt(i) == '*' || input.charAt(i) == '+') {String part1 = input.substring(0, i);String part2 = input.substring(i + 1);List<Integer> part1Ret = diffWaysToCompute(part1);List<Integer> part2Ret = diffWaysToCompute(part2);for (Integer p1 : part1Ret) {for (Integer p2 : part2Ret) {int c = 0;switch (input.charAt(i)) {case '+':c = p1 + p2;break;case '-':c = p1 - p2;break;case '*':c = p1 * p2;break;}ret.add(c);}}}}if (ret.size() == 0) {ret.add(Integer.valueOf(input));}return ret;}

Solution 2 DP 

//Recursive with memorization DPpublic static List<Integer> diffWaysToCompute2(String input) {    //cache for memorization    HashMap<String,List<Integer>> cache = new HashMap<String,List<Integer>>();    return helper(input,cache);}public static List<Integer>helper(String s, HashMap<String,List<Integer>> cache) {    if (cache.get(s)!=null) {        return cache.get(s);    }    boolean expression = false;    ArrayList<Integer> result = new ArrayList<Integer>();    for(int i=0; i<s.length(); i++) {        if("+-*".indexOf(s.charAt(i))!=-1) {            List<Integer> left = helper(s.substring(0,i),cache);            List<Integer> right = helper(s.substring(i+1),cache);            for(Integer l: left) {                for(Integer r: right) {                    result.add(cal(l,r,s.charAt(i)));                }            }            expression = true;        }    }    if (!expression) {        result.add(Integer.parseInt(s));    }    cache.put(s, result);    return result;}public static int cal(int l, int r, char op) {    int result = 0;    switch (op) {        case '+': result= l+r; break;        case '-': result = l-r; break;        case '*': result= l*r; break;        default: break;    }    return result;}